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<title>Who Is More Trusting: Liberals or Conservatives?</title>
<link>https://www.allendowney.com/blog/2026/06/12/who-is-more-trusting-liberals-or-conservatives/</link>
<dc:creator><![CDATA[AllenDowney]]></dc:creator>
<pubDate>Fri, 12 Jun 2026 13:40:20 +0000</pubDate>
<category><![CDATA[Uncategorized]]></category>
<category><![CDATA[age period cohort analysis]]></category>
<category><![CDATA[bayesian statistics]]></category>
<category><![CDATA[general social survey]]></category>
<category><![CDATA[political alignment]]></category>
<guid isPermaLink="false">https://www.allendowney.com/blog/?p=1836</guid>
<description><![CDATA[<p>When I go crawling around in data from the General Social Survey, sooner or later I run into Ryan Burge, who writes Graphs About Religion. In his most recent post, he wrote about changes in interpersonal trust, as measured by this GSS question: Generally speaking, would you say that most people can be trusted or that you can’t be too careful in dealing with people? Among other analyses, he looks at how the responses relate to self-identification as liberal, conservative,...</p>
<p class="read-more"><a class="btn btn-default" href="https://www.allendowney.com/blog/2026/06/12/who-is-more-trusting-liberals-or-conservatives/"> Read More<span class="screen-reader-text"> Read More</span></a></p>
<p>The post <a href="https://www.allendowney.com/blog/2026/06/12/who-is-more-trusting-liberals-or-conservatives/">Who Is More Trusting: Liberals or Conservatives?</a> appeared first on <a href="https://www.allendowney.com/blog">Probably Overthinking It</a>.</p>
]]></description>
<content:encoded><![CDATA[
<p class="wp-block-paragraph">When I go crawling around in data from the General Social Survey, sooner or later I run into Ryan Burge, who writes <em>Graphs About Religion</em>. In <a href="https://www.graphsaboutreligion.com/p/gen-z-doesnt-trust-anyone" target="_blank" rel="noreferrer noopener">his most recent post</a>, he wrote about changes in interpersonal trust, as measured by this GSS question:</p>
<blockquote class="wp-block-quote is-layout-flow wp-block-quote-is-layout-flow">
<p class="wp-block-paragraph">Generally speaking, would you say that most people can be trusted or that you can’t be too careful in dealing with people?</p>
</blockquote>
<p class="wp-block-paragraph">Among other analyses, he looks at how the responses relate to self-identification as liberal, conservative, or moderate. The results are … complicated. Ryan writes:</p>
<blockquote class="wp-block-quote is-layout-flow wp-block-quote-is-layout-flow">
<p class="wp-block-paragraph">Among older Americans who identify as liberal, they are more likely to trust other people. Among Gen Z liberals, it’s exactly the opposite.</p>
</blockquote>
<p class="wp-block-paragraph">To explain why older liberals are more trusting, Ryan suggests:</p>
<blockquote class="wp-block-quote is-layout-flow wp-block-quote-is-layout-flow">
<p class="wp-block-paragraph">Liberalism is based on collectivism. It embraces the idea that “together, we can achieve more.” Things like universal healthcare rely on a sense of trust among large groups of people.</p>
</blockquote>
<p class="wp-block-paragraph">But if that’s true, why does the effect go in the opposite direction with Gen Z? Ryan speculates:</p>
<blockquote class="wp-block-quote is-layout-flow wp-block-quote-is-layout-flow">
<p class="wp-block-paragraph">Well, maybe liberals feel very slighted by the fact that Donald Trump has been on the ballot for president in every election in which they’ve been eligible to vote, and he’s won twice. Or it could be that they are more impacted by the cynicism of the internet than conservatives? Or maybe it’s because they report higher rates of depression and anxiety than the rest of the ideological spectrum?</p>
</blockquote>
<p class="wp-block-paragraph">As it happened, I looked at the same GSS variable in <a href="https://www.allendowney.com/blog/2026/04/03/trust-and-well-being/" target="_blank" rel="noreferrer noopener">a recent article</a>. But I didn’t do the breakdown by political ideology, so let’s do that now.</p>
<h3 class="wp-block-heading">The Story So Far</h3>
<p class="wp-block-paragraph">First, here’s a recap of what we saw in the previous post, with the whole GSS sample. The following figure shows the percentage of respondents who said “most people can be trusted.”</p>
<figure class="wp-block-image" id="trust-recap-time-series"><img fetchpriority="high" decoding="async" width="1133" height="826" src="https://www.allendowney.com/blog/wp-content/uploads/2026/06/time_model_trust_rw2-25d010d905ca562e299e59b0e89d1713.png" alt="Time series: percent saying most people can be trusted (all respondents)" class="wp-image-1839" srcset="https://www.allendowney.com/blog/wp-content/uploads/2026/06/time_model_trust_rw2-25d010d905ca562e299e59b0e89d1713.png 1133w, https://www.allendowney.com/blog/wp-content/uploads/2026/06/time_model_trust_rw2-25d010d905ca562e299e59b0e89d1713-300x219.png 300w, https://www.allendowney.com/blog/wp-content/uploads/2026/06/time_model_trust_rw2-25d010d905ca562e299e59b0e89d1713-1024x747.png 1024w, https://www.allendowney.com/blog/wp-content/uploads/2026/06/time_model_trust_rw2-25d010d905ca562e299e59b0e89d1713-768x560.png 768w, https://www.allendowney.com/blog/wp-content/uploads/2026/06/time_model_trust_rw2-25d010d905ca562e299e59b0e89d1713-370x270.png 370w" sizes="(max-width: 1133px) 100vw, 1133px" /><figcaption class="wp-element-caption">Time series: percent saying most people can be trusted (all respondents)</figcaption></figure>
<p class="wp-block-paragraph">Interpersonal trust has declined consistently since the survey started in 1972. In the previous post, I decomposed this trend into cohort and period effects. Here’s the estimated cohort effect:</p>
<figure class="wp-block-image" id="trust-recap-cohort-effect"><img decoding="async" width="1133" height="790" src="https://www.allendowney.com/blog/wp-content/uploads/2026/06/cohort_standardized_-83920254db4863278c92f3cee792510c.png" alt="Standardized cohort effect with fixed time mix, percent saying most people can be trusted (all respondents)" class="wp-image-1840" srcset="https://www.allendowney.com/blog/wp-content/uploads/2026/06/cohort_standardized_-83920254db4863278c92f3cee792510c.png 1133w, https://www.allendowney.com/blog/wp-content/uploads/2026/06/cohort_standardized_-83920254db4863278c92f3cee792510c-300x209.png 300w, https://www.allendowney.com/blog/wp-content/uploads/2026/06/cohort_standardized_-83920254db4863278c92f3cee792510c-1024x714.png 1024w, https://www.allendowney.com/blog/wp-content/uploads/2026/06/cohort_standardized_-83920254db4863278c92f3cee792510c-768x535.png 768w, https://www.allendowney.com/blog/wp-content/uploads/2026/06/cohort_standardized_-83920254db4863278c92f3cee792510c-387x270.png 387w" sizes="(max-width: 1133px) 100vw, 1133px" /><figcaption class="wp-element-caption">Standardized cohort effect with fixed time mix, percent saying most people can be trusted (all respondents)</figcaption></figure>
<p class="wp-block-paragraph">The level of trust increased between the cohorts born in the 1900s through the 1940s, and then started a steep decline — more than 30 percentage points over 60 years. And here’s the remaining period effect, after factoring out the cohort effect.</p>
<figure class="wp-block-image" id="trust-recap-period-effect"><img decoding="async" width="1133" height="790" src="https://www.allendowney.com/blog/wp-content/uploads/2026/06/time_standardized_tr-2f029b683d9ad86a39a536e4f95c8c0f.png" alt="Standardized time trend with fixed cohort mix, percent saying most people can be trusted (all respondents)" class="wp-image-1841" srcset="https://www.allendowney.com/blog/wp-content/uploads/2026/06/time_standardized_tr-2f029b683d9ad86a39a536e4f95c8c0f.png 1133w, https://www.allendowney.com/blog/wp-content/uploads/2026/06/time_standardized_tr-2f029b683d9ad86a39a536e4f95c8c0f-300x209.png 300w, https://www.allendowney.com/blog/wp-content/uploads/2026/06/time_standardized_tr-2f029b683d9ad86a39a536e4f95c8c0f-1024x714.png 1024w, https://www.allendowney.com/blog/wp-content/uploads/2026/06/time_standardized_tr-2f029b683d9ad86a39a536e4f95c8c0f-768x535.png 768w, https://www.allendowney.com/blog/wp-content/uploads/2026/06/time_standardized_tr-2f029b683d9ad86a39a536e4f95c8c0f-387x270.png 387w" sizes="(max-width: 1133px) 100vw, 1133px" /><figcaption class="wp-element-caption">Standardized time trend with fixed cohort mix, percent saying most people can be trusted (all respondents)</figcaption></figure>
<p class="wp-block-paragraph">There is almost no period effect in the full sample.</p>
<h3 class="wp-block-heading">Breakdown by Politics</h3>
<p class="wp-block-paragraph">Now let’s get to the question we started with:</p>
<blockquote class="wp-block-quote is-layout-flow wp-block-quote-is-layout-flow">
<p class="wp-block-paragraph">Who is more trusting: liberals or conservatives?</p>
</blockquote>
<p class="wp-block-paragraph">Here’s the time series, broken down by ideology.</p>
<figure class="wp-block-image" id="trust-polviews-time-series"><img loading="lazy" decoding="async" width="1133" height="826" src="https://www.allendowney.com/blog/wp-content/uploads/2026/06/composed_trust_polvi-2191f28230cc6036ffa53c7c589783eb.png" alt="Time series: percent saying most people can be trusted, by 3-point political views" class="wp-image-1842" srcset="https://www.allendowney.com/blog/wp-content/uploads/2026/06/composed_trust_polvi-2191f28230cc6036ffa53c7c589783eb.png 1133w, https://www.allendowney.com/blog/wp-content/uploads/2026/06/composed_trust_polvi-2191f28230cc6036ffa53c7c589783eb-300x219.png 300w, https://www.allendowney.com/blog/wp-content/uploads/2026/06/composed_trust_polvi-2191f28230cc6036ffa53c7c589783eb-1024x747.png 1024w, https://www.allendowney.com/blog/wp-content/uploads/2026/06/composed_trust_polvi-2191f28230cc6036ffa53c7c589783eb-768x560.png 768w, https://www.allendowney.com/blog/wp-content/uploads/2026/06/composed_trust_polvi-2191f28230cc6036ffa53c7c589783eb-370x270.png 370w" sizes="auto, (max-width: 1133px) 100vw, 1133px" /><figcaption class="wp-element-caption">Time series: percent saying most people can be trusted, by 3-point political views</figcaption></figure>
<p class="wp-block-paragraph">Until recently, there was not much difference: liberals and conservatives were about equally likely to say people can be trusted — both a little more trusting than moderates (who are, maybe, too distrustful to join a team).</p>
<p class="wp-block-paragraph">Since the 2000s, liberals and conservatives have diverged, and now liberals are more trusting, by about 5 percentage points. But all three groups are still declining.</p>
<p class="wp-block-paragraph">Now let’s decompose those trends into cohort and period effects. Here are the cohort effects for the three groups.</p>
<figure class="wp-block-image" id="trust-polviews-cohort-effect"><img loading="lazy" decoding="async" width="1133" height="826" src="https://www.allendowney.com/blog/wp-content/uploads/2026/06/composed_trust_polvi-5e9990b3c69d8128602000b1b4e77eac.png" alt="Standardized cohort effect for generalized trust by political views (uniform weights on survey years within group)" class="wp-image-1844" srcset="https://www.allendowney.com/blog/wp-content/uploads/2026/06/composed_trust_polvi-5e9990b3c69d8128602000b1b4e77eac.png 1133w, https://www.allendowney.com/blog/wp-content/uploads/2026/06/composed_trust_polvi-5e9990b3c69d8128602000b1b4e77eac-300x219.png 300w, https://www.allendowney.com/blog/wp-content/uploads/2026/06/composed_trust_polvi-5e9990b3c69d8128602000b1b4e77eac-1024x747.png 1024w, https://www.allendowney.com/blog/wp-content/uploads/2026/06/composed_trust_polvi-5e9990b3c69d8128602000b1b4e77eac-768x560.png 768w, https://www.allendowney.com/blog/wp-content/uploads/2026/06/composed_trust_polvi-5e9990b3c69d8128602000b1b4e77eac-370x270.png 370w" sizes="auto, (max-width: 1133px) 100vw, 1133px" /><figcaption class="wp-element-caption">Standardized cohort effect for generalized trust by political views (uniform weights on survey years within group)</figcaption></figure>
<p class="wp-block-paragraph">Here we can see what Ryan reported: in most generations, liberals are more trusting than conservatives; it’s only in the most recent generation that it goes the other way. The crossover happens among people born in the mid-1990s, close to the conventional beginning of Gen Z (born 1997 to 2012).</p>
<p class="wp-block-paragraph">And here’s the period effect for the three groups.</p>
<figure class="wp-block-image" id="trust-polviews-period-effect"><img loading="lazy" decoding="async" width="1133" height="826" src="https://www.allendowney.com/blog/wp-content/uploads/2026/06/composed_trust_polvi-e873e0d24bfb4397559e322760556ee6.png" alt="Standardized period trend for generalized trust by political views (fixed within-group cohort weights)" class="wp-image-1843" srcset="https://www.allendowney.com/blog/wp-content/uploads/2026/06/composed_trust_polvi-e873e0d24bfb4397559e322760556ee6.png 1133w, https://www.allendowney.com/blog/wp-content/uploads/2026/06/composed_trust_polvi-e873e0d24bfb4397559e322760556ee6-300x219.png 300w, https://www.allendowney.com/blog/wp-content/uploads/2026/06/composed_trust_polvi-e873e0d24bfb4397559e322760556ee6-1024x747.png 1024w, https://www.allendowney.com/blog/wp-content/uploads/2026/06/composed_trust_polvi-e873e0d24bfb4397559e322760556ee6-768x560.png 768w, https://www.allendowney.com/blog/wp-content/uploads/2026/06/composed_trust_polvi-e873e0d24bfb4397559e322760556ee6-370x270.png 370w" sizes="auto, (max-width: 1133px) 100vw, 1133px" /><figcaption class="wp-element-caption">Standardized period trend for generalized trust by political views (fixed within-group cohort weights)</figcaption></figure>
<p class="wp-block-paragraph">For conservatives and moderates, the period effect is generally downward, although small. For liberals, it’s the other way around, generally increasing since about 2000.</p>
<p class="wp-block-paragraph">The cohort-period decomposition provides some hints about what’s going on:</p>
<ul class="wp-block-list">
<li>Among conservatives and moderates, the cohort and period effects are both downward, so they contributed to a steeper decline over time.</li>
<li>Among liberals, the cohort effect is also downward, but the period effect is upward, so the period effect mitigates the cohort effect.</li>
</ul>
<p class="wp-block-paragraph">To explain the cohort effect, I think Ryan’s suggestions are plausible. People born after 1995 have grown up during a discouraging time to be a liberal. Recent developments contrary to the liberal worldview include</p>
<ul class="wp-block-list">
<li>The rise of populist and nationalist movements in several countries, along with democratic backsliding or erosion of liberal norms.</li>
<li>Slow progress or reversal on climate change.</li>
<li>Increasing distrust of experts, journalists, scientists, and public institutions.</li>
<li>Declining confidence in institutions such as Congress, the media, and organized religion.</li>
<li>A series of conservative Supreme Court decisions, most notably the overturning of long-established abortion rights protections in 2022.</li>
</ul>
<p class="wp-block-paragraph">Negativity bias in the media — especially social media — is probably a contributing factor. And going to school during the pandemic probably didn’t help.</p>
<p class="wp-block-paragraph">But what about that period effect — can we think of reasons liberals would be more trusting, starting around 2005? If the recent cohort effect among young liberals is driven by the Trump era (at least in part), maybe the period effect was driven by events and trends of the Obama era that were aligned with the liberal worldview:</p>
<ul class="wp-block-list">
<li>Perception that the country was becoming more socially inclusive and diverse.</li>
<li>Greater visibility and acceptance of LGBTQ people, and growing support for same-sex marriage, culminating in nationwide legalization in 2015.</li>
<li>Expansion of health insurance coverage through the Patient Protection and Affordable Care Act.</li>
</ul>
<p class="wp-block-paragraph">And falling crime rates from the 1990s through the 2010s might have contributed more directly to increasing interpersonal trust.</p>
<p class="wp-block-paragraph">Of course these explanations are speculative, so let’s get back to what’s supported by the data:</p>
<ul class="wp-block-list">
<li>Since the 1970s, interpersonal trust has declined consistently in all three groups (liberal, conservative, and moderate).</li>
<li>Before 2005, liberals and conservatives were about equally trusting; since then, the decline among liberals has slowed, so they are now the most trusting group.</li>
<li>Among conservatives and moderates, the cohort and period effects are both downward, so they contribute to steeper decline.</li>
<li>Among liberals, the cohort effect is steeply downward in the most recent cohorts, but the decline is mitigated by a positive period effect.</li>
</ul>
<p class="wp-block-paragraph">For now, liberals are the most trusting group, but if the cohort effect persists, they might not be for long.</p>
<p class="wp-block-paragraph"></p>
<p>The post <a href="https://www.allendowney.com/blog/2026/06/12/who-is-more-trusting-liberals-or-conservatives/">Who Is More Trusting: Liberals or Conservatives?</a> appeared first on <a href="https://www.allendowney.com/blog">Probably Overthinking It</a>.</p>
]]></content:encoded>
<post-id xmlns="com-wordpress:feed-additions:1">1836</post-id>
</item>
<item>
<title>The Frog Puzzle</title>
<link>https://www.allendowney.com/blog/2026/06/04/the-frog-puzzle/</link>
<dc:creator><![CDATA[AllenDowney]]></dc:creator>
<pubDate>Thu, 04 Jun 2026 19:13:19 +0000</pubDate>
<category><![CDATA[Uncategorized]]></category>
<category><![CDATA[Bayes's Theorem]]></category>
<category><![CDATA[Frog Puzzle]]></category>
<category><![CDATA[probability]]></category>
<guid isPermaLink="false">https://www.allendowney.com/blog/?p=1828</guid>
<description><![CDATA[<p>Here’s a probability puzzle from a TED-Ed video called Can you solve the frog riddle? by Derek Abbott. It came up recently in this Reddit thread: You’re stranded in a rainforest after accidentally eating a poisonous mushroom. To survive the poison, you need to lick a certain species of frog. Only female frogs produce the antidote. Male and female frogs occur in equal numbers and look identical, but male frogs have a distinctive croak. You see one frog alone on...</p>
<p class="read-more"><a class="btn btn-default" href="https://www.allendowney.com/blog/2026/06/04/the-frog-puzzle/"> Read More<span class="screen-reader-text"> Read More</span></a></p>
<p>The post <a href="https://www.allendowney.com/blog/2026/06/04/the-frog-puzzle/">The Frog Puzzle</a> appeared first on <a href="https://www.allendowney.com/blog">Probably Overthinking It</a>.</p>
]]></description>
<content:encoded><![CDATA[
<p class="wp-block-paragraph">Here’s a probability puzzle from a TED-Ed video called <a href="https://www.youtube.com/watch?v=cpwSGsb-rTs">Can you solve the frog riddle?</a> by Derek Abbott. It came up recently in this <a href="https://www.reddit.com/r/probabilitytheory/comments/1ttzcjt/frog_riddle_again/">Reddit thread</a>:</p>
<blockquote class="wp-block-quote is-layout-flow wp-block-quote-is-layout-flow">
<p class="wp-block-paragraph">You’re stranded in a rainforest after accidentally eating a poisonous mushroom. To survive the poison, you need to lick a certain species of frog. Only female frogs produce the antidote. Male and female frogs occur in equal numbers and look identical, but male frogs have a distinctive croak.</p>
<p class="wp-block-paragraph">You see one frog alone on a tree stump. In another direction, you hear the croak of a male frog coming from a clearing with two frogs. You can’t tell which one made the sound.</p>
<p class="wp-block-paragraph">You only have time to go to one place. What are your chances of survival if you go to the clearing and lick both frogs? What if you go to the lone frog?</p>
</blockquote>
<p class="wp-block-paragraph">The second question is relatively easy: if we assume that you are equally likely to see a male or female frog, the probability is 50% that the lone frog is female.</p>
<p class="wp-block-paragraph">The first question depends on how we interpret the puzzle. In particular, it hinges on the word “distinctive” – does that mean:</p>
<ul class="wp-block-list">
<li>Only male frogs croak, and the sound is distinguishable from background noises, or</li>
<li>Both male and female frogs croak, but the male croak is distinguishable from the female croak.</li>
</ul>
<p class="wp-block-paragraph">Based on the answer presented in the video, the first meaning is intended. So we’ll start by solving that version.</p>
<p class="wp-block-paragraph">But the second meaning makes the problem a little harder, so we’ll solve that one, too.</p>
<h2 class="wp-block-heading">Only Male Frogs Croak</h2>
<p class="wp-block-paragraph">To solve the intended version of the puzzle, we’ll assume</p>
<ul class="wp-block-list">
<li>Only male frogs croak, and</li>
<li>When two frogs appear together, their sexes are independent.</li>
</ul>
<p class="wp-block-paragraph">So we’ll start with a prior where all two-frog combinations are equally likely.</p>
<pre class="wp-block-preformatted">from sympy import Rational
hypo = ['FF', 'FM', 'MF', 'MM']
prior = Rational(1)
</pre>
<p class="wp-block-paragraph">Now let’s think about the likelihood of the data under each scenario. In the video, the solution is based on these assumptions:</p>
<ul class="wp-block-list">
<li>If both frogs are female, the probability of hearing the male croak is 0.</li>
<li>If either frog is male, the probability that one of them croaks is 1.</li>
</ul>
<pre class="wp-block-preformatted">likelihood = [0, 1, 1, 1]
</pre>
<p class="wp-block-paragraph">I’ll use a <code>BayesTable</code> to compute the posterior probability for each scenario.</p>
<pre class="wp-block-preformatted">import pandas as pd
import numpy as np
class BayesTable(pd.DataFrame):
def __init__(self, hypo, prior=1, **options):
columns = ['prior', 'likelihood', 'unnorm', 'posterior']
super().__init__(index=hypo, columns=columns, **options)
self.prior = prior
def update(self, likelihood):
self.likelihood = likelihood
self.unnorm = self.prior * self.likelihood
nc = self.unnorm.sum()
self.posterior = self.unnorm / nc
</pre>
<pre class="wp-block-preformatted">table = BayesTable(hypo, prior)
table.update(likelihood)
table
</pre>
<figure class="wp-block-table"><table class="has-fixed-layout"><thead><tr><th></th><th>prior</th><th>likelihood</th><th>unnorm</th><th>posterior</th></tr></thead><tbody><tr><th>FF</th><td>1</td><td>0</td><td>0</td><td>0</td></tr><tr><th>FM</th><td>1</td><td>1</td><td>1</td><td>1/3</td></tr><tr><th>MF</th><td>1</td><td>1</td><td>1</td><td>1/3</td></tr><tr><th>MM</th><td>1</td><td>1</td><td>1</td><td>1/3</td></tr></tbody></table></figure>
<p class="wp-block-paragraph">From the table, we can extract the posterior probability that both frogs are male.</p>
<pre class="wp-block-preformatted">from sympy import init_printing
init_printing(use_latex=False)
</pre>
<pre class="wp-block-preformatted">table.posterior['MM']
</pre>
<pre class="wp-block-preformatted">1/3
</pre>
<p class="wp-block-paragraph">With these assumptions, the probability 1/3 that both frogs are male (and you die), so the probability is 2/3 that at least one is female (and you live).</p>
<p class="wp-block-paragraph">And that’s the answer in the video.</p>
<h2 class="wp-block-heading">Poisson (not Poison) Frogs</h2>
<p class="wp-block-paragraph">But is that the right likelihood? Suppose frogs are equally likely to croak at any instant in time, so their croaks follow a Poisson process. If we assume that these croaking processes are independent, two frogs would be more likely to croak, during a given interval, than one.</p>
<p class="wp-block-paragraph">If the interval is much longer than the average time between croaks, the probability that either frog croaks approaches 1, which is consistent with the previous solution.</p>
<p class="wp-block-paragraph">But if the interval is short – as it might be if you were deciding whether to approach the first frog – the probability of hearing a croak would be double if there are two male frogs rather than one.</p>
<p class="wp-block-paragraph">In that case, the likelihood of the data would be:</p>
<pre class="wp-block-preformatted">half = Rational(1, 2)
likelihood = [0, half, half, 1]
</pre>
<p class="wp-block-paragraph">And here are the posterior probabilities:</p>
<pre class="wp-block-preformatted">table = BayesTable(hypo, prior)
table.update(likelihood)
table
</pre>
<figure class="wp-block-table"><table class="has-fixed-layout"><thead><tr><th></th><th>prior</th><th>likelihood</th><th>unnorm</th><th>posterior</th></tr></thead><tbody><tr><th>FF</th><td>1</td><td>0</td><td>0</td><td>0</td></tr><tr><th>FM</th><td>1</td><td>1/2</td><td>1/2</td><td>1/4</td></tr><tr><th>MF</th><td>1</td><td>1/2</td><td>1/2</td><td>1/4</td></tr><tr><th>MM</th><td>1</td><td>1</td><td>1</td><td>1/2</td></tr></tbody></table></figure>
<p class="wp-block-paragraph">With Poisson frogs and a short interval, the probability of two male frogs is 1/2, so it doesn’t matter whether you approach the lone frog or the pair of frogs.</p>
<h2 class="wp-block-heading">Female Frogs Croak, Too</h2>
<p class="wp-block-paragraph">Now let’s think about the other interpretation of the puzzle: suppose both male and female frogs croak, but we can distinguish one from the other. And suppose male and female frogs croak at different rates, but they are still independent.</p>
<p class="wp-block-paragraph">Assume that male frogs croak at a rate of 1 per time unit, and female frogs at a rate of <code>r</code> per time unit. In that case, if we start listening at a random time, the probability that we hear a male frog first is <code>1 / (r+1)</code> if there’s only one male frog, and <code>1</code> if there are two male frogs.</p>
<p class="wp-block-paragraph">So the likelihood in this case is:</p>
<pre class="wp-block-preformatted">from sympy import symbols
r = symbols('r')
likelihood = [0, 1 / (r+1), 1 / (r+1), 1]
</pre>
<p class="wp-block-paragraph">And here are the posteriors</p>
<pre class="wp-block-preformatted">table = BayesTable(hypo, prior)
table.update(likelihood)
table
</pre>
<figure class="wp-block-table"><table class="has-fixed-layout"><thead><tr><th></th><th>prior</th><th>likelihood</th><th>unnorm</th><th>posterior</th></tr></thead><tbody><tr><th>FF</th><td>1</td><td>0</td><td>0</td><td>0</td></tr><tr><th>FM</th><td>1</td><td>1/(r + 1)</td><td>1/(r + 1)</td><td>1/((1 + 2/(r + 1))*(r + 1))</td></tr><tr><th>MF</th><td>1</td><td>1/(r + 1)</td><td>1/(r + 1)</td><td>1/((1 + 2/(r + 1))*(r + 1))</td></tr><tr><th>MM</th><td>1</td><td>1</td><td>1</td><td>1/(1 + 2/(r + 1))</td></tr></tbody></table></figure>
<p class="wp-block-paragraph">In this scenario, here’s the probability you die.</p>
<pre class="wp-block-preformatted">prob_die = table.posterior['MM']
prob_die.simplify()
</pre>
<pre class="wp-block-preformatted">r + 1
─────
r + 3
</pre>
<p class="wp-block-paragraph">If female frogs don’t croak, we get the same answer as in the first scenario.</p>
<pre class="wp-block-preformatted">prob_die.subs({r: 0})
</pre>
<pre class="wp-block-preformatted">1/3
</pre>
<p class="wp-block-paragraph">If male and female frogs croak at the same rate, the probability that both frogs are male is 1/2.</p>
<pre class="wp-block-preformatted">prob_die.subs({r: 1})
</pre>
<pre class="wp-block-preformatted">1/2
</pre>
<p class="wp-block-paragraph">But if female frogs croak much more often, the fact that a male croaked first is strong evidence that both are male, so the posterior probability is close to 1.</p>
<pre class="wp-block-preformatted">prob_die.subs({r: 1000}).evalf()
</pre>
<pre class="wp-block-preformatted">0.998005982053839
</pre>
<h2 class="wp-block-heading">Assortative Mating</h2>
<p class="wp-block-paragraph">Now suppose that when we see two frogs together, their sexes are not independent; specifically, let’s assume that the probability of a same-sex pair is <code>p</code>, so the probability of a mixed-sex pair is <code>1-p</code>. In this scenario, the priors (before we hear the croak) are not equal.</p>
<pre class="wp-block-preformatted">p = symbols('p')
prior = [p, 1-p, 1-p, p]
</pre>
<p class="wp-block-paragraph">Here are the posterior probabilities, assuming again that both male and female frogs, possibly at different rates.</p>
<pre class="wp-block-preformatted">likelihood = [0, 1 / (r+1), 1 / (r+1), 1]
table = BayesTable(hypo, prior)
table.update(likelihood)
table
</pre>
<figure class="wp-block-table"><table class="has-fixed-layout"><thead><tr><th></th><th>prior</th><th>likelihood</th><th>unnorm</th><th>posterior</th></tr></thead><tbody><tr><th>FF</th><td>p</td><td>0</td><td>0</td><td>0</td></tr><tr><th>FM</th><td>1 – p</td><td>1/(r + 1)</td><td>(1 – p)/(r + 1)</td><td>(1 – p)/((p + 2*(1 – p)/(r + 1))*(r + 1))</td></tr><tr><th>MF</th><td>1 – p</td><td>1/(r + 1)</td><td>(1 – p)/(r + 1)</td><td>(1 – p)/((p + 2*(1 – p)/(r + 1))*(r + 1))</td></tr><tr><th>MM</th><td>p</td><td>1</td><td>p</td><td>p/(p + 2*(1 – p)/(r + 1))</td></tr></tbody></table></figure>
<pre class="wp-block-preformatted">table.posterior['MM'].simplify()
</pre>
<pre class="wp-block-preformatted"> p⋅(r + 1)
───────────
p⋅r - p + 2
</pre>
<p class="wp-block-paragraph">If <code>p=1/2</code>, this simplifies to the previous scenario.</p>
<pre class="wp-block-preformatted">table.posterior['MM'].subs({p: half}).simplify()
</pre>
<pre class="wp-block-preformatted">r + 1
─────
r + 3
</pre>
<p class="wp-block-paragraph">And if <code>r=0</code> (female frogs don’t croak), we get the answer presented in the video.</p>
<pre class="wp-block-preformatted">table.posterior['MM'].subs({p: half, r: 0}).simplify()
</pre>
<pre class="wp-block-preformatted">1/3
</pre>
<p class="wp-block-paragraph">But depending on the assumptions, the probability can be as low as <code>0</code></p>
<pre class="wp-block-preformatted">table.posterior['MM'].subs({p: 0, r: 1}).simplify()
</pre>
<pre class="wp-block-preformatted">0
</pre>
<p class="wp-block-paragraph">Or as high as <code>1</code>.</p>
<pre class="wp-block-preformatted">table.posterior['MM'].subs({p: 1, r: 0}).simplify()
</pre>
<pre class="wp-block-preformatted">1
</pre>
<p class="wp-block-paragraph">Or anything in between. As is often the case with problems like these, the answer depends on a precise specification of the data-generating process.</p>
<h2 class="wp-block-heading">Discussion</h2>
<p class="wp-block-paragraph">If all of this seems like more trouble than it’s worth, let me suggest a metacognitive shortcut for solving puzzles like this.</p>
<ol class="wp-block-list">
<li>Notice that in all probability puzzles, the answer is either 1/2 or 1/3.</li>
<li>Also, the answer is always counterintuitive; otherwise it wouldn’t be a puzzle.</li>
<li>Therefore, if your intuition says the answer is 1/2, it’s actually 1/3, and vice versa.</li>
</ol>
<p class="wp-block-paragraph">That might save you some time.</p>
<p class="wp-block-paragraph">This notebook uses methods and materials from <em>Think Bayes</em>, second edition. If you like this sort of thing, you can read the whole book, and more examples, at <a href="https://allendowney.github.io/ThinkBayes2/">allendowney.github.io/ThinkBayes2/</a>.</p>
<p class="wp-block-paragraph"><br><br></p>
<p class="wp-block-paragraph"></p>
<p>The post <a href="https://www.allendowney.com/blog/2026/06/04/the-frog-puzzle/">The Frog Puzzle</a> appeared first on <a href="https://www.allendowney.com/blog">Probably Overthinking It</a>.</p>
]]></content:encoded>
<post-id xmlns="com-wordpress:feed-additions:1">1828</post-id>
</item>
<item>
<title>Sexual morality</title>
<link>https://www.allendowney.com/blog/2026/05/28/sexual-morality/</link>
<dc:creator><![CDATA[AllenDowney]]></dc:creator>
<pubDate>Thu, 28 May 2026 18:21:52 +0000</pubDate>
<category><![CDATA[Uncategorized]]></category>
<category><![CDATA[age period cohort analysis]]></category>
<category><![CDATA[bayesian statistics]]></category>
<category><![CDATA[general social survey]]></category>
<guid isPermaLink="false">https://www.allendowney.com/blog/?p=1818</guid>
<description><![CDATA[<p>This article is one of a series looking at changes in public opinion over the last 50 years, with a focus on culture war topics. In this installment, we’ll look at responses to four questions in the General Social Survey (GSS) related to sexual activity: As we’ll see, answers to these questions have diverged in the last 50 years. A large majority answer that extramarital and teen sex are wrong, and that has barely changed (although opposition). At the same...</p>
<p class="read-more"><a class="btn btn-default" href="https://www.allendowney.com/blog/2026/05/28/sexual-morality/"> Read More<span class="screen-reader-text"> Read More</span></a></p>
<p>The post <a href="https://www.allendowney.com/blog/2026/05/28/sexual-morality/">Sexual morality</a> appeared first on <a href="https://www.allendowney.com/blog">Probably Overthinking It</a>.</p>
]]></description>
<content:encoded><![CDATA[
<p class="wp-block-paragraph">This article is one of a series looking at changes in public opinion over the last 50 years, with a focus on culture war topics. In this installment, we’ll look at responses to four questions in the General Social Survey (GSS) related to sexual activity:</p>
<ol start="1" class="wp-block-list">
<li><strong>Premarital sex</strong> (<code>premarsx</code>): <em>There’s been a lot of discussion about the way morals and attitudes about sex are changing in this country. If a man and woman have sex relations before marriage, do you think it is always wrong, almost always wrong, wrong only sometimes, or not wrong at all?</em></li>
<li><strong>Teen premarital sex</strong> (<code>teensex</code>): <em>What if they are in their early teens, say 14 to 16 years old? In that case, do you think sex relations before marriage are always wrong, almost always wrong, wrong only sometimes, or not wrong at all?</em></li>
<li><strong>Extramarital sex</strong> (<code>xmarsex</code>): <em>What is your opinion about a married person having sexual relations with someone other than the marriage partner—is it always wrong, almost always wrong, wrong only sometimes, or not wrong at all?</em></li>
<li><strong>Same-sex relations</strong> (<code>homosex</code>): <em>What about sexual relations between two adults of the same sex—do you think it is always wrong, almost always wrong, wrong only sometimes, or not wrong at all?</em></li>
</ol>
<p class="wp-block-paragraph">As we’ll see, answers to these questions have diverged in the last 50 years. A large majority answer that extramarital and teen sex are wrong, and that has barely changed (although opposition). At the same time, opposition to premarital sex and same-sex relations has declined substantially.</p>
<p class="wp-block-paragraph">In this article, we’ll look at these trends and decompose them into cohort and period effects. In the next article, we’ll look at the relationship between these responses and religion, both affiliation and attendance.</p>
<p class="wp-block-paragraph">We’ll start with the first question, on premarital sex.</p>
<h2 class="wp-block-heading">Premarital sex</h2>
<p class="wp-block-paragraph">The following figure shows the percentage of respondents saying premarital sex is always or almost always wrong, from 1972 to 2024. The shaded area shows the results from a Bayesian model that estimates the latent trend — that is, a slowly varying underlying level of opposition to premarital sex.</p>
<figure class="wp-block-image" id="premarsx-time-model"><img loading="lazy" decoding="async" width="1145" height="826" src="https://www.allendowney.com/blog/wp-content/uploads/2026/05/time_model_premarsx_-92782a5d81ed3c322ce3a3b74a1a1525.png" alt="Time series national trend: percent saying premarital sex is always or almost always wrong (premarsx)." class="wp-image-1820" srcset="https://www.allendowney.com/blog/wp-content/uploads/2026/05/time_model_premarsx_-92782a5d81ed3c322ce3a3b74a1a1525.png 1145w, https://www.allendowney.com/blog/wp-content/uploads/2026/05/time_model_premarsx_-92782a5d81ed3c322ce3a3b74a1a1525-300x216.png 300w, https://www.allendowney.com/blog/wp-content/uploads/2026/05/time_model_premarsx_-92782a5d81ed3c322ce3a3b74a1a1525-1024x739.png 1024w, https://www.allendowney.com/blog/wp-content/uploads/2026/05/time_model_premarsx_-92782a5d81ed3c322ce3a3b74a1a1525-768x554.png 768w, https://www.allendowney.com/blog/wp-content/uploads/2026/05/time_model_premarsx_-92782a5d81ed3c322ce3a3b74a1a1525-374x270.png 374w" sizes="auto, (max-width: 1145px) 100vw, 1145px" /></figure>
<p class="wp-block-paragraph">Opposition to premarital sex has declined since 1972, from about 47% to about 20%.</p>
<p class="wp-block-paragraph">As always, when we see this kind of change over time, it might be caused by cohort or period effects, or a combination of the two. Using a Bayesian model, I estimate a cohort effect for each birth year and a period effect for each survey year. The following figure shows the resulting trajectory for each cohort over time.</p>
<figure class="wp-block-image" id="premarsx-cohort-trajectories"><img loading="lazy" decoding="async" width="1330" height="773" src="https://www.allendowney.com/blog/wp-content/uploads/2026/05/cohort_trajectory_pr-795031a5150bdfce6ad7635df8bae9d3.png" alt="Cohort trajectories: percent always or almost always wrong (premarsx), one line per birth year." class="wp-image-1826" srcset="https://www.allendowney.com/blog/wp-content/uploads/2026/05/cohort_trajectory_pr-795031a5150bdfce6ad7635df8bae9d3.png 1330w, https://www.allendowney.com/blog/wp-content/uploads/2026/05/cohort_trajectory_pr-795031a5150bdfce6ad7635df8bae9d3-300x174.png 300w, https://www.allendowney.com/blog/wp-content/uploads/2026/05/cohort_trajectory_pr-795031a5150bdfce6ad7635df8bae9d3-1024x595.png 1024w, https://www.allendowney.com/blog/wp-content/uploads/2026/05/cohort_trajectory_pr-795031a5150bdfce6ad7635df8bae9d3-768x446.png 768w, https://www.allendowney.com/blog/wp-content/uploads/2026/05/cohort_trajectory_pr-795031a5150bdfce6ad7635df8bae9d3-465x270.png 465w" sizes="auto, (max-width: 1330px) 100vw, 1330px" /></figure>
<p class="wp-block-paragraph">Each line represents a single birth year. For example, the yellow line at the top shows the fitted trajectory for people born in 1900, who were 72 when the survey started in 1972 and 90 when they aged out in 1990. The blue line in the bottom right shows responses of people born in 2000, who became eligible to participate in the survey when they turned 18 in 2018.</p>
<p class="wp-block-paragraph">One pattern is clear: each cohort is less likely than the previous cohort to say that premarital sex is wrong. Among people born in 1900, it was more than 70%. Among people born in the 2000s, it is close to 10%. So that’s a big difference.</p>
<p class="wp-block-paragraph">From these results, we can estimate the cohort and period effects separately. The following figure shows the cohort effect, standardized to control for the period effect by simulating responses as if every cohort was interviewed during every iteration of the survey.</p>
<figure class="wp-block-image" id="premarsx-cohort-standardized"><img loading="lazy" decoding="async" width="1145" height="826" src="https://www.allendowney.com/blog/wp-content/uploads/2026/05/cohort_standardized_-2ddcc0ce51962fa548b8944732f56f2c.png" alt="Standardized cohort component with uniform weights on observed survey years (premarsx)." class="wp-image-1821" srcset="https://www.allendowney.com/blog/wp-content/uploads/2026/05/cohort_standardized_-2ddcc0ce51962fa548b8944732f56f2c.png 1145w, https://www.allendowney.com/blog/wp-content/uploads/2026/05/cohort_standardized_-2ddcc0ce51962fa548b8944732f56f2c-300x216.png 300w, https://www.allendowney.com/blog/wp-content/uploads/2026/05/cohort_standardized_-2ddcc0ce51962fa548b8944732f56f2c-1024x739.png 1024w, https://www.allendowney.com/blog/wp-content/uploads/2026/05/cohort_standardized_-2ddcc0ce51962fa548b8944732f56f2c-768x554.png 768w, https://www.allendowney.com/blog/wp-content/uploads/2026/05/cohort_standardized_-2ddcc0ce51962fa548b8944732f56f2c-374x270.png 374w" sizes="auto, (max-width: 1145px) 100vw, 1145px" /></figure>
<p class="wp-block-paragraph">The decline was steepest between the cohorts born in 1900 and 1950. After that, it leveled off, then declined again among the cohorts born in the 1980s.</p>
<p class="wp-block-paragraph">Now we can estimate the period effect, standardized to control for the cohort effect, shown in the following figure.</p>
<figure class="wp-block-image" id="premarsx-period-standardized"><img loading="lazy" decoding="async" width="1145" height="826" src="https://www.allendowney.com/blog/wp-content/uploads/2026/05/time_standardized_pr-3ad2679bfedff58845cbd5c8219ec152.png" alt="Standardized period component with fixed cohort mix (premarsx)." class="wp-image-1822" srcset="https://www.allendowney.com/blog/wp-content/uploads/2026/05/time_standardized_pr-3ad2679bfedff58845cbd5c8219ec152.png 1145w, https://www.allendowney.com/blog/wp-content/uploads/2026/05/time_standardized_pr-3ad2679bfedff58845cbd5c8219ec152-300x216.png 300w, https://www.allendowney.com/blog/wp-content/uploads/2026/05/time_standardized_pr-3ad2679bfedff58845cbd5c8219ec152-1024x739.png 1024w, https://www.allendowney.com/blog/wp-content/uploads/2026/05/time_standardized_pr-3ad2679bfedff58845cbd5c8219ec152-768x554.png 768w, https://www.allendowney.com/blog/wp-content/uploads/2026/05/time_standardized_pr-3ad2679bfedff58845cbd5c8219ec152-374x270.png 374w" sizes="auto, (max-width: 1145px) 100vw, 1145px" /></figure>
<p class="wp-block-paragraph">The period effect is smaller than the cohort effect — about 8 percentage points from peak to trough — and less consistent. Opposition to premarital sex increased between 1980 and 2000, which coincides with increasing awareness of AIDS and public messaging about sexual risk, as well as the rise of the Religious Right and “family values” politics.</p>
<p class="wp-block-paragraph">But before I speculate about the causes of these patterns, it will be useful to look at the responses to the other questions.</p>
<h2 class="wp-block-heading">When is sex wrong?</h2>
<p class="wp-block-paragraph">The following figure shows the estimated percentage who think sex is wrong (always or almost always) in each of the four scenarios: premarital, teen, extramarital, and same-sex.</p>
<figure class="wp-block-image" id="sex-wrongness-composite-time-model"><img loading="lazy" decoding="async" width="1145" height="766" src="https://www.allendowney.com/blog/wp-content/uploads/2026/05/section1a_sex_wrongn-80473854b8315d2c65a20e45ee21992c.png" alt="Composite overlay: sexual-behavior wrongness scale — national time-series model (four items)." class="wp-image-1824" srcset="https://www.allendowney.com/blog/wp-content/uploads/2026/05/section1a_sex_wrongn-80473854b8315d2c65a20e45ee21992c.png 1145w, https://www.allendowney.com/blog/wp-content/uploads/2026/05/section1a_sex_wrongn-80473854b8315d2c65a20e45ee21992c-300x201.png 300w, https://www.allendowney.com/blog/wp-content/uploads/2026/05/section1a_sex_wrongn-80473854b8315d2c65a20e45ee21992c-1024x685.png 1024w, https://www.allendowney.com/blog/wp-content/uploads/2026/05/section1a_sex_wrongn-80473854b8315d2c65a20e45ee21992c-768x514.png 768w, https://www.allendowney.com/blog/wp-content/uploads/2026/05/section1a_sex_wrongn-80473854b8315d2c65a20e45ee21992c-404x270.png 404w" sizes="auto, (max-width: 1145px) 100vw, 1145px" /></figure>
<p class="wp-block-paragraph">Reading from top to bottom:</p>
<ul class="wp-block-list">
<li>Nearly everyone thinks “a married person having sexual relations with someone other than the marriage partner” is wrong, and the percentage has barely changed in more than 50 years.</li>
<li>Opposition to teen sex (the question specifies ages 14-16) is nearly as high, although it has declined since 2005 by about 15 percentage points.</li>
<li>Opposition to same-sex relations was high and mostly unchanged between 1972 and 1990. Since then it has decreased by almost 50 percentage points in 30 years, which is an astonishing speed for this kind of social change. Since 2020, opposition has increased a little.</li>
<li>Finally, as we’ve already seen, opposition to premarital sex declined substantially since the beginning of the survey.</li>
</ul>
<p class="wp-block-paragraph">For all four scenarios, we can estimate the cohort effect, controlling for the period effect, shown in the following figure.</p>
<figure class="wp-block-image" id="sex-wrongness-composite-cohort"><img loading="lazy" decoding="async" width="1145" height="766" src="https://www.allendowney.com/blog/wp-content/uploads/2026/05/section1a_sex_wrongn-f61ab0124fa6ad280ce97c7fe9addcba.png" alt="Composite overlay: standardized cohort component with uniform weights on observed years (four items)." class="wp-image-1825" srcset="https://www.allendowney.com/blog/wp-content/uploads/2026/05/section1a_sex_wrongn-f61ab0124fa6ad280ce97c7fe9addcba.png 1145w, https://www.allendowney.com/blog/wp-content/uploads/2026/05/section1a_sex_wrongn-f61ab0124fa6ad280ce97c7fe9addcba-300x201.png 300w, https://www.allendowney.com/blog/wp-content/uploads/2026/05/section1a_sex_wrongn-f61ab0124fa6ad280ce97c7fe9addcba-1024x685.png 1024w, https://www.allendowney.com/blog/wp-content/uploads/2026/05/section1a_sex_wrongn-f61ab0124fa6ad280ce97c7fe9addcba-768x514.png 768w, https://www.allendowney.com/blog/wp-content/uploads/2026/05/section1a_sex_wrongn-f61ab0124fa6ad280ce97c7fe9addcba-404x270.png 404w" sizes="auto, (max-width: 1145px) 100vw, 1145px" /></figure>
<p class="wp-block-paragraph">For all four scenarios, there is a consistent downward trend in the cohort effect, modest for extramarital and teen sex, much steeper for premarital and same-sex relations.</p>
<p class="wp-block-paragraph">The following figure shows the period effects.</p>
<figure class="wp-block-image" id="sex-wrongness-composite-period"><img loading="lazy" decoding="async" width="1145" height="766" src="https://www.allendowney.com/blog/wp-content/uploads/2026/05/section1a_sex_wrongn-f67ed5b82acbc806401f00d555e7c43e.png" alt="Composite overlay: standardized period component with fixed cohort mix (four items)." class="wp-image-1823" srcset="https://www.allendowney.com/blog/wp-content/uploads/2026/05/section1a_sex_wrongn-f67ed5b82acbc806401f00d555e7c43e.png 1145w, https://www.allendowney.com/blog/wp-content/uploads/2026/05/section1a_sex_wrongn-f67ed5b82acbc806401f00d555e7c43e-300x201.png 300w, https://www.allendowney.com/blog/wp-content/uploads/2026/05/section1a_sex_wrongn-f67ed5b82acbc806401f00d555e7c43e-1024x685.png 1024w, https://www.allendowney.com/blog/wp-content/uploads/2026/05/section1a_sex_wrongn-f67ed5b82acbc806401f00d555e7c43e-768x514.png 768w, https://www.allendowney.com/blog/wp-content/uploads/2026/05/section1a_sex_wrongn-f67ed5b82acbc806401f00d555e7c43e-404x270.png 404w" sizes="auto, (max-width: 1145px) 100vw, 1145px" /></figure>
<p class="wp-block-paragraph">After controlling for the cohort effects, the remaining period effects are more modest.</p>
<ul class="wp-block-list">
<li>Opposition to teen sex is mostly unchanged, with some decline since 2010.</li>
<li>Opposition to extramarital sex increased between 1972 and 2010, and decreased since then.</li>
<li>Opposition to same-sex relations shows by far the largest period effect, increasing between 1972 and 1990, and decreasing since then — although increasing again since 2020.</li>
<li>Opposition to premarital sex has increased and decreased modestly.</li>
</ul>
<p class="wp-block-paragraph">In most scenarios, the cohort effect accounts for more of the observed change — but for same-sex relations, the period effect also makes a substantial contribution.</p>
<h2 class="wp-block-heading">Dogma, morality, and health</h2>
<p class="wp-block-paragraph">To make sense of these patterns, let’s think about what people might mean when they say that sex is wrong.</p>
<p class="wp-block-paragraph">Taking premarital sex as an example, some people consider sex outside marriage to be contrary to spiritual values or religious teachings. Others might be concerned with sexually-transmitted disease or the social consequences of children born outside of stable families.</p>
<p class="wp-block-paragraph">And for teens specifically, some object because they see adolescence as a period of innocence that should be protected, believe sexual activity compromises purity or chastity, or think sexual restraint reflects virtues like self-discipline and respect for social norms. Also, some might think teenagers don’t have the knowledge, experience, and impulse control to avoid health consequences of sex, especially pregnancy, or the maturity to handle emotional challenges.</p>
<p class="wp-block-paragraph">Similarly, some people object to same-sex relations because they see them as contrary to religious teachings, inconsistent with traditional ideas about gender and family, or incompatible with social norms about sexuality.</p>
<p class="wp-block-paragraph">And people might object to extramarital sex because of the emotional harm it causes, because it breaks a vow, because it threatens families and social stability, or because it violates holy matrimony.</p>
<p class="wp-block-paragraph">In each scenario, objections arise from different concerns: practical risks and harms, social concerns about norms and stability, and moral or religious beliefs. Looking only at multiple-choice responses, we don’t know what respondents had in mind.</p>
<p class="wp-block-paragraph">But the differences we see — between teen and extramarital sex on one hand, and premarital sex and same-sex relations on the other — suggest a conjecture: objections rooted in immediate harms and concrete consequences might be more stable over time; objections rooted in social norms, morality, and religion might be more historically contingent.</p>
<p class="wp-block-paragraph">In the next article, we’ll test this conjecture by looking at relationships between religion and attitudes about sex — and how both have changed over time.</p>
<p class="wp-block-paragraph"><a href="https://allendowney.github.io/CultureWar//blog8-confidence"></a><a href="https://allendowney.github.io/CultureWar//blog8-confidence"></a></p>
<p class="wp-block-paragraph"></p>
<p>The post <a href="https://www.allendowney.com/blog/2026/05/28/sexual-morality/">Sexual morality</a> appeared first on <a href="https://www.allendowney.com/blog">Probably Overthinking It</a>.</p>
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<post-id xmlns="com-wordpress:feed-additions:1">1818</post-id>
</item>
<item>
<title>Confidence in Institutions</title>
<link>https://www.allendowney.com/blog/2026/05/19/confidence-in-institutions/</link>
<dc:creator><![CDATA[AllenDowney]]></dc:creator>
<pubDate>Tue, 19 May 2026 15:04:04 +0000</pubDate>
<category><![CDATA[Uncategorized]]></category>
<category><![CDATA[age period cohort analysis]]></category>
<category><![CDATA[bayesian statistics]]></category>
<category><![CDATA[general social survey]]></category>
<guid isPermaLink="false">https://www.allendowney.com/blog/?p=1803</guid>
<description><![CDATA[<p>This article is one of a series exploring responses to core questions in the General Social Survey (GSS), estimating period and cohort effects, and looking for historical events that might explain the trends we see. Confidence in American institutions In this installment, we’ll look at 13 questions related to confidence in institutions. We’ll start with a detailed look at confidence in “the people running Congress”, and then summarize results from the other questions. The complete survey question is: I am...</p>
<p class="read-more"><a class="btn btn-default" href="https://www.allendowney.com/blog/2026/05/19/confidence-in-institutions/"> Read More<span class="screen-reader-text"> Read More</span></a></p>
<p>The post <a href="https://www.allendowney.com/blog/2026/05/19/confidence-in-institutions/">Confidence in Institutions</a> appeared first on <a href="https://www.allendowney.com/blog">Probably Overthinking It</a>.</p>
]]></description>
<content:encoded><![CDATA[
<p class="wp-block-paragraph">This article is one of a series exploring responses to core questions in the General Social Survey (GSS), estimating period and cohort effects, and looking for historical events that might explain the trends we see.<a href="https://github.com/AllenDowney/CultureWar" target="_blank" rel="noreferrer noopener"></a><a href="https://github.com/AllenDowney/CultureWar/edit/main/jb/blog8_confidence.md" target="_blank" rel="noreferrer noopener"></a></p>
<h2 class="wp-block-heading" id="confidence-in-american-institutions">Confidence in American institutions</h2>
<p class="wp-block-paragraph">In this installment, we’ll look at 13 questions related to confidence in institutions. We’ll start with a detailed look at confidence in “the people running Congress”, and then summarize results from the other questions. The <a href="https://gssdataexplorer.norc.org/variables/459/vshow" target="_blank" rel="noreferrer noopener">complete survey question</a> is:</p>
<blockquote class="wp-block-quote is-layout-flow wp-block-quote-is-layout-flow">
<p class="wp-block-paragraph">I am going to name some institutions in this country. As far as the people running these institutions are concerned, would you say you have a great deal of confidence, only some confidence, or hardly any confidence at all in […] Congress.</p>
</blockquote>
<p class="wp-block-paragraph">The following figure shows the fraction of people who answered “a great deal of confidence” or “only some confidence,” and a smooth line fitted to the raw percentages.</p>
<figure class="wp-block-image" id="conlegis-time-model"><img loading="lazy" decoding="async" width="1145" height="790" src="https://www.allendowney.com/blog/wp-content/uploads/2026/05/time_model_conlegis_-e47a9b867ea68609944d3abe98446e29.png" alt="Time-only model, confidence in the people running Congress." class="wp-image-1808" srcset="https://www.allendowney.com/blog/wp-content/uploads/2026/05/time_model_conlegis_-e47a9b867ea68609944d3abe98446e29.png 1145w, https://www.allendowney.com/blog/wp-content/uploads/2026/05/time_model_conlegis_-e47a9b867ea68609944d3abe98446e29-300x207.png 300w, https://www.allendowney.com/blog/wp-content/uploads/2026/05/time_model_conlegis_-e47a9b867ea68609944d3abe98446e29-1024x707.png 1024w, https://www.allendowney.com/blog/wp-content/uploads/2026/05/time_model_conlegis_-e47a9b867ea68609944d3abe98446e29-768x530.png 768w, https://www.allendowney.com/blog/wp-content/uploads/2026/05/time_model_conlegis_-e47a9b867ea68609944d3abe98446e29-391x270.png 391w" sizes="auto, (max-width: 1145px) 100vw, 1145px" /></figure>
<p class="wp-block-paragraph">The long-term trend is downward, from about 80% during the first iteration of the survey to below 50% in the most recent iterations. But there are ups and downs.</p>
<p class="wp-block-paragraph">It looks like confidence was increasing during the 1980s before collapsing in the early 1990s. Possible causes of the decline include:</p>
<ul class="wp-block-list">
<li>The <a href="https://en.wikipedia.org/wiki/House_banking_scandal" target="_blank" rel="noreferrer noopener">House banking scandal</a>, also known as Rubbergate, and the <a href="https://en.wikipedia.org/wiki/Congressional_Post_Office_scandal" target="_blank" rel="noreferrer noopener">Congressional Post Office scandal</a>.</li>
<li>Increased polarization and perception of dysfunction during the period when <a href="https://en.wikipedia.org/wiki/Newt_Gingrich#Speaker_of_the_House" target="_blank" rel="noreferrer noopener">Newt Gingrich</a> was minority whip (1989-1995).</li>
<li>An <a href="https://en.wikipedia.org/wiki/Early_1990s_recession_in_the_United_States" target="_blank" rel="noreferrer noopener">economic recession</a> from 1990 into 1991.</li>
</ul>
<p class="wp-block-paragraph">Confidence in Congress recovered between 1995 and 2005, and declined again between 2005 and 2015. A likely contributor is the <a href="https://en.wikipedia.org/wiki/Great_Recession" target="_blank" rel="noreferrer noopener">Great Recession</a> from late 2007 to mid-2009.</p>
<p class="wp-block-paragraph">This period also saw the rise of anti-establishment politics, including the <a href="https://en.wikipedia.org/wiki/Tea_Party_movement" target="_blank" rel="noreferrer noopener">Tea Party movement</a> and <a href="https://en.wikipedia.org/wiki/Ron_Paul" target="_blank" rel="noreferrer noopener">Ron Paul’s</a> presidential campaign.</p>
<p class="wp-block-paragraph">Now we’ll decompose these changes into period and cohort effects.</p>
<h3 class="wp-block-heading" id="period-and-cohort-effects">Period and cohort effects</h3>
<p class="wp-block-paragraph">Using the <a href="https://allendowney.github.io/CultureWar/tech-report/" target="_blank" rel="noreferrer noopener">Bayesian model described here</a> we can estimate a latent “confidence in Congress” factor for each birth cohort over time. The following figure shows these estimates; each line represents a single birth year.</p>
<figure class="wp-block-image" id="conlegis-cohort-trajectories"><img loading="lazy" decoding="async" width="1330" height="778" src="https://www.allendowney.com/blog/wp-content/uploads/2026/05/cohort_trajectory_co-d5cd0d30431d1f3f08bcc503ebb4d786.png" alt="Cohort trajectories, percent with a great deal or only some confidence in the people running Congress." class="wp-image-1814" srcset="https://www.allendowney.com/blog/wp-content/uploads/2026/05/cohort_trajectory_co-d5cd0d30431d1f3f08bcc503ebb4d786.png 1330w, https://www.allendowney.com/blog/wp-content/uploads/2026/05/cohort_trajectory_co-d5cd0d30431d1f3f08bcc503ebb4d786-300x175.png 300w, https://www.allendowney.com/blog/wp-content/uploads/2026/05/cohort_trajectory_co-d5cd0d30431d1f3f08bcc503ebb4d786-1024x599.png 1024w, https://www.allendowney.com/blog/wp-content/uploads/2026/05/cohort_trajectory_co-d5cd0d30431d1f3f08bcc503ebb4d786-768x449.png 768w, https://www.allendowney.com/blog/wp-content/uploads/2026/05/cohort_trajectory_co-d5cd0d30431d1f3f08bcc503ebb4d786-462x270.png 462w" sizes="auto, (max-width: 1330px) 100vw, 1330px" /></figure>
<p class="wp-block-paragraph">Those results are easier to interpret if we factor out the cohort effect (keeping the mixture of survey years constant) and the period effect (keeping the mixture of cohorts constant). The following figure shows the standardized cohort effect.</p>
<figure class="wp-block-image" id="conlegis-cohort-standardized"><img loading="lazy" decoding="async" width="1145" height="790" src="https://www.allendowney.com/blog/wp-content/uploads/2026/05/cohort_standardized_-aca7608b25112981c03dc33fffe90a93.png" alt="Standardized cohort effect with fixed time mix, confidence in Congress." class="wp-image-1812" srcset="https://www.allendowney.com/blog/wp-content/uploads/2026/05/cohort_standardized_-aca7608b25112981c03dc33fffe90a93.png 1145w, https://www.allendowney.com/blog/wp-content/uploads/2026/05/cohort_standardized_-aca7608b25112981c03dc33fffe90a93-300x207.png 300w, https://www.allendowney.com/blog/wp-content/uploads/2026/05/cohort_standardized_-aca7608b25112981c03dc33fffe90a93-1024x707.png 1024w, https://www.allendowney.com/blog/wp-content/uploads/2026/05/cohort_standardized_-aca7608b25112981c03dc33fffe90a93-768x530.png 768w, https://www.allendowney.com/blog/wp-content/uploads/2026/05/cohort_standardized_-aca7608b25112981c03dc33fffe90a93-391x270.png 391w" sizes="auto, (max-width: 1145px) 100vw, 1145px" /></figure>
<p class="wp-block-paragraph">Among people born between 1900 and 1950, there is almost no change. Then starting with people born in the 1960s, confidence in Congress has increased consistently and substantially.</p>
<p class="wp-block-paragraph">To interpret this result, it is helpful to go back to the previous figure. Starting in the upper left:</p>
<ul class="wp-block-list">
<li>Among people born in the 1960s and 1970s, about 80% reported confidence in Congress when they were surveyed as young adults.</li>
<li>Among people born in the 1980s and 1990s, it was closer to 70%.</li>
<li>And among people born in the 2000s it’s below 70%.</li>
</ul>
<p class="wp-block-paragraph">The entry point of each cohort is below the entry point of previous cohorts, but because these entry points are above the declining trend of previous generations, this <em>relative</em> optimism is interpreted as an increasing cohort effect.</p>
<p class="wp-block-paragraph">So we should not conclude that younger generations are more confident in Congress, only that when they are first surveyed, they start out above the trajectory of previous cohorts.</p>
<p class="wp-block-paragraph">As a simplification, we might imagine an 18-year-old entering adulthood with a relatively idealized understanding of American government — shaped by civics classes and maybe a school trip to Washington D.C. — before later political experiences erode some of that confidence.</p>
<p class="wp-block-paragraph">Another possibility is that younger generations have grown up with lower expectations of government, so when they say they have “some confidence”, they might be evaluating Congress against a lower standard.</p>
<p class="wp-block-paragraph">The following figure shows the estimated period effect, with the mix of cohorts held constant.</p>
<figure class="wp-block-image" id="conlegis-period-standardized"><img loading="lazy" decoding="async" width="1145" height="790" src="https://www.allendowney.com/blog/wp-content/uploads/2026/05/time_standardized_co-d65cdea9156d375abd801cc2826c9844.png" alt="Standardized period effect with fixed cohort mix, Congress." class="wp-image-1807" srcset="https://www.allendowney.com/blog/wp-content/uploads/2026/05/time_standardized_co-d65cdea9156d375abd801cc2826c9844.png 1145w, https://www.allendowney.com/blog/wp-content/uploads/2026/05/time_standardized_co-d65cdea9156d375abd801cc2826c9844-300x207.png 300w, https://www.allendowney.com/blog/wp-content/uploads/2026/05/time_standardized_co-d65cdea9156d375abd801cc2826c9844-1024x707.png 1024w, https://www.allendowney.com/blog/wp-content/uploads/2026/05/time_standardized_co-d65cdea9156d375abd801cc2826c9844-768x530.png 768w, https://www.allendowney.com/blog/wp-content/uploads/2026/05/time_standardized_co-d65cdea9156d375abd801cc2826c9844-391x270.png 391w" sizes="auto, (max-width: 1145px) 100vw, 1145px" /></figure>
<p class="wp-block-paragraph">This decline is steeper than what we saw in the time-only model, because we have factored out the mitigating effect of relative optimism in recent generations.</p>
<h3 class="wp-block-heading" id="government-institutions">Government Institutions</h3>
<p class="wp-block-paragraph">Now we’ll apply the same analysis to questions about the executive branch of the federal government, the Supreme Court, and the military (technically part of the executive branch).</p>
<p class="wp-block-paragraph">The following figure shows the estimated cohort effects for each of these institutions.</p>
<figure class="wp-block-image" id="cluster-gov-cohort"><img loading="lazy" decoding="async" width="1145" height="764" src="https://www.allendowney.com/blog/wp-content/uploads/2026/05/con_cluster_1_govern-7c461121f9363f4e9a2440f4a41ce384.png" alt="Government and security institutions, standardized cohort component (uniform survey years)." class="wp-image-1811" srcset="https://www.allendowney.com/blog/wp-content/uploads/2026/05/con_cluster_1_govern-7c461121f9363f4e9a2440f4a41ce384.png 1145w, https://www.allendowney.com/blog/wp-content/uploads/2026/05/con_cluster_1_govern-7c461121f9363f4e9a2440f4a41ce384-300x200.png 300w, https://www.allendowney.com/blog/wp-content/uploads/2026/05/con_cluster_1_govern-7c461121f9363f4e9a2440f4a41ce384-1024x683.png 1024w, https://www.allendowney.com/blog/wp-content/uploads/2026/05/con_cluster_1_govern-7c461121f9363f4e9a2440f4a41ce384-768x512.png 768w, https://www.allendowney.com/blog/wp-content/uploads/2026/05/con_cluster_1_govern-7c461121f9363f4e9a2440f4a41ce384-405x270.png 405w" sizes="auto, (max-width: 1145px) 100vw, 1145px" /></figure>
<p class="wp-block-paragraph">And the following figure shows the period effect, after factoring out the cohort effect.</p>
<figure class="wp-block-image" id="cluster-gov-standardized-period"><img loading="lazy" decoding="async" width="1145" height="764" src="https://www.allendowney.com/blog/wp-content/uploads/2026/05/con_cluster_1_govern-b24ed098d4d8b3b779b1face8e1cd0be.png" alt="Government and security institutions, standardized period component (fixed cohort mix)." class="wp-image-1813" srcset="https://www.allendowney.com/blog/wp-content/uploads/2026/05/con_cluster_1_govern-b24ed098d4d8b3b779b1face8e1cd0be.png 1145w, https://www.allendowney.com/blog/wp-content/uploads/2026/05/con_cluster_1_govern-b24ed098d4d8b3b779b1face8e1cd0be-300x200.png 300w, https://www.allendowney.com/blog/wp-content/uploads/2026/05/con_cluster_1_govern-b24ed098d4d8b3b779b1face8e1cd0be-1024x683.png 1024w, https://www.allendowney.com/blog/wp-content/uploads/2026/05/con_cluster_1_govern-b24ed098d4d8b3b779b1face8e1cd0be-768x512.png 768w, https://www.allendowney.com/blog/wp-content/uploads/2026/05/con_cluster_1_govern-b24ed098d4d8b3b779b1face8e1cd0be-405x270.png 405w" sizes="auto, (max-width: 1145px) 100vw, 1145px" /></figure>
<p class="wp-block-paragraph">The results for the executive branch are similar to the results for Congress.</p>
<ul class="wp-block-list">
<li>The cohort effect is flat between people born in the 1900s and 1950s, and increasing after that.</li>
<li>The period effect declines substantially and consistently — without the ups and downs of confidence in Congress.</li>
</ul>
<p class="wp-block-paragraph">When respondents are asked about the “executive branch”, it’s not clear whether they think primarily about the president, federal agencies, or the federal government in general.</p>
<p class="wp-block-paragraph">The patterns for the military and Supreme Court are different.</p>
<ul class="wp-block-list">
<li>Confidence in the military is generally high. The cohort effect declined gradually, and possibly more steeply among people born after 1980. The period effect gradually increased.</li>
<li>Confidence in the Supreme Court is higher than confidence in other branches, although the period effect has dropped steeply since 2015. The cohort effect increased among people born between 1900 and 1960; among more recent generations it is gradually declining.</li>
</ul>
<p class="wp-block-paragraph">Historically, the Court cultivated an image of being above politics; that perception weakened substantially in the 2010s. In March 2016, Merrick Garland was nominated to the Supreme Court after the death of Antonin Scalia. The Republican majority in the Senate refused to hold a hearing or vote on his nomination. The seat remained empty until Donald Trump nominated, and the Senate confirmed, Neil Gorsuch, who is considered to be more conservative. To many liberals, the Senate’s 293-day blockade undermined the legitimacy of the Court.</p>
<p class="wp-block-paragraph">Then when Ruth Bader Ginsburg died in September 2020, Donald Trump nominated Amy Coney Barrett and the Senate confirmed her 8 days before the 2020 presidential election, in a process criticized by Democratic leaders as illegitimate.</p>
<p class="wp-block-paragraph">These appointments, along with the confirmation of Brett Kavanaugh in 2018, shifted the composition of the Court toward conservatives, forming what is now described as a 6-3 supermajority of conservative justices.</p>
<p class="wp-block-paragraph">Since then, the Supreme Court has issued several decisions contrary to majority public opinion, most notably the 2022 decision overturning <em>Roe v. Wade</em>. Other unpopular decisions weakened gun control and limited federal regulatory authority, especially over environmental policy. Many of these decisions have been perceived, especially on the left, to be motivated by politics rather than constitutional principles and precedent.</p>
<p class="wp-block-paragraph">The slope of the cohort effect might reflect a generational change in associations with the Supreme Court. Older cohorts may associate the Supreme Court with landmark decisions like Brown v. Board of Education and the expansion of civil rights. Younger cohorts may instead associate it with partisan conflict, blocked reforms, and ideological polarization. Older generations might also have been more deferential toward the institution itself. Younger generations, exposed to more adversarial and partisan media coverage, might be less inclined to deference.</p>
<h3 class="wp-block-heading" id="economic-institutions">Economic institutions</h3>
<p class="wp-block-paragraph">The following figures show the cohort and period effects for confidence in economic institutions: banks, major companies, and organized labor.</p>
<figure class="wp-block-image" id="cluster-econ-cohort"><img loading="lazy" decoding="async" width="1145" height="764" src="https://www.allendowney.com/blog/wp-content/uploads/2026/05/con_cluster_2_econom-b4cf1eea3eb5290377d151bac981fdaf.png" alt="Economic institutions, standardized cohort component." class="wp-image-1809" srcset="https://www.allendowney.com/blog/wp-content/uploads/2026/05/con_cluster_2_econom-b4cf1eea3eb5290377d151bac981fdaf.png 1145w, https://www.allendowney.com/blog/wp-content/uploads/2026/05/con_cluster_2_econom-b4cf1eea3eb5290377d151bac981fdaf-300x200.png 300w, https://www.allendowney.com/blog/wp-content/uploads/2026/05/con_cluster_2_econom-b4cf1eea3eb5290377d151bac981fdaf-1024x683.png 1024w, https://www.allendowney.com/blog/wp-content/uploads/2026/05/con_cluster_2_econom-b4cf1eea3eb5290377d151bac981fdaf-768x512.png 768w, https://www.allendowney.com/blog/wp-content/uploads/2026/05/con_cluster_2_econom-b4cf1eea3eb5290377d151bac981fdaf-405x270.png 405w" sizes="auto, (max-width: 1145px) 100vw, 1145px" /></figure>
<p class="wp-block-paragraph"></p>
<figure class="wp-block-image" id="cluster-econ-standardized-period"><img loading="lazy" decoding="async" width="1145" height="764" src="https://www.allendowney.com/blog/wp-content/uploads/2026/05/con_cluster_2_econom-76a4be0f163f28d139a677ac90cfd0e5.png" alt="Economic institutions, standardized period component." class="wp-image-1806" srcset="https://www.allendowney.com/blog/wp-content/uploads/2026/05/con_cluster_2_econom-76a4be0f163f28d139a677ac90cfd0e5.png 1145w, https://www.allendowney.com/blog/wp-content/uploads/2026/05/con_cluster_2_econom-76a4be0f163f28d139a677ac90cfd0e5-300x200.png 300w, https://www.allendowney.com/blog/wp-content/uploads/2026/05/con_cluster_2_econom-76a4be0f163f28d139a677ac90cfd0e5-1024x683.png 1024w, https://www.allendowney.com/blog/wp-content/uploads/2026/05/con_cluster_2_econom-76a4be0f163f28d139a677ac90cfd0e5-768x512.png 768w, https://www.allendowney.com/blog/wp-content/uploads/2026/05/con_cluster_2_econom-76a4be0f163f28d139a677ac90cfd0e5-405x270.png 405w" sizes="auto, (max-width: 1145px) 100vw, 1145px" /></figure>
<p class="wp-block-paragraph">Confidence in these institutions is generally high. Looking at the cohort effects, the most salient feature is increased confidence in organized labor among people born after 1940.</p>
<p class="wp-block-paragraph">A possible explanation is that younger cohorts have less exposure to organized labor. Older generations were more likely to be affected by strikes and related economic disruption, and more likely to be aware of corruption in labor unions. As union membership has declined and the gig economy has expanded, younger cohorts are less aware of the negative aspects of organized labor, including dues, and more likely to perceive their lack of negotiating power in the labor market. Also, anti-labor ideology has declined since the end of the Cold War, as the framing has shifted from “labor versus management” to “workers versus corporations”.</p>
<p class="wp-block-paragraph">By comparison with the cohort effects, the period effects are modest:</p>
<ul class="wp-block-list">
<li>The period effect on organized labor is almost unchanged since the 1980s — the change we see over time is almost entirely due to generational replacement.</li>
<li>The period effect on confidence in major companies has declined somewhat.</li>
<li>The trend for banks and financial institutions is more complicated — arguably driven by shorter-term period effects like scandals and financial crises. The first notable downturn, in the 1980s, coincides with the <a href="https://en.wikipedia.org/wiki/Savings_and_loan_crisis" target="_blank" rel="noreferrer noopener">savings and loan crisis</a>, when hundreds of financial institutions failed and taxpayers absorbed large bailout costs, followed by an <a href="https://en.wikipedia.org/wiki/Early_1990s_recession_in_the_United_States" target="_blank" rel="noreferrer noopener">economic recession</a> from 1990 into 1991. The larger downturn around 2008 coincides with the <a href="https://en.wikipedia.org/wiki/2008_financial_crisis" target="_blank" rel="noreferrer noopener">2008 global financial crisis</a>, when taxpayers were hit with even larger bailout costs, and public anger at “private gains, public losses” came to a focus in the <a href="https://en.wikipedia.org/wiki/Occupy_Wall_Street" target="_blank" rel="noreferrer noopener">Occupy Wall Street protests</a>.</li>
</ul>
<h3 class="wp-block-heading" id="professions-knowledge-and-religion">Professions, knowledge, and religion</h3>
<p class="wp-block-paragraph">The following figures show estimated cohort and period effects for confidence in education, medicine, the scientific community, and organized religion.</p>
<figure class="wp-block-image" id="cluster-prof-cohort"><img loading="lazy" decoding="async" width="1145" height="764" src="https://www.allendowney.com/blog/wp-content/uploads/2026/05/con_cluster_3_profes-14bdbff63efcff6380045908aa3157ab.png" alt="Professions and knowledge institutions, standardized cohort component." class="wp-image-1816" srcset="https://www.allendowney.com/blog/wp-content/uploads/2026/05/con_cluster_3_profes-14bdbff63efcff6380045908aa3157ab.png 1145w, https://www.allendowney.com/blog/wp-content/uploads/2026/05/con_cluster_3_profes-14bdbff63efcff6380045908aa3157ab-300x200.png 300w, https://www.allendowney.com/blog/wp-content/uploads/2026/05/con_cluster_3_profes-14bdbff63efcff6380045908aa3157ab-1024x683.png 1024w, https://www.allendowney.com/blog/wp-content/uploads/2026/05/con_cluster_3_profes-14bdbff63efcff6380045908aa3157ab-768x512.png 768w, https://www.allendowney.com/blog/wp-content/uploads/2026/05/con_cluster_3_profes-14bdbff63efcff6380045908aa3157ab-405x270.png 405w" sizes="auto, (max-width: 1145px) 100vw, 1145px" /></figure>
<p class="wp-block-paragraph"></p>
<figure class="wp-block-image" id="cluster-prof-standardized-period"><img loading="lazy" decoding="async" width="1145" height="764" src="https://www.allendowney.com/blog/wp-content/uploads/2026/05/con_cluster_3_profes-f5418c000cfe9c18849ed481e1182500.png" alt="Professions and knowledge institutions, standardized period component." class="wp-image-1805" srcset="https://www.allendowney.com/blog/wp-content/uploads/2026/05/con_cluster_3_profes-f5418c000cfe9c18849ed481e1182500.png 1145w, https://www.allendowney.com/blog/wp-content/uploads/2026/05/con_cluster_3_profes-f5418c000cfe9c18849ed481e1182500-300x200.png 300w, https://www.allendowney.com/blog/wp-content/uploads/2026/05/con_cluster_3_profes-f5418c000cfe9c18849ed481e1182500-1024x683.png 1024w, https://www.allendowney.com/blog/wp-content/uploads/2026/05/con_cluster_3_profes-f5418c000cfe9c18849ed481e1182500-768x512.png 768w, https://www.allendowney.com/blog/wp-content/uploads/2026/05/con_cluster_3_profes-f5418c000cfe9c18849ed481e1182500-405x270.png 405w" sizes="auto, (max-width: 1145px) 100vw, 1145px" /></figure>
<p class="wp-block-paragraph">Confidence in these institutions is highest for science and medicine, lower for education and religion.</p>
<p class="wp-block-paragraph">Looking at the period effects, they are all in decline. Confidence in education declined most steeply; confidence in the scientific community is relatively stable, although it declines after 2020.</p>
<p class="wp-block-paragraph">Thinking about confidence in education, it might be useful to separate colleges and universities from K-12 schools.</p>
<ul class="wp-block-list">
<li>In higher education, the decline might be due to increasing tuition and student debt, credential inflation, and increasing uncertainty about the economic return on a college degree, especially among majors in the arts and humanities. More recently, confidence in universities has decreased steeply, especially among conservatives, due to the perception of ideological bias.</li>
<li>In K-12 education, declining confidence might be related to anxiety about standardized testing, international competition, and especially around the <a href="https://en.wikipedia.org/wiki/No_Child_Left_Behind_Act" target="_blank" rel="noreferrer noopener">No Child Left Behind Act</a> in 2001, the framing of public schools as underperforming institutions requiring accountability reforms and federal intervention. Also, public schools have increasingly become focal points for political conflicts about curriculum, race, gender, religion, and parental authority.</li>
</ul>
<p class="wp-block-paragraph">Most of the cohort effects have increased modestly; in particular confidence in education is higher among people born after 1980, compared to previous generations observed at the same time. But for these institutions, the interaction of the period and cohort effect is similar to what we saw for Congress — it’s not that recent generations have <em>more</em> confidence, it’s just that when they are surveyed as young adults, they come in at entry points above the declining trend of previous generations.</p>
<p class="wp-block-paragraph">Confidence in organized religion is the exception — the period and cohort effects both trend downward, so the decline is additive. A likely contributor to the period effect is growing public awareness of <a href="https://en.wikipedia.org/wiki/Catholic_Church_sex_abuse_cases_in_the_United_States" target="_blank" rel="noreferrer noopener">sexual abuse and institutional coverups in the Catholic Church</a>, which received national attention beginning in the 1980s, escalated after the <a href="https://en.wikipedia.org/wiki/Sexual_abuse_scandal_in_the_Archdiocese_of_Boston" target="_blank" rel="noreferrer noopener">Boston Globe investigations</a> published in 2002, and continues to the present with additional revelations in the United States and other countries. But the decline is not limited to the Catholic Church, and it began before these scandals were widely known.</p>
<p class="wp-block-paragraph">The cohort effect likely reflects broader secularization trends, including declining religious affiliation, lower church attendance, and weakening institutional authority among younger generations.</p>
<h3 class="wp-block-heading" id="media">Media</h3>
<p class="wp-block-paragraph">Finally, the following figures show estimated cohort and period effects for confidence in television and the press.</p>
<figure class="wp-block-image" id="cluster-media-cohort"><img loading="lazy" decoding="async" width="1145" height="764" src="https://www.allendowney.com/blog/wp-content/uploads/2026/05/con_cluster_4_media_-8bf3f75d17ac4f1f8991025f1051ce52.png" alt="Media, standardized cohort component." class="wp-image-1815" srcset="https://www.allendowney.com/blog/wp-content/uploads/2026/05/con_cluster_4_media_-8bf3f75d17ac4f1f8991025f1051ce52.png 1145w, https://www.allendowney.com/blog/wp-content/uploads/2026/05/con_cluster_4_media_-8bf3f75d17ac4f1f8991025f1051ce52-300x200.png 300w, https://www.allendowney.com/blog/wp-content/uploads/2026/05/con_cluster_4_media_-8bf3f75d17ac4f1f8991025f1051ce52-1024x683.png 1024w, https://www.allendowney.com/blog/wp-content/uploads/2026/05/con_cluster_4_media_-8bf3f75d17ac4f1f8991025f1051ce52-768x512.png 768w, https://www.allendowney.com/blog/wp-content/uploads/2026/05/con_cluster_4_media_-8bf3f75d17ac4f1f8991025f1051ce52-405x270.png 405w" sizes="auto, (max-width: 1145px) 100vw, 1145px" /></figure>
<p class="wp-block-paragraph"></p>
<figure class="wp-block-image" id="cluster-media-standardized-period"><img loading="lazy" decoding="async" width="1145" height="764" src="https://www.allendowney.com/blog/wp-content/uploads/2026/05/con_cluster_4_media_-db77e283c289a556c23c800a199f1ce9.png" alt="Media, standardized period component." class="wp-image-1810" srcset="https://www.allendowney.com/blog/wp-content/uploads/2026/05/con_cluster_4_media_-db77e283c289a556c23c800a199f1ce9.png 1145w, https://www.allendowney.com/blog/wp-content/uploads/2026/05/con_cluster_4_media_-db77e283c289a556c23c800a199f1ce9-300x200.png 300w, https://www.allendowney.com/blog/wp-content/uploads/2026/05/con_cluster_4_media_-db77e283c289a556c23c800a199f1ce9-1024x683.png 1024w, https://www.allendowney.com/blog/wp-content/uploads/2026/05/con_cluster_4_media_-db77e283c289a556c23c800a199f1ce9-768x512.png 768w, https://www.allendowney.com/blog/wp-content/uploads/2026/05/con_cluster_4_media_-db77e283c289a556c23c800a199f1ce9-405x270.png 405w" sizes="auto, (max-width: 1145px) 100vw, 1145px" /></figure>
<p class="wp-block-paragraph">There is almost no cohort effect, although the most recent cohorts might have a little more confidence in television.</p>
<p class="wp-block-paragraph">The headline here is the period effect, which is consistently downward, and steeper for the press than television. The steepest part of the decline for both media started around 1990, shortly after the 1987 abolition of the <a href="https://en.wikipedia.org/wiki/Fairness_doctrine" target="_blank" rel="noreferrer noopener">fairness doctrine</a>, which required broadcast coverage of controversial topics to be “fair in the sense that it provides an opportunity for the presentation of contrasting points of view,” as described in the <a href="https://www.fcc.gov/document/editorializing-broadcast-licensees" target="_blank" rel="noreferrer noopener">1949 FCC report</a> that established the doctrine.</p>
<p class="wp-block-paragraph">The end of the fairness doctrine coincided with the rise of talk radio programs with explicit political viewpoints, including <a href="https://en.wikipedia.org/wiki/The_Rush_Limbaugh_Show" target="_blank" rel="noreferrer noopener">The Rush Limbaugh Show</a>, which was nationally syndicated in 1988.</p>
<p class="wp-block-paragraph">Cable television news followed, including <a href="https://en.wikipedia.org/wiki/Fox_News" target="_blank" rel="noreferrer noopener">Fox News Channel</a> in 1996, with an explicit conservative orientation, and <a href="https://en.wikipedia.org/wiki/MSNBC" target="_blank" rel="noreferrer noopener">MSNBC</a>, which developed a more liberal identity in the 2000s.</p>
<p class="wp-block-paragraph">During this period, more generally, media audiences became more fragmented. Prior to 1980, most Americans were exposed to a small number of shared news sources, notably the three major television networks. Talk radio and cable television offered more options and less common experience.</p>
<p class="wp-block-paragraph">And then the internet happened, starting in the 1990s with online news and political blogs, including the <a href="https://en.wikipedia.org/wiki/Drudge_Report" target="_blank" rel="noreferrer noopener">Drudge Report</a> which started as a weekly email newsletter in 1995, and rose to national prominence when it broke the <a href="https://en.wikipedia.org/wiki/Clinton%E2%80%93Lewinsky_scandal" target="_blank" rel="noreferrer noopener">Clinton-Lewinsky scandal</a> in 1998.</p>
<p class="wp-block-paragraph">Social media followed. YouTube was founded in 2005; Facebook and Twitter launched in 2006. While these platforms have become important sources of news for many Americans, engagement-driven algorithms often promote emotionally provocative and polarizing content over careful reporting. The rise of the internet contributed to the decline of local newspapers, and eventually national newspapers as well.</p>
<p class="wp-block-paragraph">Ownership of television stations became increasingly consolidated following the <a href="https://en.wikipedia.org/wiki/Telecommunications_Act_of_1996" target="_blank" rel="noreferrer noopener">1996 Telecommunications Act</a>, allowing a small number of national media companies to control larger shares of local news programming. The effect of this consolidation is explained in <a href="https://www.vox.com/policy-and-politics/2018/4/2/17189302/sinclair-broadcast-fake-news-biased-trump-viral-video" target="_blank" rel="noreferrer noopener">this Vox article</a> and memorably demonstrated in <a href="https://www.youtube.com/watch?v=hWLjYJ4BzvI" target="_blank" rel="noreferrer noopener">this Deadspin compilation</a> showing dozens of TV news anchors reading nearly identical scripts provided by the <a href="https://en.wikipedia.org/wiki/Sinclair_Broadcast_Group" target="_blank" rel="noreferrer noopener">Sinclair Broadcast Group</a>, which requires the channels it owns to air segments called <a href="https://www.nytimes.com/2017/05/12/business/media/sinclair-broadcast-komo-conservative-media.html" target="_blank" rel="noreferrer noopener">“must-runs”</a> — many of them presenting conservative talking points.</p>
<p class="wp-block-paragraph">Finally, since the beginning of his presidential campaign in 2015, Donald Trump has repeatedly denigrated television and print media, frequently describing unfavorable coverage as “fake news” and labeling journalists “enemies of the people.” These attacks likely contribute to declining confidence in the press, especially among Republicans.</p>
<h3 class="wp-block-heading" id="negativity-bias">Negativity Bias</h3>
<p class="wp-block-paragraph">In the previous examples, you might notice that I offer explanations for the downturns, but no explanation for the upturns. That’s because bad things, like scandals and economic crises, often happen quickly and they get a lot of coverage; good things often happen slowly and continue without comment.</p>
<p class="wp-block-paragraph">For many institutions, no news is good news. When they do their jobs, they don’t get much attention, and public confidence drifts higher, even without specific positive events or coverage.</p>
<p class="wp-block-paragraph">So I want to end this article by highlighting some of the positive results we see in this data:</p>
<ul class="wp-block-list">
<li>Confidence in education, science, and medicine is high and although the period effects are negative, the cohort effects are positive, which bodes well for the future.</li>
<li>Confidence in financial institutions and organized labor is high.</li>
<li>Confidence in government is lower and declining, but as each generation of young adults starts out more optimistic than their elders, there is hope for a turnaround.</li>
</ul>
<p class="wp-block-paragraph">But the recent steep decline of confidence in the Supreme Court is a concern, as is the loss of confidence in the media. It’s hard to find a positive take on those trends.</p>
<p class="wp-block-paragraph"><a href="https://allendowney.github.io/CultureWar//blog7-hapgen"></a><a href="https://allendowney.github.io/CultureWar//blog7-hapgen"></a></p>
<p class="wp-block-paragraph"></p>
<p>The post <a href="https://www.allendowney.com/blog/2026/05/19/confidence-in-institutions/">Confidence in Institutions</a> appeared first on <a href="https://www.allendowney.com/blog">Probably Overthinking It</a>.</p>
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<post-id xmlns="com-wordpress:feed-additions:1">1803</post-id>
</item>
<item>
<title>Planning for your midlife crisis</title>
<link>https://www.allendowney.com/blog/2026/05/01/planning-for-your-midlife-crisis/</link>
<dc:creator><![CDATA[AllenDowney]]></dc:creator>
<pubDate>Fri, 01 May 2026 19:34:53 +0000</pubDate>
<category><![CDATA[Uncategorized]]></category>
<category><![CDATA[life expectancy]]></category>
<category><![CDATA[mortality]]></category>
<category><![CDATA[ODSC]]></category>
<guid isPermaLink="false">https://www.allendowney.com/blog/?p=1794</guid>
<description><![CDATA[<p>Yesterday I presented a talk at ODSC East 2026, called “Counterfactual Analysis with Bayesian Models: What Drives the Life Expectancy Gap?” Here’s the abstract Across nearly every country in the world, women live longer than men—but the size of this gap varies from about two years in some countries to more than twelve in others. What explains these differences, and how much of the gap can be closed? In this talk, I present a practical approach to counterfactual analysis using...</p>
<p class="read-more"><a class="btn btn-default" href="https://www.allendowney.com/blog/2026/05/01/planning-for-your-midlife-crisis/"> Read More<span class="screen-reader-text"> Read More</span></a></p>
<p>The post <a href="https://www.allendowney.com/blog/2026/05/01/planning-for-your-midlife-crisis/">Planning for your midlife crisis</a> appeared first on <a href="https://www.allendowney.com/blog">Probably Overthinking It</a>.</p>
]]></description>
<content:encoded><![CDATA[
<p class="wp-block-paragraph">Yesterday I presented a talk at ODSC East 2026, called “Counterfactual Analysis with Bayesian Models: What Drives the Life Expectancy Gap?” Here’s the abstract</p>
<blockquote class="wp-block-quote is-layout-flow wp-block-quote-is-layout-flow">
<p class="wp-block-paragraph">Across nearly every country in the world, women live longer than men—but the size of this gap varies from about two years in some countries to more than twelve in others. What explains these differences, and how much of the gap can be closed?</p>
<p class="wp-block-paragraph">In this talk, I present a practical approach to counterfactual analysis using Bayesian regression models. Using publicly available mortality data, we build a model that relates the life expectancy gap between men and women to differences in cause-specific death rates, including homicide, drug overdoses, traffic fatalities, smoking-related disease, and chronic illness.</p>
<p class="wp-block-paragraph">The model generates posterior simulations that answer “what-if” questions. For example: How much smaller would the U.S. life expectancy gap be if homicide rates matched those in Western Europe?</p>
<p class="wp-block-paragraph">The talk presents the workflow—from assembling global datasets to fitting interpretable Bayesian models with PyMC and generating counterfactual simulations. Attendees will learn how Bayesian models can support explainable modeling and analysis under uncertainty.</p>
</blockquote>
<p class="wp-block-paragraph">I think the talk went well, and we got some good questions at the end. There’s no recording, unfortunately, <a href="https://docs.google.com/presentation/d/e/2PACX-1vSiwjA6Mi95poqGQJiXw7Mdy0BgPa-aEmVhJHXwP35QRjt2dduEEN53yZi4fnpAReVaS-EDWS3CwMt1/pub?start=false&loop=false&delayms=3000">but my slides are here</a>. And if you want to know more, I have a series of blog posts on Substack</p>
<ul class="wp-block-list">
<li><a href="https://allendowney.substack.com/p/the-gender-gap-in-life-expectancy">The Gender Gap in Life Expectancy</a></li>
<li><a href="https://allendowney.substack.com/p/what-drives-the-life-expectancy-gender">What Drives the Life Expectancy Gender Gap?</a></li>
<li><a href="https://allendowney.substack.com/p/how-much-of-the-life-expectancy-gap">How Much of the Life Expectancy Gap Could We Close?</a></li>
<li><a href="https://allendowney.substack.com/p/international-patterns-in-the-life">International Patterns in the Life Expectancy Gap</a></li>
</ul>
<p class="wp-block-paragraph">The fifth and final post is on the way. In the meantime, here’s a quick post on a related topic.</p>
<h2 class="wp-block-heading">Are you middle-aged?</h2>
<p class="wp-block-paragraph">Here’s a question from Reddit’s <a href="https://www.reddit.com/r/stupidquestions/comments/1sxesux/what_age_is_actually_considered_middle_age/">Stupid Questions forum</a>:</p>
<blockquote class="wp-block-quote is-layout-flow wp-block-quote-is-layout-flow">
<p class="wp-block-paragraph">I always thought middle age was in your 40s but since life expectancy is around 75 or so, wouldn’t it be about 35?</p>
</blockquote>
<p class="wp-block-paragraph">If life expectancy is 75, you might think the midpoint is half that, which is 37.5. But if 75 is life expectancy <em>at birth</em> and you survive to age 37.5, your life expectancy <em>at that age</em> is higher than 75. So 37.5 is not halfway!</p>
<p class="wp-block-paragraph">If we really want to find the midpoint – and it wouldn’t be <em>Probably Overthinking It</em> if we didn’t – we have to find the age where your expected remaining lifetime equals your current age.</p>
<p class="wp-block-paragraph">Let’s do it.</p>
<h2 class="wp-block-heading">Data</h2>
<p class="wp-block-paragraph">From the <a href="https://www.mortality.org/Country/Country?cntr=USA">Human Mortality Database</a> I downloaded life tables for the United States, combined and broken down for men and women. The following function reads and cleans a table.</p>
<pre id="codecell1" class="wp-block-preformatted">def read_life_table(filename):
lt = pd.read_fwf(filename, skiprows=2, infer_nrows=200)
lt['Age'] = lt['Age'].str.replace('+', '', regex=False).astype(int)
return lt
</pre>
<p class="wp-block-paragraph">Here are the first few rows of the combined table (see notes below for details).</p>
<pre id="codecell2" class="wp-block-preformatted">blt = read_life_table('../data/bltper_1x1.txt')
blt.head()
</pre>
<figure class="wp-block-table"><table class="has-fixed-layout"><thead><tr><th></th><th>Year</th><th>Age</th><th>mx</th><th>qx</th><th>ax</th><th>lx</th><th>dx</th><th>Lx</th><th>Tx</th><th>ex</th></tr></thead><tbody><tr><th>0</th><td>1933</td><td>0</td><td>0.06129</td><td>0.05861</td><td>0.25</td><td>100000</td><td>5861</td><td>95624</td><td>6089609</td><td>60.90</td></tr><tr><th>1</th><td>1933</td><td>1</td><td>0.00946</td><td>0.00941</td><td>0.50</td><td>94139</td><td>886</td><td>93696</td><td>5993985</td><td>63.67</td></tr><tr><th>2</th><td>1933</td><td>2</td><td>0.00435</td><td>0.00434</td><td>0.50</td><td>93253</td><td>405</td><td>93050</td><td>5900289</td><td>63.27</td></tr><tr><th>3</th><td>1933</td><td>3</td><td>0.00310</td><td>0.00310</td><td>0.50</td><td>92848</td><td>288</td><td>92704</td><td>5807239</td><td>62.55</td></tr><tr><th>4</th><td>1933</td><td>4</td><td>0.00239</td><td>0.00238</td><td>0.50</td><td>92560</td><td>221</td><td>92450</td><td>5714535</td><td>61.74</td></tr></tbody></table></figure>
<p class="wp-block-paragraph">We’ll also read the female and male tables.</p>
<pre id="codecell3" class="wp-block-preformatted">flt = read_life_table('../data/fltper_1x1.txt')
</pre>
<pre id="codecell4" class="wp-block-preformatted">mlt = read_life_table('../data/mltper_1x1.txt')
</pre>
<p class="wp-block-paragraph">The tables include data from 1933 to 2024, so we’ll select the most recent data.</p>
<pre id="codecell5" class="wp-block-preformatted">year = blt['Year'].unique()[-1]
table = blt.query('Year == @year').set_index('Age')
</pre>
<p class="wp-block-paragraph">The column we’ll use is <code>ex</code>, which is life expectancy as a function of age.</p>
<pre id="codecell6" class="wp-block-preformatted">age = table.index.to_series()
ex = table['ex']
</pre>
<p class="wp-block-paragraph">Life expectancy at birth is 79 years, so the naive midpoint is 39.5.</p>
<pre id="codecell7" class="wp-block-preformatted">ex[0], ex[0] / 2
</pre>
<pre id="codecell8" class="wp-block-preformatted">(79.08, 39.54)
</pre>
<p class="wp-block-paragraph">But at age 40, expected remaining lifetime is 41.1, so 39.5 is not the midpoint.</p>
<pre id="codecell9" class="wp-block-preformatted">ex[39], ex[40]
</pre>
<pre id="codecell10" class="wp-block-preformatted">(42.04, 41.12)
</pre>
<p class="wp-block-paragraph">This plot shows life expectancy at each age, compared to age.</p>
<pre id="codecell11" class="wp-block-preformatted">ex.plot(label='Remaining life expectancy')
age.plot(label='Age')
decorate(ylabel='Years',
title='Remaining life expectancy vs age, United States 2024')
</pre>
<figure class="wp-block-image"><img loading="lazy" decoding="async" width="438" height="250" src="https://www.allendowney.com/blog/wp-content/uploads/2026/05/a55e9cbde25b36d9c42e2ede2a78a827460d537f230b5cc4e7dfcb519a44bbc6.png" alt="_images/a55e9cbde25b36d9c42e2ede2a78a827460d537f230b5cc4e7dfcb519a44bbc6.png" class="wp-image-1797" srcset="https://www.allendowney.com/blog/wp-content/uploads/2026/05/a55e9cbde25b36d9c42e2ede2a78a827460d537f230b5cc4e7dfcb519a44bbc6.png 438w, https://www.allendowney.com/blog/wp-content/uploads/2026/05/a55e9cbde25b36d9c42e2ede2a78a827460d537f230b5cc4e7dfcb519a44bbc6-300x171.png 300w" sizes="auto, (max-width: 438px) 100vw, 438px" /></figure>
<p class="wp-block-paragraph">“Middle age” is where the lines cross, which we can compute by linear interpolation.</p>
<pre id="codecell12" class="wp-block-preformatted">from scipy.interpolate import interp1d
inverse = interp1d(ex - age, age)
inverse(0)
</pre>
<pre id="codecell13" class="wp-block-preformatted">array(40.58638743)
</pre>
<p class="wp-block-paragraph">So the overall midpoint is 40.6 years. But as you might expect, it’s different for men and women. Let’s put the analysis we did in a function.</p>
<pre id="codecell14" class="wp-block-preformatted">def get_midpoint(filename):
lt = read_life_table(filename)
year = lt['Year'].unique()[-1]
table = lt.query('Year == @year').set_index('Age')
age = pd.Series(table.index)
ex = table['ex']
inverse = interp1d(ex - age, age)
return inverse(0)
</pre>
<p class="wp-block-paragraph">And run it for men.</p>
<pre id="codecell15" class="wp-block-preformatted">get_midpoint('../data/mltper_1x1.txt')
</pre>
<pre id="codecell16" class="wp-block-preformatted">array(39.57142857)
</pre>
<p class="wp-block-paragraph">And women.</p>
<pre id="codecell17" class="wp-block-preformatted">get_midpoint('../data/fltper_1x1.txt')
</pre>
<pre id="codecell18" class="wp-block-preformatted">array(41.56185567)
</pre>
<p class="wp-block-paragraph">Men hit middle age at 39.6, women at 41.6.</p>
<h2 class="wp-block-heading">The Gender Gap and Age</h2>
<p class="wp-block-paragraph">Finally, let’s see how the gender gap in life expectancy changes as a function of age.</p>
<pre id="codecell19" class="wp-block-preformatted">ex_male = mlt.query('Year == @year').set_index('Age')['ex']
ex_female = flt.query('Year == @year').set_index('Age')['ex']
gap = ex_female - ex_male
</pre>
<pre id="codecell20" class="wp-block-preformatted">gap.plot(label='')
decorate(ylabel='Years',
title='Life expectancy gender gap vs age')
</pre>
<figure class="wp-block-image"><img loading="lazy" decoding="async" width="438" height="250" src="https://www.allendowney.com/blog/wp-content/uploads/2026/05/2cf48be5acc971ad8f6973506c224767a25ef2e38bcf53c5b12b0f895c26ed11.png" alt="_images/2cf48be5acc971ad8f6973506c224767a25ef2e38bcf53c5b12b0f895c26ed11.png" class="wp-image-1796" srcset="https://www.allendowney.com/blog/wp-content/uploads/2026/05/2cf48be5acc971ad8f6973506c224767a25ef2e38bcf53c5b12b0f895c26ed11.png 438w, https://www.allendowney.com/blog/wp-content/uploads/2026/05/2cf48be5acc971ad8f6973506c224767a25ef2e38bcf53c5b12b0f895c26ed11-300x171.png 300w" sizes="auto, (max-width: 438px) 100vw, 438px" /></figure>
<p class="wp-block-paragraph">At birth the life expectancy gap is close to five years. At age 100, it is close to zero.</p>
<p class="wp-block-paragraph">But just looking at the gap might be misleading. For a more complete picture let’s also look at the ratio.</p>
<pre id="codecell21" class="wp-block-preformatted">ratio = ex_female / ex_male
ratio.plot(label='')
decorate(ylabel='Ratio',
title='Life expectancy gender ratio (female / male)')
</pre>
<figure class="wp-block-image"><img loading="lazy" decoding="async" width="446" height="250" src="https://www.allendowney.com/blog/wp-content/uploads/2026/05/1a514d22895c3e18a767184700d6edf467975abb4b302afe044fd42c002ae21c.png" alt="_images/1a514d22895c3e18a767184700d6edf467975abb4b302afe044fd42c002ae21c.png" class="wp-image-1798" srcset="https://www.allendowney.com/blog/wp-content/uploads/2026/05/1a514d22895c3e18a767184700d6edf467975abb4b302afe044fd42c002ae21c.png 446w, https://www.allendowney.com/blog/wp-content/uploads/2026/05/1a514d22895c3e18a767184700d6edf467975abb4b302afe044fd42c002ae21c-300x168.png 300w" sizes="auto, (max-width: 446px) 100vw, 446px" /></figure>
<p class="wp-block-paragraph">The life expectancy ratio tells a more complicated story.</p>
<ul class="wp-block-list">
<li>At birth, the ratio is 1.06, which means female babies live 6% longer, on average.</li>
<li>Around age 80, the ratio peaks at nearly 1.14 – so between female and male octogenarians, we expect the women to live 14% longer.</li>
<li>At advanced ages, the ratio declines steeply and actually crosses over after age 100 – although the crossover is minimal and might not be statistically valid.</li>
</ul>
<p class="wp-block-paragraph">To interpret these results, we can think about the causes of death that contribute to age-specific death rates at different stages of life.</p>
<ul class="wp-block-list">
<li>In young adulthood, the causes of death that contribute most to gender gaps include road traffic, homicide, accidental injury, drug use disorders.</li>
<li>In advanced adulthood, they include cancer, cardiovascular disease, respiratory disease, liver disease, diabetes, and suicide.</li>
</ul>
<p class="wp-block-paragraph">The causes that affect younger people have large gender gaps, but relatively low death rates. As people get older, these low-rate causes contribute less to age-specific death rates, and the higher-rate causes contribute more.</p>
<p class="wp-block-paragraph">I think that’s a plausible explanation for the increasing ratio from age 0 to 80. For the decline that follows, I can only speculate that there is a selection effect: people who get to these advanced ages are likely to have better-than-average lifestyle histories (less smoking and drinking, better diet, more exercise) – and among people with better lifestyles, the gender gap is small.</p>
<h2 class="wp-block-heading">Notes</h2>
<p class="wp-block-paragraph">Data credit: HMD. Human Mortality Database. Max Planck Institute for Demographic Research (Germany), University of California, Berkeley (USA), and French Institute for Demographic Studies (France). Available at [<a href="http://www.mortality.org">www.mortality.org</a>].</p>
<p class="wp-block-paragraph">Here are the columns of the 1×1 Period Life Tables:</p>
<ul class="wp-block-list">
<li><strong>Year</strong>: Calendar year to which the period life table refers.</li>
<li><strong>Age</strong>: Exact age (x), in years, at the beginning of the interval ([x, x+1)).</li>
<li><strong>mx</strong>: Central death rate at age (x):</li>
</ul>
<ul class="wp-block-list">
<li><strong>qx</strong>: Probability of dying between ages (x) and (x+1):</li>
</ul>
<ul class="wp-block-list">
<li><strong>ax</strong>: Average fraction of the interval lived by those who die in ([x, x+1)). Typically around 0.5 for most ages, lower for infants (reflecting higher early mortality within the year).</li>
<li><strong>lx</strong>: Number of survivors at exact age (x), out of a radix (usually 100,000 births).</li>
<li><strong>dx</strong>: Number of deaths between ages (x) and (x+1):</li>
</ul>
<ul class="wp-block-list">
<li><strong>Lx</strong>: Person-years lived between ages (x) and (x+1), approximately</li>
</ul>
<ul class="wp-block-list">
<li><strong>Tx</strong>: Total person-years remaining above age (x):</li>
</ul>
<ul class="wp-block-list">
<li><strong>ex</strong>: Life expectancy at age (x):</li>
</ul>
<p class="wp-block-paragraph">The details are in<a href="https://github.com/AllenDowney/ProbablyOverthinkingIt/blob/book/examples/midlife.ipynb"> this Jupyter notebook</a>.</p>
<p>The post <a href="https://www.allendowney.com/blog/2026/05/01/planning-for-your-midlife-crisis/">Planning for your midlife crisis</a> appeared first on <a href="https://www.allendowney.com/blog">Probably Overthinking It</a>.</p>
]]></content:encoded>
<post-id xmlns="com-wordpress:feed-additions:1">1794</post-id>
</item>
<item>
<title>Changing Opinions on Assisted Suicide</title>
<link>https://www.allendowney.com/blog/2026/04/16/changing-opinions-on-assisted-suicide/</link>
<dc:creator><![CDATA[AllenDowney]]></dc:creator>
<pubDate>Thu, 16 Apr 2026 20:01:37 +0000</pubDate>
<category><![CDATA[Uncategorized]]></category>
<category><![CDATA[age period cohort analysis]]></category>
<category><![CDATA[bayesian statistics]]></category>
<category><![CDATA[general social survey]]></category>
<guid isPermaLink="false">https://www.allendowney.com/blog/?p=1782</guid>
<description><![CDATA[<p>In Graphs About Religion, Ryan Burge recently wrote about changing opinions about assisted suicide and how they relate to religion. As always, when I see survey responses changing over time, I wonder whether it is driven primarily by period or cohort effects. And if you’ve read my last few posts, you know I’ve been working on a Bayesian model to answer that question. Ryan’s analysis is based on four questions from the General Social Survey (GSS): In addition, we’ll look...</p>
<p class="read-more"><a class="btn btn-default" href="https://www.allendowney.com/blog/2026/04/16/changing-opinions-on-assisted-suicide/"> Read More<span class="screen-reader-text"> Read More</span></a></p>
<p>The post <a href="https://www.allendowney.com/blog/2026/04/16/changing-opinions-on-assisted-suicide/">Changing Opinions on Assisted Suicide</a> appeared first on <a href="https://www.allendowney.com/blog">Probably Overthinking It</a>.</p>
]]></description>
<content:encoded><![CDATA[
<p class="wp-block-paragraph">In <a href="https://www.graphsaboutreligion.com/p/god-death-and-the-right-to-choose" target="_blank" rel="noreferrer noopener">Graphs About Religion</a>, Ryan Burge recently wrote about changing opinions about assisted suicide and how they relate to religion.</p>
<p class="wp-block-paragraph">As always, when I see survey responses changing over time, I wonder whether it is driven primarily by period or cohort effects. And if you’ve read my last few posts, you know I’ve been working on a Bayesian model to answer that question.</p>
<p class="wp-block-paragraph">Ryan’s analysis is based on four questions from the General Social Survey (GSS):</p>
<blockquote class="wp-block-quote is-layout-flow wp-block-quote-is-layout-flow">
<p class="wp-block-paragraph">Do you think a person has the right to end his or her own life if this person:</p>
<ul class="wp-block-list">
<li>Has an incurable disease? (<code>suicide1</code>)</li>
<li>Has gone bankrupt? (<code>suicide2</code>)</li>
<li>Has dishonored his or her family? (<code>suicide3</code>)</li>
<li>Is tired of living and ready to die? (<code>suicide4</code>)</li>
</ul>
</blockquote>
<p class="wp-block-paragraph">In addition, we’ll look at results from a related question (<code>letdie1</code>):</p>
<blockquote class="wp-block-quote is-layout-flow wp-block-quote-is-layout-flow">
<p class="wp-block-paragraph">When a person has a disease that cannot be cured, do you think doctors should be allowed by law to end the patient’s life by some painless means if the patient and his family request it?</p>
</blockquote>
<p class="wp-block-paragraph">The framing of the questions is different: the first four are about the right to end one’s life and the last is about the legality of doctor-assisted suicide.</p>
<p class="wp-block-paragraph">Before we look at the breakdown of period and cohort effects, here are the results from a model that estimates latent opposition to each proposition as a smooth function over time.</p>
<figure class="wp-block-image" id="letdie-single-time"><img loading="lazy" decoding="async" width="1108" height="704" src="https://www.allendowney.com/blog/wp-content/uploads/2026/04/letdie_compare_time_-340f828df36b2086971ded6f63293cf6.png" alt="Time-only trends." class="wp-image-1784" srcset="https://www.allendowney.com/blog/wp-content/uploads/2026/04/letdie_compare_time_-340f828df36b2086971ded6f63293cf6.png 1108w, https://www.allendowney.com/blog/wp-content/uploads/2026/04/letdie_compare_time_-340f828df36b2086971ded6f63293cf6-300x191.png 300w, https://www.allendowney.com/blog/wp-content/uploads/2026/04/letdie_compare_time_-340f828df36b2086971ded6f63293cf6-1024x651.png 1024w, https://www.allendowney.com/blog/wp-content/uploads/2026/04/letdie_compare_time_-340f828df36b2086971ded6f63293cf6-768x488.png 768w, https://www.allendowney.com/blog/wp-content/uploads/2026/04/letdie_compare_time_-340f828df36b2086971ded6f63293cf6-425x270.png 425w" sizes="auto, (max-width: 1108px) 100vw, 1108px" /></figure>
<p class="wp-block-paragraph">Opposition to suicide is high in three of the scenarios — bankrupt, dishonored family, and tired of living — and lower in the incurable disease scenarios.</p>
<p class="wp-block-paragraph">In all five questions, opposition has declined over time, although for the incurable disease scenarios, it might have leveled off after 1990.</p>
<h2 class="wp-block-heading" id="doctor-assisted-death">Doctor-assisted death</h2>
<p class="wp-block-paragraph">Now let’s see if we can decompose these changes into period and cohort effects. We’ll start with the question about doctor-assisted death when the patient has an incurable disease.</p>
<p class="wp-block-paragraph">As in the previous posts, I used a Bayesian model to estimate a trajectory over time for each birth cohort, shown in the following figure.</p>
<figure class="wp-block-image" id="letdie1-cohort-trajectories"><img loading="lazy" decoding="async" width="1330" height="778" src="https://www.allendowney.com/blog/wp-content/uploads/2026/04/cohort_trajectory_le-28df4a8cc3e21cad9b463f53ddf9a3ef.png" alt="Cohort trajectories: letdie1." class="wp-image-1785" srcset="https://www.allendowney.com/blog/wp-content/uploads/2026/04/cohort_trajectory_le-28df4a8cc3e21cad9b463f53ddf9a3ef.png 1330w, https://www.allendowney.com/blog/wp-content/uploads/2026/04/cohort_trajectory_le-28df4a8cc3e21cad9b463f53ddf9a3ef-300x175.png 300w, https://www.allendowney.com/blog/wp-content/uploads/2026/04/cohort_trajectory_le-28df4a8cc3e21cad9b463f53ddf9a3ef-1024x599.png 1024w, https://www.allendowney.com/blog/wp-content/uploads/2026/04/cohort_trajectory_le-28df4a8cc3e21cad9b463f53ddf9a3ef-768x449.png 768w, https://www.allendowney.com/blog/wp-content/uploads/2026/04/cohort_trajectory_le-28df4a8cc3e21cad9b463f53ddf9a3ef-462x270.png 462w" sizes="auto, (max-width: 1330px) 100vw, 1330px" /></figure>
<p class="wp-block-paragraph">Reading from top to bottom, we can see that opposition has declined from one cohort to the next, and reading from left to right, we can see that opposition has varied over time within each cohort.</p>
<p class="wp-block-paragraph">The following figure shows the cohort component alone, standardized to factor out the period effect.</p>
<figure class="wp-block-image" id="letdie1-cohort-component"><img loading="lazy" decoding="async" width="1166" height="790" src="https://www.allendowney.com/blog/wp-content/uploads/2026/04/cohort_standardized_-d780162e3521c3e8c568d864d1d04042.png" alt="Cohort component (uniform years): letdie1." class="wp-image-1786" srcset="https://www.allendowney.com/blog/wp-content/uploads/2026/04/cohort_standardized_-d780162e3521c3e8c568d864d1d04042.png 1166w, https://www.allendowney.com/blog/wp-content/uploads/2026/04/cohort_standardized_-d780162e3521c3e8c568d864d1d04042-300x203.png 300w, https://www.allendowney.com/blog/wp-content/uploads/2026/04/cohort_standardized_-d780162e3521c3e8c568d864d1d04042-1024x694.png 1024w, https://www.allendowney.com/blog/wp-content/uploads/2026/04/cohort_standardized_-d780162e3521c3e8c568d864d1d04042-768x520.png 768w, https://www.allendowney.com/blog/wp-content/uploads/2026/04/cohort_standardized_-d780162e3521c3e8c568d864d1d04042-399x270.png 399w" sizes="auto, (max-width: 1166px) 100vw, 1166px" /></figure>
<p class="wp-block-paragraph">Opposition to doctor-assisted suicide has declined from more than 40% in the earliest cohorts to 20% among people born in 2006.</p>
<p class="wp-block-paragraph">A possible explanation for the cohort pattern is that people anchor their moral judgments to the legal environment they encounter when they are young. During the “impressionable years” of late adolescence and early adulthood, existing laws can establish a moral baseline, so that what is illegal is inferred to be wrong, and therefore should remain illegal. As a result, gradual legalization can generate long-run attitudinal change through cohort replacement: people who grow up after a practice becomes legal are less likely to see it as morally problematic.</p>
<p class="wp-block-paragraph">The following figure shows the period effect alone, along with the results from the time model (which includes both period and cohort effects).</p>
<figure class="wp-block-image" id="letdie1-period-time"><img loading="lazy" decoding="async" width="1166" height="790" src="https://www.allendowney.com/blog/wp-content/uploads/2026/04/time_standardized_le-c7580a12cc292dbce6e525849d0e6220.png" alt="Standardized period component with time model: letdie1." class="wp-image-1788" srcset="https://www.allendowney.com/blog/wp-content/uploads/2026/04/time_standardized_le-c7580a12cc292dbce6e525849d0e6220.png 1166w, https://www.allendowney.com/blog/wp-content/uploads/2026/04/time_standardized_le-c7580a12cc292dbce6e525849d0e6220-300x203.png 300w, https://www.allendowney.com/blog/wp-content/uploads/2026/04/time_standardized_le-c7580a12cc292dbce6e525849d0e6220-1024x694.png 1024w, https://www.allendowney.com/blog/wp-content/uploads/2026/04/time_standardized_le-c7580a12cc292dbce6e525849d0e6220-768x520.png 768w, https://www.allendowney.com/blog/wp-content/uploads/2026/04/time_standardized_le-c7580a12cc292dbce6e525849d0e6220-399x270.png 399w" sizes="auto, (max-width: 1166px) 100vw, 1166px" /></figure>
<p class="wp-block-paragraph">Comparing the two lines, we can conclude that the decline we see over time is entirely due to the cohort effect — when we control for generational replacement, the estimated period effect has generally <em>increased</em> since 1990.</p>
<p class="wp-block-paragraph">The increase between 1990 and 2005 might reflect increasing moral concern due to advances in life-sustaining medical technology, high-profile legal disputes like the <a href="https://en.wikipedia.org/wiki/Terri_Schiavo_case" target="_blank" rel="noreferrer noopener">Terri Schiavo case</a>, and broader discussions of the sanctity of life.</p>
<p class="wp-block-paragraph">The decline between 2005 to 2015 might reflect normalization of assisted dying following legalization in several states (Oregon in 1997, Washington in 2008, and Montana in 2009, Vermont in 2013), along with a shift in public discourse toward autonomy, dignity, and patient choice, reinforced by high-profile cases like <a href="https://en.wikipedia.org/wiki/Brittany_Maynard" target="_blank" rel="noreferrer noopener">Brittany Maynard</a>.</p>
<h2 class="wp-block-heading" id="other-scenarios">Other Scenarios</h2>
<p class="wp-block-paragraph">The following figure shows the estimated cohort effects for all five questions.</p>
<figure class="wp-block-image" id="letdie-single-cohort"><img loading="lazy" decoding="async" width="1108" height="704" src="https://www.allendowney.com/blog/wp-content/uploads/2026/04/letdie_compare_cohor-ca0769cc27ba5266de2e551bbf9f7ec3.png" alt="Cohort margins, single panel." class="wp-image-1789" srcset="https://www.allendowney.com/blog/wp-content/uploads/2026/04/letdie_compare_cohor-ca0769cc27ba5266de2e551bbf9f7ec3.png 1108w, https://www.allendowney.com/blog/wp-content/uploads/2026/04/letdie_compare_cohor-ca0769cc27ba5266de2e551bbf9f7ec3-300x191.png 300w, https://www.allendowney.com/blog/wp-content/uploads/2026/04/letdie_compare_cohor-ca0769cc27ba5266de2e551bbf9f7ec3-1024x651.png 1024w, https://www.allendowney.com/blog/wp-content/uploads/2026/04/letdie_compare_cohor-ca0769cc27ba5266de2e551bbf9f7ec3-768x488.png 768w, https://www.allendowney.com/blog/wp-content/uploads/2026/04/letdie_compare_cohor-ca0769cc27ba5266de2e551bbf9f7ec3-425x270.png 425w" sizes="auto, (max-width: 1108px) 100vw, 1108px" /></figure>
<p class="wp-block-paragraph">For the incurable disease scenario, opposition has declined from more than 60% in the earliest cohorts to less than 40% among cohorts born after 1950 — although it might have leveled off since then.</p>
<p class="wp-block-paragraph">In the other scenarios, opposition has also declined from one cohort to the next, but the size of the effect is smaller.</p>
<p class="wp-block-paragraph">The following figure shows the estimated period effects, controlling for generational replacement.</p>
<figure class="wp-block-image" id="letdie-single-period"><img loading="lazy" decoding="async" width="1108" height="704" src="https://www.allendowney.com/blog/wp-content/uploads/2026/04/letdie_compare_perio-76fe4f16ad277fcdde3a47797ddbb13e.png" alt="Period margins, single panel." class="wp-image-1787" srcset="https://www.allendowney.com/blog/wp-content/uploads/2026/04/letdie_compare_perio-76fe4f16ad277fcdde3a47797ddbb13e.png 1108w, https://www.allendowney.com/blog/wp-content/uploads/2026/04/letdie_compare_perio-76fe4f16ad277fcdde3a47797ddbb13e-300x191.png 300w, https://www.allendowney.com/blog/wp-content/uploads/2026/04/letdie_compare_perio-76fe4f16ad277fcdde3a47797ddbb13e-1024x651.png 1024w, https://www.allendowney.com/blog/wp-content/uploads/2026/04/letdie_compare_perio-76fe4f16ad277fcdde3a47797ddbb13e-768x488.png 768w, https://www.allendowney.com/blog/wp-content/uploads/2026/04/letdie_compare_perio-76fe4f16ad277fcdde3a47797ddbb13e-425x270.png 425w" sizes="auto, (max-width: 1108px) 100vw, 1108px" /></figure>
<p class="wp-block-paragraph">Since 1990, most of the period effects are small. The only exception is the “tired of living” scenario, where there is some decline over time, independent of generational replacement.</p>
<p class="wp-block-paragraph">In the next post, we’ll do the same analysis with questions about abortion and the situations where it should be legal or not.</p>
<p class="wp-block-paragraph"></p>
<p>The post <a href="https://www.allendowney.com/blog/2026/04/16/changing-opinions-on-assisted-suicide/">Changing Opinions on Assisted Suicide</a> appeared first on <a href="https://www.allendowney.com/blog">Probably Overthinking It</a>.</p>
]]></content:encoded>
<post-id xmlns="com-wordpress:feed-additions:1">1782</post-id>
</item>
<item>
<title>Trust and Well-Being</title>
<link>https://www.allendowney.com/blog/2026/04/03/trust-and-well-being/</link>
<dc:creator><![CDATA[AllenDowney]]></dc:creator>
<pubDate>Fri, 03 Apr 2026 14:48:45 +0000</pubDate>
<category><![CDATA[Uncategorized]]></category>
<category><![CDATA[age period cohort analysis]]></category>
<category><![CDATA[general social survey]]></category>
<category><![CDATA[happiness]]></category>
<category><![CDATA[logistic regression]]></category>
<guid isPermaLink="false">https://www.allendowney.com/blog/?p=1766</guid>
<description><![CDATA[<p>In a previous article, I claimed that Young adults are not very happy. Now the World Happiness Report 2026 has confirmed that young people in North America and Western Europe are less happy than they were fifteen years ago, and less happy than previous generations. In this article, we’ll look at results from three related questions in the General Social Survey (GSS): As we’ll see, young adults in the United States have a more negative outlook than previous generations: they...</p>
<p class="read-more"><a class="btn btn-default" href="https://www.allendowney.com/blog/2026/04/03/trust-and-well-being/"> Read More<span class="screen-reader-text"> Read More</span></a></p>
<p>The post <a href="https://www.allendowney.com/blog/2026/04/03/trust-and-well-being/">Trust and Well-Being</a> appeared first on <a href="https://www.allendowney.com/blog">Probably Overthinking It</a>.</p>
]]></description>
<content:encoded><![CDATA[
<p class="wp-block-paragraph">In a previous article, I claimed that <a href="https://www.allendowney.com/blog/2026/03/19/young-adults-are-not-very-happy/" target="_blank" rel="noreferrer noopener">Young adults are not very happy</a>. Now the <a href="https://worldhappiness.report/ed/2026/" target="_blank" rel="noreferrer noopener">World Happiness Report 2026</a> has confirmed that young people in North America and Western Europe are less happy than they were fifteen years ago, and less happy than previous generations.</p>
<p class="wp-block-paragraph">In this article, we’ll look at results from three related questions in the General Social Survey (GSS):</p>
<ul class="wp-block-list">
<li><strong>Trust:</strong> “Generally speaking, would you say that most people can be trusted or that you can’t be too careful in dealing with people?”</li>
<li><strong>Fair:</strong> “Do you think most people would try to take advantage of you if they got a chance, or would they try to be fair?”</li>
<li><strong>Helpful:</strong> “Would you say that most of the time people try to be helpful, or that they are mostly just looking out for themselves?”</li>
</ul>
<p class="wp-block-paragraph">As we’ll see, young adults in the United States have a more negative outlook than previous generations: they are less likely to say that people can be trusted, that they are fair, or that they are helpful. And we’ll consider connections between this bleak outlook and unhappiness.</p>
<h2 class="wp-block-heading" id="trust">Trust</h2>
<p class="wp-block-paragraph">Using the same model from the previous articles, I estimated the percentage who say people can be trusted, following each birth year over time.</p>
<figure class="wp-block-image" id="cohort-trajectories-trust"><img loading="lazy" decoding="async" width="1330" height="778" src="https://www.allendowney.com/blog/wp-content/uploads/2026/04/cohort_trajectory_tr-5809c4884f70b4b9b75cfe97047f2fe8.png" alt="Cohort trajectories, percent saying most people can be trusted" class="wp-image-1769" srcset="https://www.allendowney.com/blog/wp-content/uploads/2026/04/cohort_trajectory_tr-5809c4884f70b4b9b75cfe97047f2fe8.png 1330w, https://www.allendowney.com/blog/wp-content/uploads/2026/04/cohort_trajectory_tr-5809c4884f70b4b9b75cfe97047f2fe8-300x175.png 300w, https://www.allendowney.com/blog/wp-content/uploads/2026/04/cohort_trajectory_tr-5809c4884f70b4b9b75cfe97047f2fe8-1024x599.png 1024w, https://www.allendowney.com/blog/wp-content/uploads/2026/04/cohort_trajectory_tr-5809c4884f70b4b9b75cfe97047f2fe8-768x449.png 768w, https://www.allendowney.com/blog/wp-content/uploads/2026/04/cohort_trajectory_tr-5809c4884f70b4b9b75cfe97047f2fe8-462x270.png 462w" sizes="auto, (max-width: 1330px) 100vw, 1330px" /></figure>
<p class="wp-block-paragraph"><em>Cohort trajectories, percent saying most people can be trusted</em></p>
<p class="wp-block-paragraph">With these trajectories, we can decompose the cohort and period effects. The following figure shows the cohort effect, standardized by holding the period effect constant.</p>
<figure class="wp-block-image" id="cohort-profile-trust"><img loading="lazy" decoding="async" width="1133" height="790" src="https://www.allendowney.com/blog/wp-content/uploads/2026/04/cohort_standardized_-83920254db4863278c92f3cee792510c.png" alt="Standardized cohort effect with fixed time mix, percent saying most people can be trusted" class="wp-image-1772" srcset="https://www.allendowney.com/blog/wp-content/uploads/2026/04/cohort_standardized_-83920254db4863278c92f3cee792510c.png 1133w, https://www.allendowney.com/blog/wp-content/uploads/2026/04/cohort_standardized_-83920254db4863278c92f3cee792510c-300x209.png 300w, https://www.allendowney.com/blog/wp-content/uploads/2026/04/cohort_standardized_-83920254db4863278c92f3cee792510c-1024x714.png 1024w, https://www.allendowney.com/blog/wp-content/uploads/2026/04/cohort_standardized_-83920254db4863278c92f3cee792510c-768x535.png 768w, https://www.allendowney.com/blog/wp-content/uploads/2026/04/cohort_standardized_-83920254db4863278c92f3cee792510c-387x270.png 387w" sizes="auto, (max-width: 1133px) 100vw, 1133px" /></figure>
<p class="wp-block-paragraph">Standardized cohort effect with fixed time mix, percent saying most people can be trusted</p>
<p class="wp-block-paragraph">The level of trust increased between the cohorts born in the 1900s through the 1940s, and then started a steep decline. This is a large cohort effect, dropping about 30 percentage points over 60 years.</p>
<p class="wp-block-paragraph">The following figure shows the period effect, standardized by holding the cohort mix constant.</p>
<figure class="wp-block-image" id="time-trend-trust"><img loading="lazy" decoding="async" width="1133" height="790" src="https://www.allendowney.com/blog/wp-content/uploads/2026/04/time_standardized_tr-2f029b683d9ad86a39a536e4f95c8c0f.png" alt="Standardized time trend with fixed cohort mix, percent saying most people can be trusted" class="wp-image-1773" srcset="https://www.allendowney.com/blog/wp-content/uploads/2026/04/time_standardized_tr-2f029b683d9ad86a39a536e4f95c8c0f.png 1133w, https://www.allendowney.com/blog/wp-content/uploads/2026/04/time_standardized_tr-2f029b683d9ad86a39a536e4f95c8c0f-300x209.png 300w, https://www.allendowney.com/blog/wp-content/uploads/2026/04/time_standardized_tr-2f029b683d9ad86a39a536e4f95c8c0f-1024x714.png 1024w, https://www.allendowney.com/blog/wp-content/uploads/2026/04/time_standardized_tr-2f029b683d9ad86a39a536e4f95c8c0f-768x535.png 768w, https://www.allendowney.com/blog/wp-content/uploads/2026/04/time_standardized_tr-2f029b683d9ad86a39a536e4f95c8c0f-387x270.png 387w" sizes="auto, (max-width: 1133px) 100vw, 1133px" /></figure>
<p class="wp-block-paragraph"><em>Standardized time trend with fixed cohort mix, percent saying most people can be trusted</em></p>
<p class="wp-block-paragraph">In contrast, there is almost no period effect.</p>
<h2 class="wp-block-heading" id="the-conjecture-part">The conjecture part</h2>
<p class="wp-block-paragraph">About my previous article, one of my former colleagues said he appreciated my attempt to offer explanations, but reminded me that with this kind of data alone, it is hard to say what causes what with any confidence. That’s true, and it’s a good reminder — but we can get some clues:</p>
<ul class="wp-block-list">
<li>When we see a strong cohort effect and almost no period effect, that’s evidence that we’re seeing patterns set in childhood.</li>
<li>When we see period effects, we should look for events that affected all cohorts at the same time.</li>
</ul>
<p class="wp-block-paragraph">So let’s think about what was happening in the formative years of these cohorts, starting with the 1940 cohort, which was the high point in trust, before the decline:</p>
<ul class="wp-block-list">
<li>Cohort 1940 (childhood: 1940–1960): dense local communities, strong civic and religious institutions, frequent face-to-face interaction, and shared media environment.</li>
<li>Cohort 1950 (1950–1970): suburbanization expands, some weakening of community density, television becomes widespread but still shared.</li>
<li>Cohort 1960 (1960–1980): civil rights conflict, Vietnam War, Watergate scandal, rising crime.</li>
<li>Cohort 1970 (1970–1990): reduced civic participation, rising inequality, more cautious parenting, less unstructured social interaction.</li>
<li>Cohort 1980 (1980–2000): increasing inequality, more segregation by class and education, early internet exposure, continued decline in shared institutions.</li>
</ul>
<p class="wp-block-paragraph">At this point a multi-generational effect comes into play — the parents of Cohort 1980, born in the 1950s and 1960s, were less trusting than previous generations of parents.</p>
<ul class="wp-block-list">
<li>Cohort 1990 (1990–2010): widespread internet use, early social media, more structured childhood, increasing awareness of global risks.</li>
<li>Cohort 2000 (2000–2020): smartphones and social media throughout formative years, algorithmic content, reduced in-person interaction.</li>
</ul>
<p class="wp-block-paragraph">If trust is largely set early in life, then differences between cohorts reflect the environments they experienced during their first two decades.</p>
<p class="wp-block-paragraph">In addition to this question about trust, the GSS includes related questions about fairness and mutual assistance.</p>
<h2 class="wp-block-heading" id="fair">Fair</h2>
<p class="wp-block-paragraph">Do you think most people would try to take advantage of you if they got a chance, or would they try to be fair? The following figure shows the percentage who thought people would be fair.</p>
<figure class="wp-block-image" id="cohort-trajectories-fair"><img loading="lazy" decoding="async" width="1330" height="783" src="https://www.allendowney.com/blog/wp-content/uploads/2026/04/cohort_trajectory_fa-941da70cb9e1fdb60ecd622a8e79f682.png" alt="Cohort trajectories, percent saying people would try to be fair" class="wp-image-1771" srcset="https://www.allendowney.com/blog/wp-content/uploads/2026/04/cohort_trajectory_fa-941da70cb9e1fdb60ecd622a8e79f682.png 1330w, https://www.allendowney.com/blog/wp-content/uploads/2026/04/cohort_trajectory_fa-941da70cb9e1fdb60ecd622a8e79f682-300x177.png 300w, https://www.allendowney.com/blog/wp-content/uploads/2026/04/cohort_trajectory_fa-941da70cb9e1fdb60ecd622a8e79f682-1024x603.png 1024w, https://www.allendowney.com/blog/wp-content/uploads/2026/04/cohort_trajectory_fa-941da70cb9e1fdb60ecd622a8e79f682-768x452.png 768w, https://www.allendowney.com/blog/wp-content/uploads/2026/04/cohort_trajectory_fa-941da70cb9e1fdb60ecd622a8e79f682-459x270.png 459w" sizes="auto, (max-width: 1330px) 100vw, 1330px" /></figure>
<p class="wp-block-paragraph"><em>Cohort trajectories, percent saying people would try to be fair</em></p>
<p class="wp-block-paragraph">And here’s the cohort effect.</p>
<figure class="wp-block-image" id="cohort-profile-fair"><img loading="lazy" decoding="async" width="1266" height="764" src="https://www.allendowney.com/blog/wp-content/uploads/2026/04/cohort_standardized_-e471d5b01144d15bbf17ba11755d7731.png" alt="Standardized cohort effect with fixed time mix, percent saying people would try to be fair" class="wp-image-1774" srcset="https://www.allendowney.com/blog/wp-content/uploads/2026/04/cohort_standardized_-e471d5b01144d15bbf17ba11755d7731.png 1266w, https://www.allendowney.com/blog/wp-content/uploads/2026/04/cohort_standardized_-e471d5b01144d15bbf17ba11755d7731-300x181.png 300w, https://www.allendowney.com/blog/wp-content/uploads/2026/04/cohort_standardized_-e471d5b01144d15bbf17ba11755d7731-1024x618.png 1024w, https://www.allendowney.com/blog/wp-content/uploads/2026/04/cohort_standardized_-e471d5b01144d15bbf17ba11755d7731-768x463.png 768w, https://www.allendowney.com/blog/wp-content/uploads/2026/04/cohort_standardized_-e471d5b01144d15bbf17ba11755d7731-447x270.png 447w" sizes="auto, (max-width: 1266px) 100vw, 1266px" /></figure>
<p class="wp-block-paragraph"><em>Standardized cohort effect with fixed time mix, percent saying people would try to be fair</em></p>
<p class="wp-block-paragraph">And the period effect.</p>
<figure class="wp-block-image" id="time-trend-fair"><img loading="lazy" decoding="async" width="1266" height="764" src="https://www.allendowney.com/blog/wp-content/uploads/2026/04/time_standardized_fa-c4e6dd0e53f81bd5148e3461a47a3664.png" alt="Standardized time trend with fixed cohort mix, percent saying people would try to be fair" class="wp-image-1775" srcset="https://www.allendowney.com/blog/wp-content/uploads/2026/04/time_standardized_fa-c4e6dd0e53f81bd5148e3461a47a3664.png 1266w, https://www.allendowney.com/blog/wp-content/uploads/2026/04/time_standardized_fa-c4e6dd0e53f81bd5148e3461a47a3664-300x181.png 300w, https://www.allendowney.com/blog/wp-content/uploads/2026/04/time_standardized_fa-c4e6dd0e53f81bd5148e3461a47a3664-1024x618.png 1024w, https://www.allendowney.com/blog/wp-content/uploads/2026/04/time_standardized_fa-c4e6dd0e53f81bd5148e3461a47a3664-768x463.png 768w, https://www.allendowney.com/blog/wp-content/uploads/2026/04/time_standardized_fa-c4e6dd0e53f81bd5148e3461a47a3664-447x270.png 447w" sizes="auto, (max-width: 1266px) 100vw, 1266px" /></figure>
<p class="wp-block-paragraph"><em>Standardized time trend with fixed cohort mix, percent saying people would try to be fair</em></p>
<p class="wp-block-paragraph">The cohort pattern is similar to what we saw in trust: small changes between the 1900s and 1940s cohorts, and then a steep decline — almost 40 percentage points over 60 years.</p>
<p class="wp-block-paragraph">The period effect is relatively small, varying by only 10 percentage points from lowest to highest point, but it was generally positive until about 2015 (the onset of the Trump Era?).</p>
<h2 class="wp-block-heading" id="helpful">Helpful</h2>
<p class="wp-block-paragraph">Would you say that most of the time people try to be helpful, or that they are mostly just looking out for themselves?</p>
<p class="wp-block-paragraph">Here is a period–cohort fingerprint of the responses, showing the percentage who thought people try to be helpful.</p>
<figure class="wp-block-image" id="cohort-trajectories-helpful"><img loading="lazy" decoding="async" width="1330" height="783" src="https://www.allendowney.com/blog/wp-content/uploads/2026/04/cohort_trajectory_he-73b3c2f2b5af024ffd374acb439b3ec8.png" alt="Cohort trajectories, percent saying people try to be helpful" class="wp-image-1770" srcset="https://www.allendowney.com/blog/wp-content/uploads/2026/04/cohort_trajectory_he-73b3c2f2b5af024ffd374acb439b3ec8.png 1330w, https://www.allendowney.com/blog/wp-content/uploads/2026/04/cohort_trajectory_he-73b3c2f2b5af024ffd374acb439b3ec8-300x177.png 300w, https://www.allendowney.com/blog/wp-content/uploads/2026/04/cohort_trajectory_he-73b3c2f2b5af024ffd374acb439b3ec8-1024x603.png 1024w, https://www.allendowney.com/blog/wp-content/uploads/2026/04/cohort_trajectory_he-73b3c2f2b5af024ffd374acb439b3ec8-768x452.png 768w, https://www.allendowney.com/blog/wp-content/uploads/2026/04/cohort_trajectory_he-73b3c2f2b5af024ffd374acb439b3ec8-459x270.png 459w" sizes="auto, (max-width: 1330px) 100vw, 1330px" /></figure>
<p class="wp-block-paragraph"><em>Cohort trajectories, percent saying people try to be helpful</em></p>
<p class="wp-block-paragraph">Here’s the cohort effect:</p>
<figure class="wp-block-image" id="cohort-profile-helpful"><img loading="lazy" decoding="async" width="1337" height="764" src="https://www.allendowney.com/blog/wp-content/uploads/2026/04/cohort_standardized_-24a4cd718ef72385d57fbc3eb0dbc47d.png" alt="Standardized cohort effect with fixed time mix, percent saying people try to be helpful" class="wp-image-1777" srcset="https://www.allendowney.com/blog/wp-content/uploads/2026/04/cohort_standardized_-24a4cd718ef72385d57fbc3eb0dbc47d.png 1337w, https://www.allendowney.com/blog/wp-content/uploads/2026/04/cohort_standardized_-24a4cd718ef72385d57fbc3eb0dbc47d-300x171.png 300w, https://www.allendowney.com/blog/wp-content/uploads/2026/04/cohort_standardized_-24a4cd718ef72385d57fbc3eb0dbc47d-1024x585.png 1024w, https://www.allendowney.com/blog/wp-content/uploads/2026/04/cohort_standardized_-24a4cd718ef72385d57fbc3eb0dbc47d-768x439.png 768w, https://www.allendowney.com/blog/wp-content/uploads/2026/04/cohort_standardized_-24a4cd718ef72385d57fbc3eb0dbc47d-473x270.png 473w" sizes="auto, (max-width: 1337px) 100vw, 1337px" /></figure>
<p class="wp-block-paragraph"><em>Standardized cohort effect with fixed time mix, percent saying people try to be helpful</em></p>
<p class="wp-block-paragraph">And the period effect.</p>
<figure class="wp-block-image" id="time-trend-helpful"><img loading="lazy" decoding="async" width="1337" height="764" src="https://www.allendowney.com/blog/wp-content/uploads/2026/04/time_standardized_he-28e70c9d0a1b012cf525b854897416f2.png" alt="Standardized time trend with fixed cohort mix, percent saying people try to be helpful" class="wp-image-1776" srcset="https://www.allendowney.com/blog/wp-content/uploads/2026/04/time_standardized_he-28e70c9d0a1b012cf525b854897416f2.png 1337w, https://www.allendowney.com/blog/wp-content/uploads/2026/04/time_standardized_he-28e70c9d0a1b012cf525b854897416f2-300x171.png 300w, https://www.allendowney.com/blog/wp-content/uploads/2026/04/time_standardized_he-28e70c9d0a1b012cf525b854897416f2-1024x585.png 1024w, https://www.allendowney.com/blog/wp-content/uploads/2026/04/time_standardized_he-28e70c9d0a1b012cf525b854897416f2-768x439.png 768w, https://www.allendowney.com/blog/wp-content/uploads/2026/04/time_standardized_he-28e70c9d0a1b012cf525b854897416f2-473x270.png 473w" sizes="auto, (max-width: 1337px) 100vw, 1337px" /></figure>
<p class="wp-block-paragraph"><em>Standardized time trend with fixed cohort mix, percent saying people try to be helpful</em></p>
<p class="wp-block-paragraph">Again we see the same pattern: little change between the cohorts born between 1900 and 1940, and then a decline of more than 30 percentage points over 60 years.</p>
<p class="wp-block-paragraph">And again, the period effect is comparatively small and generally increasing — but possibly declining in the most recent cycles of the survey.</p>
<h2 class="wp-block-heading" id="cause-and-effect">Cause and Effect?</h2>
<p class="wp-block-paragraph">It is plausible that the decline in trust is a contributing factor to the decline in happiness. If you believe that people are out to get you, and 80% of your friends agree, that’s not a worldview conducive to a sense of well-being. And generational decline in trust precedes the decline in happiness, so it is at least a potential cause.</p>
<p class="wp-block-paragraph">The decline in trust-related beliefs also supports the interpretation that recent cohorts are <em>actually</em> unhappy, rather than interpreting the question differently, or being more willing than previous generations to say they are unhappy.</p>
<p class="wp-block-paragraph">I haven’t done full-on causal modeling to quantify these relationships, but I ran a few regression models to explore. To reduce the number of researcher degrees of freedom, I asked ChatGPT to interpret the results:</p>
<blockquote class="wp-block-quote is-layout-flow wp-block-quote-is-layout-flow">
<p class="wp-block-paragraph">Differences in happiness across cohorts appear to be partly explained by differences in social outlook (trust, fairness, helpfulness), and these outlook variables behave like stable, cohort-structured traits rather than period-driven fluctuations.</p>
</blockquote>
<p class="wp-block-paragraph">The AI-generated summary of the experiments follows.</p>
<h3 class="wp-block-heading" id="model-1-cross-sectional-association-complete-cases">Model 1: Cross-sectional association (complete cases)</h3>
<p class="wp-block-paragraph"><strong>Specification:</strong></p>
<ul class="wp-block-list">
<li>Outcome: <code>very_happy</code> (binary)</li>
<li>Predictors: <code>trust</code>, <code>fair</code>, <code>helpful</code> (all binary)</li>
<li>Sample: complete cases with all variables observed</li>
</ul>
<p class="wp-block-paragraph"><strong>Purpose:</strong></p>
<ul class="wp-block-list">
<li>Estimate the <strong>cross-sectional relationship</strong> between social outlook and happiness.</li>
<li>Provides baseline associations without accounting for cohort or period effects.</li>
</ul>
<p class="wp-block-paragraph"><strong>Interpretation:</strong></p>
<ul class="wp-block-list">
<li>Coefficients represent <strong>conditional associations</strong> among individuals at a point in time.</li>
<li>Answers: <em>Are people with a more positive outlook more likely to be very happy?</em></li>
</ul>
<hr class="wp-block-separator has-alpha-channel-opacity"/>
<h3 class="wp-block-heading" id="model-2-outlook-cohort-period-restricted-sample">Model 2: Outlook + cohort + period (restricted sample)</h3>
<p class="wp-block-paragraph"><strong>Specification:</strong></p>
<ul class="wp-block-list">
<li>Outcome: <code>very_happy</code></li>
<li>Predictors:
<ul class="wp-block-list">
<li><code>trust</code>, <code>fair</code>, <code>helpful</code></li>
<li><code>cohort_c</code> (mean-centered birth year)</li>
<li><code>year_c</code> (mean-centered survey year)</li>
</ul>
</li>
<li>Sample: respondents born ≥ 1940 with complete data</li>
</ul>
<p class="wp-block-paragraph"><strong>Purpose:</strong></p>
<ul class="wp-block-list">
<li>Assess whether the outlook–happiness relationship persists after accounting for:
<ul class="wp-block-list">
<li><strong>Cohort effects</strong> (differences across birth cohorts)</li>
<li><strong>Period effects</strong> (changes over survey years)</li>
</ul>
</li>
</ul>
<p class="wp-block-paragraph"><strong>Interpretation:</strong></p>
<ul class="wp-block-list">
<li>Coefficients for outlook variables reflect <strong>within-cohort, within-period associations</strong>.</li>
<li>Cohort and year coefficients capture <strong>linear trends</strong> in happiness after controlling for outlook.</li>
<li>Answers:
<ul class="wp-block-list">
<li><em>Are outlook variables still associated with happiness after adjusting for historical context?</em></li>
<li><em>Is there an independent cohort or period trend?</em></li>
</ul>
</li>
</ul>
<hr class="wp-block-separator has-alpha-channel-opacity"/>
<h3 class="wp-block-heading" id="model-3-cohort-period-only-no-outlook-variables">Model 3: Cohort + period only (no outlook variables)</h3>
<p class="wp-block-paragraph"><strong>Specification:</strong></p>
<ul class="wp-block-list">
<li>Outcome: <code>very_happy</code></li>
<li>Predictors:
<ul class="wp-block-list">
<li><code>cohort_c</code></li>
<li><code>year_c</code></li>
</ul>
</li>
<li>Sample: respondents born > 1940 (larger sample since outlook variables not required)</li>
</ul>
<p class="wp-block-paragraph"><strong>Purpose:</strong></p>
<ul class="wp-block-list">
<li>Estimate <strong>total cohort and period effects</strong> on happiness without controlling for outlook.</li>
<li>Provides a baseline for comparison with Model 2.</li>
</ul>
<p class="wp-block-paragraph"><strong>Interpretation:</strong></p>
<ul class="wp-block-list">
<li>Cohort and year coefficients reflect <strong>combined (direct + indirect) effects</strong>.</li>
<li>Comparing to Model 2 shows how much of these effects are <strong>accounted for by outlook variables</strong>.</li>
<li>Answers:
<ul class="wp-block-list">
<li><em>How does happiness vary across cohorts and over time in aggregate?</em></li>
<li><em>How much do these patterns change when outlook is included?</em></li>
</ul>
</li>
</ul>
<h3 class="wp-block-heading" id="key-findings">Key Findings</h3>
<ul class="wp-block-list">
<li><strong>Positive social outlook is associated with higher happiness.</strong>
<ul class="wp-block-list">
<li>Trust, fairness, and helpfulness all have positive and statistically significant associations with being “very happy.”</li>
<li>Estimated odds ratios:
<ul class="wp-block-list">
<li>Trust: ~1.25</li>
<li>Fairness: ~1.36 (strongest)</li>
<li>Helpfulness: ~1.29</li>
</ul>
</li>
<li>These effects are modest in size and explain a small fraction of overall variation (Pseudo R² ≈ 0.016).</li>
</ul>
</li>
<li><strong>These relationships are stable across cohorts and time.</strong>
<ul class="wp-block-list">
<li>Adding cohort and survey year controls has little effect on the coefficients.</li>
<li>This suggests the outlook–happiness relationship is primarily cross-sectional, not driven by historical shifts.</li>
</ul>
</li>
</ul>
<hr class="wp-block-separator has-alpha-channel-opacity"/>
<h3 class="wp-block-heading" id="cohort-and-period-effects">Cohort and Period Effects</h3>
<ul class="wp-block-list">
<li><strong>Without controlling for outlook:</strong>
<ul class="wp-block-list">
<li>Later cohorts are less likely to report being very happy.</li>
<li>There is also a negative period trend (declining happiness over time).</li>
</ul>
</li>
<li><strong>With outlook variables included:</strong>
<ul class="wp-block-list">
<li>The cohort effect becomes small and statistically insignificant.</li>
<li>The period effect remains negative and significant.</li>
</ul>
</li>
</ul>
<hr class="wp-block-separator has-alpha-channel-opacity"/>
<h3 class="wp-block-heading" id="interpretation">Interpretation</h3>
<ul class="wp-block-list">
<li><strong>Outlook variables appear to mediate cohort differences in happiness.</strong>
<ul class="wp-block-list">
<li>Later cohorts tend to report lower trust, fairness, and helpfulness.</li>
<li>These differences account for much of the observed cohort decline in happiness.</li>
</ul>
</li>
<li><strong>Period effects persist independently.</strong>
<ul class="wp-block-list">
<li>There is a modest downward trend in happiness over time that is not explained by outlook variables.</li>
</ul>
</li>
</ul>
<hr class="wp-block-separator has-alpha-channel-opacity"/>
<h3 class="wp-block-heading" id="data-considerations">Data Considerations</h3>
<ul class="wp-block-list">
<li>Approximately <strong>40% of observations are missing at least one outlook variable</strong>, reducing the complete-case sample.</li>
<li>This raises the possibility of <strong>selection bias</strong> in the estimates.</li>
</ul>
<hr class="wp-block-separator has-alpha-channel-opacity"/>
<h3 class="wp-block-heading" id="bottom-line">Bottom Line</h3>
<ul class="wp-block-list">
<li>A more positive view of others (trust, fairness, helpfulness) is consistently associated with higher happiness.</li>
<li>Differences in these outlook measures help explain why later cohorts report lower happiness.</li>
<li>However, there is also an independent downward trend in happiness over time.</li>
</ul>
<p class="wp-block-paragraph"><a href="https://allendowney.github.io/CultureWar//blog1-happy"></a><a href="https://allendowney.github.io/CultureWar//blog1-happy"></a></p>
<p>The post <a href="https://www.allendowney.com/blog/2026/04/03/trust-and-well-being/">Trust and Well-Being</a> appeared first on <a href="https://www.allendowney.com/blog">Probably Overthinking It</a>.</p>
]]></content:encoded>
<post-id xmlns="com-wordpress:feed-additions:1">1766</post-id>
</item>
<item>
<title>Have the Nones hit a ceiling?</title>
<link>https://www.allendowney.com/blog/2026/03/30/have-the-nones-hit-a-ceiling/</link>
<dc:creator><![CDATA[AllenDowney]]></dc:creator>
<pubDate>Mon, 30 Mar 2026 15:51:55 +0000</pubDate>
<category><![CDATA[Uncategorized]]></category>
<category><![CDATA[bayesian statistics]]></category>
<category><![CDATA[general social survey]]></category>
<category><![CDATA[religion]]></category>
<guid isPermaLink="false">https://www.allendowney.com/blog/?p=1756</guid>
<description><![CDATA[<p>Someone asked me recently why I stopped writing about religion, and I said there were two reasons: One is that the primary dataset I was following stopped updating; the other is that Ryan Burge is doing such a good job, I felt redundant. His most recent article presents evidence that the Nones have hit a ceiling — that is, that the percentage of people in the U.S. with no religious affiliation, which has consistently increased for several decades, has either...</p>
<p class="read-more"><a class="btn btn-default" href="https://www.allendowney.com/blog/2026/03/30/have-the-nones-hit-a-ceiling/"> Read More<span class="screen-reader-text"> Read More</span></a></p>
<p>The post <a href="https://www.allendowney.com/blog/2026/03/30/have-the-nones-hit-a-ceiling/">Have the Nones hit a ceiling?</a> appeared first on <a href="https://www.allendowney.com/blog">Probably Overthinking It</a>.</p>
]]></description>
<content:encoded><![CDATA[
<p class="wp-block-paragraph">Someone asked me recently why I stopped writing about religion, and I said there were two reasons: One is that the <a href="https://heri.ucla.edu/publications-tfs/" target="_blank" rel="noreferrer noopener">primary dataset I was following</a> stopped updating; the other is that <a href="https://en.wikipedia.org/wiki/Ryan_Burge_(political_scientist)" target="_blank" rel="noreferrer noopener">Ryan Burge</a> is doing such a good job, I felt redundant.</p>
<p class="wp-block-paragraph">His <a href="https://substack.com/home/post/p-192339927" target="_blank" rel="noreferrer noopener">most recent article</a> presents evidence that the Nones have hit a ceiling — that is, that the percentage of people in the U.S. with no religious affiliation, which has consistently increased for several decades, has either leveled off or started to reverse.</p>
<p class="wp-block-paragraph">He reports on new data from the Cooperative Election Study and the 2024 General Social Survey, including this figure based on the GSS.</p>
<figure class="wp-block-image" id="relig-burge-gss"><img loading="lazy" decoding="async" width="2048" height="1365" src="https://www.allendowney.com/blog/wp-content/uploads/2026/03/gss_relig_raw_data_s-2320d07fdfaaf7f3e756fbec933e265b.png" alt="The percentage of “Nones” from Ryan Burge’s Graphs About Religion." class="wp-image-1761" srcset="https://www.allendowney.com/blog/wp-content/uploads/2026/03/gss_relig_raw_data_s-2320d07fdfaaf7f3e756fbec933e265b.png 2048w, https://www.allendowney.com/blog/wp-content/uploads/2026/03/gss_relig_raw_data_s-2320d07fdfaaf7f3e756fbec933e265b-300x200.png 300w, https://www.allendowney.com/blog/wp-content/uploads/2026/03/gss_relig_raw_data_s-2320d07fdfaaf7f3e756fbec933e265b-1024x683.png 1024w, https://www.allendowney.com/blog/wp-content/uploads/2026/03/gss_relig_raw_data_s-2320d07fdfaaf7f3e756fbec933e265b-768x512.png 768w, https://www.allendowney.com/blog/wp-content/uploads/2026/03/gss_relig_raw_data_s-2320d07fdfaaf7f3e756fbec933e265b-1536x1024.png 1536w, https://www.allendowney.com/blog/wp-content/uploads/2026/03/gss_relig_raw_data_s-2320d07fdfaaf7f3e756fbec933e265b-405x270.png 405w" sizes="auto, (max-width: 2048px) 100vw, 2048px" /></figure>
<p class="wp-block-paragraph">The percentage of “Nones” from Ryan Burge’s <a target="_blank" rel="noreferrer noopener" href="https://www.graphsaboutreligion.com/">Graphs About Religion</a></p>
<p class="wp-block-paragraph">The observed percentage of Nones peaked in the 2021 survey and has dropped in the last two cycles. The CES data show a similar pattern, with a much larger sample size. So I’m not going to disagree with Ryan: it sure looks like the rise of the Nones has stalled or even reversed.</p>
<p class="wp-block-paragraph">However, since I am developing a model that decomposes trends like this into cohort and period effects, we can use it to check whether the turnaround is a cohort or a period effect. It turns out to be both.</p>
<h2 class="wp-block-heading" id="the-model">The Model</h2>
<p class="wp-block-paragraph">The model assumes that each cohort in each year has an unobserved (latent) propensity to report a religious affiliation or none.</p>
<p class="wp-block-paragraph">The cohort and period effects are modeled as second-order Gaussian random walks, which means the model assumes these effects evolve smoothly over time, unless the data provide strong evidence otherwise. The amount of smoothing is estimated from the data.</p>
<p class="wp-block-paragraph">An additional random year effect captures variation from one survey to the next that is not explained by long-term trends, like current events and topics of discussion.</p>
<p class="wp-block-paragraph">The “time only” version of the model estimates a latent propensity for each cycle of the survey, so the result is a smooth curve through the raw proportions.</p>
<p class="wp-block-paragraph">The “time-cohort” version estimates a latent propensity for each cohort during each cycle, so the result is a trajectory over time for each birth year.</p>
<h2 class="wp-block-heading" id="results">Results</h2>
<p class="wp-block-paragraph">Here are the results for the time-only model, showing the posterior mean and a 94% credible interval.</p>
<figure class="wp-block-image" id="time-model-relig"><img loading="lazy" decoding="async" width="1133" height="764" src="https://www.allendowney.com/blog/wp-content/uploads/2026/03/time_model_relig_rw2-ab3b53dbf72feed6f35a356232032396.png" alt="Time-only model, percent with no religious preference" class="wp-image-1759" srcset="https://www.allendowney.com/blog/wp-content/uploads/2026/03/time_model_relig_rw2-ab3b53dbf72feed6f35a356232032396.png 1133w, https://www.allendowney.com/blog/wp-content/uploads/2026/03/time_model_relig_rw2-ab3b53dbf72feed6f35a356232032396-300x202.png 300w, https://www.allendowney.com/blog/wp-content/uploads/2026/03/time_model_relig_rw2-ab3b53dbf72feed6f35a356232032396-1024x690.png 1024w, https://www.allendowney.com/blog/wp-content/uploads/2026/03/time_model_relig_rw2-ab3b53dbf72feed6f35a356232032396-768x518.png 768w, https://www.allendowney.com/blog/wp-content/uploads/2026/03/time_model_relig_rw2-ab3b53dbf72feed6f35a356232032396-400x270.png 400w" sizes="auto, (max-width: 1133px) 100vw, 1133px" /></figure>
<p class="wp-block-paragraph">The posterior mean indicates that the trend in the latent factor has probably slowed; the credible interval indicates that it might have leveled off or reversed.</p>
<p class="wp-block-paragraph">And here are the trajectories for each cohort:</p>
<figure class="wp-block-image" id="cohort-trajectories-relig"><img loading="lazy" decoding="async" width="1330" height="783" src="https://www.allendowney.com/blog/wp-content/uploads/2026/03/cohort_trajectory_re-2dd48c8df781b26e84647025ea5891b6.png" alt="Cohort trajectories, percent with no religious preference" class="wp-image-1762" srcset="https://www.allendowney.com/blog/wp-content/uploads/2026/03/cohort_trajectory_re-2dd48c8df781b26e84647025ea5891b6.png 1330w, https://www.allendowney.com/blog/wp-content/uploads/2026/03/cohort_trajectory_re-2dd48c8df781b26e84647025ea5891b6-300x177.png 300w, https://www.allendowney.com/blog/wp-content/uploads/2026/03/cohort_trajectory_re-2dd48c8df781b26e84647025ea5891b6-1024x603.png 1024w, https://www.allendowney.com/blog/wp-content/uploads/2026/03/cohort_trajectory_re-2dd48c8df781b26e84647025ea5891b6-768x452.png 768w, https://www.allendowney.com/blog/wp-content/uploads/2026/03/cohort_trajectory_re-2dd48c8df781b26e84647025ea5891b6-459x270.png 459w" sizes="auto, (max-width: 1330px) 100vw, 1330px" /></figure>
<p class="wp-block-paragraph">Starting at the bottom, we can see that cohorts born between 1900 and 1930 were not very different — fewer than 10% of them were Nones.</p>
<p class="wp-block-paragraph">People born in the 1940s were increasingly non-religious, but this first wave of secularization stalled in the cohorts born in the 1950s. The second wave got started with people born in the 1960s, and continued until the 2000s cohorts, where it seems to have stalled again.</p>
<h2 class="wp-block-heading" id="decomposition">Decomposition</h2>
<p class="wp-block-paragraph">With these trajectories, we can decompose the cohort and period effects. The following figure shows the cohort effect, standardized by holding the period effect constant.</p>
<figure class="wp-block-image" id="cohort-profile-relig"><img loading="lazy" decoding="async" width="1133" height="764" src="https://www.allendowney.com/blog/wp-content/uploads/2026/03/cohort_standardized_-8a992073e7d82ea3a375589a5651bb5d.png" alt="Standardized cohort effect with fixed time mix, percent with no religious preference" class="wp-image-1760" srcset="https://www.allendowney.com/blog/wp-content/uploads/2026/03/cohort_standardized_-8a992073e7d82ea3a375589a5651bb5d.png 1133w, https://www.allendowney.com/blog/wp-content/uploads/2026/03/cohort_standardized_-8a992073e7d82ea3a375589a5651bb5d-300x202.png 300w, https://www.allendowney.com/blog/wp-content/uploads/2026/03/cohort_standardized_-8a992073e7d82ea3a375589a5651bb5d-1024x690.png 1024w, https://www.allendowney.com/blog/wp-content/uploads/2026/03/cohort_standardized_-8a992073e7d82ea3a375589a5651bb5d-768x518.png 768w, https://www.allendowney.com/blog/wp-content/uploads/2026/03/cohort_standardized_-8a992073e7d82ea3a375589a5651bb5d-400x270.png 400w" sizes="auto, (max-width: 1133px) 100vw, 1133px" /></figure>
<p class="wp-block-paragraph">As we saw in the previous figure, there was a period of relatively fast change in the 1940s cohorts that stalled among people born in the 1950s and then resumed among people born in the 1960s through the 1980s (primarily Gen X).</p>
<p class="wp-block-paragraph">Again, it looks like the most recent cohorts have leveled off, but with the width of the credible interval, it’s possible that the trend has continued or reversed.</p>
<p class="wp-block-paragraph">The following figure shows the period effect, standardized by holding the cohort mix constant.</p>
<figure class="wp-block-image" id="time-trend-relig"><img loading="lazy" decoding="async" width="1133" height="764" src="https://www.allendowney.com/blog/wp-content/uploads/2026/03/time_standardized_re-748498d5f8212df060fbdbfffbe5f356.png" alt="Standardized time trend with fixed cohort mix, percent with no religious preference" class="wp-image-1757" srcset="https://www.allendowney.com/blog/wp-content/uploads/2026/03/time_standardized_re-748498d5f8212df060fbdbfffbe5f356.png 1133w, https://www.allendowney.com/blog/wp-content/uploads/2026/03/time_standardized_re-748498d5f8212df060fbdbfffbe5f356-300x202.png 300w, https://www.allendowney.com/blog/wp-content/uploads/2026/03/time_standardized_re-748498d5f8212df060fbdbfffbe5f356-1024x690.png 1024w, https://www.allendowney.com/blog/wp-content/uploads/2026/03/time_standardized_re-748498d5f8212df060fbdbfffbe5f356-768x518.png 768w, https://www.allendowney.com/blog/wp-content/uploads/2026/03/time_standardized_re-748498d5f8212df060fbdbfffbe5f356-400x270.png 400w" sizes="auto, (max-width: 1133px) 100vw, 1133px" /></figure>
<p class="wp-block-paragraph">The period effect was generally increasing from 1990 to 2020, but seems to have leveled off or rolled over.</p>
<p class="wp-block-paragraph">So, if the rise of the Nones has stalled, at least temporarily, it seems to be a combination of a cohort effect among people born after 2000 and a period effect starting around 2020. This decomposition suggests we should look for at least two kinds of explanations:</p>
<ul class="wp-block-list">
<li>Differences in the childhood of people born after 2000 that might make them more likely to have a religious affiliation as young adults, and</li>
<li>Events since 2020 that have affected all cohorts in ways that might make them more religious.</li>
</ul>
<p class="wp-block-paragraph">I’ll hold off on speculating.</p>
<p class="wp-block-paragraph">For purposes of comparison, here is the trend from the time-only model (blue) and the standardized time trend from the time-cohort model (purple).</p>
<figure class="wp-block-image" id="time-trend-relig-comparison"><img loading="lazy" decoding="async" width="1133" height="764" src="https://www.allendowney.com/blog/wp-content/uploads/2026/03/time_standardized_re-251c2eac1b194a6d2418a92654e81829.png" alt="Time-only trend (blue) and standardized time trend from the cohort–period model (purple), percent with no religious preference" class="wp-image-1758" srcset="https://www.allendowney.com/blog/wp-content/uploads/2026/03/time_standardized_re-251c2eac1b194a6d2418a92654e81829.png 1133w, https://www.allendowney.com/blog/wp-content/uploads/2026/03/time_standardized_re-251c2eac1b194a6d2418a92654e81829-300x202.png 300w, https://www.allendowney.com/blog/wp-content/uploads/2026/03/time_standardized_re-251c2eac1b194a6d2418a92654e81829-1024x690.png 1024w, https://www.allendowney.com/blog/wp-content/uploads/2026/03/time_standardized_re-251c2eac1b194a6d2418a92654e81829-768x518.png 768w, https://www.allendowney.com/blog/wp-content/uploads/2026/03/time_standardized_re-251c2eac1b194a6d2418a92654e81829-400x270.png 400w" sizes="auto, (max-width: 1133px) 100vw, 1133px" /></figure>
<p class="wp-block-paragraph">The difference between these lines is the part of the change due to the cohort effect. So we can see that most of the change over this interval is due to generational replacement rather than disaffiliation.</p>
<p class="wp-block-paragraph"><strong>Methods</strong>: Details about the model are in the <a href="https://allendowney.github.io/CultureWar//tech-report">Technical Report</a>.</p>
<p class="wp-block-paragraph"></p>
<p>The post <a href="https://www.allendowney.com/blog/2026/03/30/have-the-nones-hit-a-ceiling/">Have the Nones hit a ceiling?</a> appeared first on <a href="https://www.allendowney.com/blog">Probably Overthinking It</a>.</p>
]]></content:encoded>
<post-id xmlns="com-wordpress:feed-additions:1">1756</post-id>
</item>
<item>
<title>Attention, Chinese Readers</title>
<link>https://www.allendowney.com/blog/2026/03/29/attention-chinese-readers/</link>
<dc:creator><![CDATA[AllenDowney]]></dc:creator>
<pubDate>Sun, 29 Mar 2026 00:31:52 +0000</pubDate>
<category><![CDATA[Uncategorized]]></category>
<category><![CDATA[book]]></category>
<category><![CDATA[censorship]]></category>
<category><![CDATA[chinese]]></category>
<guid isPermaLink="false">https://www.allendowney.com/blog/?p=1664</guid>
<description><![CDATA[<p>The Chinese edition of Probably Overthinking It is available now (also here)! If you have the Chinese edition, there are two sections you won’t get to read — so I am including them here. Here is an excerpt from Chapter 3, including the deleted paragraph: In the Present The women surveyed in 1990 rejected the childbearing example of their mothers emphatically. On average, each woman had 2.3 fewer children than her mother. If that pattern had continued for another generation,...</p>
<p class="read-more"><a class="btn btn-default" href="https://www.allendowney.com/blog/2026/03/29/attention-chinese-readers/"> Read More<span class="screen-reader-text"> Read More</span></a></p>
<p>The post <a href="https://www.allendowney.com/blog/2026/03/29/attention-chinese-readers/">Attention, Chinese Readers</a> appeared first on <a href="https://www.allendowney.com/blog">Probably Overthinking It</a>.</p>
]]></description>
<content:encoded><![CDATA[
<p class="wp-block-paragraph">The Chinese edition of <em>Probably Overthinking It</em> is <a href="https://www.books.com.tw/products/CN17947121">available now</a> (also <a href="https://product.dangdang.com/12469358967.html">here</a>)!</p>
<figure class="wp-block-image size-full"><img loading="lazy" decoding="async" width="246" height="346" src="https://www.allendowney.com/blog/wp-content/uploads/2026/03/image-1.png" alt="" class="wp-image-1750" srcset="https://www.allendowney.com/blog/wp-content/uploads/2026/03/image-1.png 246w, https://www.allendowney.com/blog/wp-content/uploads/2026/03/image-1-213x300.png 213w, https://www.allendowney.com/blog/wp-content/uploads/2026/03/image-1-192x270.png 192w" sizes="auto, (max-width: 246px) 100vw, 246px" /></figure>
<p class="wp-block-paragraph">If you have the Chinese edition, there are two sections you won’t get to read — so I am including them here.</p>
<blockquote class="wp-block-quote is-layout-flow wp-block-quote-is-layout-flow">
<p class="wp-block-paragraph">Here is an excerpt from <a href="https://allendowney.github.io/ProbablyOverthinkingBook/preston.html#in-the-present">Chapter 3</a>, including the deleted paragraph:</p>
</blockquote>
<h2 class="wp-block-heading">In the Present</h2>
<p class="wp-block-paragraph">The women surveyed in 1990 rejected the childbearing example of their mothers emphatically. On average, each woman had 2.3 fewer children than her mother. If that pattern had continued for another generation, the average family size in 2018 would have been about 0.8. But it wasn’t.</p>
<p class="wp-block-paragraph">In fact, the average family size in 2018 was very close to 2, just as in 1990. So how did that happen?</p>
<p class="wp-block-paragraph">As it turns out, this is close to what we would expect if every woman had one child fewer than her mother. The following distribution shows the actual distribution in 2018, compared to the result if we start with the 1990 distribution and simulate the “one child fewer” scenario.</p>
<figure class="wp-block-image"><img loading="lazy" decoding="async" width="438" height="250" src="https://www.allendowney.com/blog/wp-content/uploads/2026/03/ddb1f82d657fad8171d5c400c9a539aead9ac1a4f85b7460f3a4ae7f7cb00237.png" alt="_images/ddb1f82d657fad8171d5c400c9a539aead9ac1a4f85b7460f3a4ae7f7cb00237.png" class="wp-image-1752" srcset="https://www.allendowney.com/blog/wp-content/uploads/2026/03/ddb1f82d657fad8171d5c400c9a539aead9ac1a4f85b7460f3a4ae7f7cb00237.png 438w, https://www.allendowney.com/blog/wp-content/uploads/2026/03/ddb1f82d657fad8171d5c400c9a539aead9ac1a4f85b7460f3a4ae7f7cb00237-300x171.png 300w" sizes="auto, (max-width: 438px) 100vw, 438px" /></figure>
<p class="wp-block-paragraph">The means of the two distributions are almost the same, but the shapes are different. In reality, there were more zero- and two-child families in 1990 than the simulation predicts, and fewer one-child families. But at least on average, it seems like women in the U.S. have been following the “one child fewer” policy for the last 30 years.</p>
<p class="wp-block-paragraph">The scenario at the beginning of this chapter is meant to be light-hearted, but in reality governments in many places and times have enacted policies meant to control family sizes and population growth. <strong>Most famously, China implemented a one-child policy in 1980 that imposed severe penalties on families with more than one child. Of course, this policy is objectionable to anyone who considers reproductive freedom a fundamental human right. But even as a practical matter, the unintended consequences were profound.</strong></p>
<p class="wp-block-paragraph"><strong>Rather than catalog them, I will mention one that is particularly ironic: while this policy was in effect, economic and social forces reduced the average <em>desired</em> family size so much that, when the policy was relaxed in 2015 and again in 2021, average lifetime fertility increased to only 1.3, far below the level needed to keep the population constant, near 2.1. Since then, China has implemented new policies intended to <em>increase</em> family sizes, but it is not clear whether they will have much effect. Demographers predict that by the time you read this, the population of China will probably be shrinking </strong>[UPDATE: It is.]<strong>. The consequences of the one-child policy are widespread and will affect China and the rest of the world for a long time.</strong></p>
<blockquote class="wp-block-quote is-layout-flow wp-block-quote-is-layout-flow">
<p class="wp-block-paragraph">And here is an excerpt from <a href="https://allendowney.github.io/ProbablyOverthinkingBook/nbue.html#child-mortality">Chapter 5</a>, including the deleted explanation.</p>
</blockquote>
<h2 class="wp-block-heading">Child mortality</h2>
<p class="wp-block-paragraph">Fortunately, child mortality has decreased since 1900. The following figure shows the percentage of children who die before age 5 for four geographical regions, from 1900 to 2019. These data were combined from several sources by Gapminder, a foundation based in Sweden that “promotes sustainable global development […] by increased use and understanding of statistics.”</p>
<figure class="wp-block-image"><img loading="lazy" decoding="async" width="436" height="250" src="https://www.allendowney.com/blog/wp-content/uploads/2026/03/220c5c7e411ef012b610deab7f65ab6dbd0a010aa40d46318a9a14823f2a268e.png" alt="_images/220c5c7e411ef012b610deab7f65ab6dbd0a010aa40d46318a9a14823f2a268e.png" class="wp-image-1754" srcset="https://www.allendowney.com/blog/wp-content/uploads/2026/03/220c5c7e411ef012b610deab7f65ab6dbd0a010aa40d46318a9a14823f2a268e.png 436w, https://www.allendowney.com/blog/wp-content/uploads/2026/03/220c5c7e411ef012b610deab7f65ab6dbd0a010aa40d46318a9a14823f2a268e-300x172.png 300w" sizes="auto, (max-width: 436px) 100vw, 436px" /></figure>
<p class="wp-block-paragraph">In every region, child mortality has decreased consistently and substantially. The only exceptions are indicated by the vertical lines: the 1918 influenza pandemic, which visibly affected Asia, the Americas, and Europe; World War II in Europe (1939-1945); <strong>and the Great Leap Forward in China (1958-1962)</strong>. In every case, these exceptions did not affect the long-term trend.</p>
<blockquote class="wp-block-quote is-layout-flow wp-block-quote-is-layout-flow">
<p class="wp-block-paragraph">[COMMENT: I thought I was being diplomatic by referring generally to the <a href="https://en.wikipedia.org/wiki/Great_Leap_Forward">Great Leap Forward</a> — rather than the <a href="https://en.wikipedia.org/wiki/Great_Chinese_Famine">Great Chinese Famine</a> or “Three Years of Great Famine” (三年大饥荒) — but apparently that was not enough.]</p>
</blockquote>
<p class="wp-block-paragraph">Although there is more work to do, especially in Africa, child mortality is substantially lower now, in every region of the world, than in 1900. As a result most people now are better new than used.</p>
<p class="wp-block-paragraph">To demonstrate this change, I collected recent mortality data from the Global Health Observatory of the World Health Organization (WHO). For people born in 2019, we don’t know what their future lifetimes will be, but we can estimate it if we assume that the mortality rate in each age group will not change over their lifetimes.</p>
<p class="wp-block-paragraph">Based on that simplification, the following figure shows average remaining lifetime as a function of age for Sweden and Nigeria in 2019, compared to Sweden in 1905.</p>
<figure class="wp-block-image"><img loading="lazy" decoding="async" width="438" height="250" src="https://www.allendowney.com/blog/wp-content/uploads/2026/03/6a45a65e6a7b3201af0f74c7b7df4d57ce5c5976972ce0e69538a1914fa5cc5b.png" alt="_images/6a45a65e6a7b3201af0f74c7b7df4d57ce5c5976972ce0e69538a1914fa5cc5b.png" class="wp-image-1753" srcset="https://www.allendowney.com/blog/wp-content/uploads/2026/03/6a45a65e6a7b3201af0f74c7b7df4d57ce5c5976972ce0e69538a1914fa5cc5b.png 438w, https://www.allendowney.com/blog/wp-content/uploads/2026/03/6a45a65e6a7b3201af0f74c7b7df4d57ce5c5976972ce0e69538a1914fa5cc5b-300x171.png 300w" sizes="auto, (max-width: 438px) 100vw, 438px" /></figure>
<p class="wp-block-paragraph">Since 1905, Sweden has continued to make progress; life expectancy at every age is higher in 2019 than in 1905. And Swedes now have the new-better-than-used property. Their life expectancy at birth is about 82 years, and it declines consistently over their lives, just like a light bulb.</p>
<p class="wp-block-paragraph">Unfortunately, Nigeria has one of the highest rates of child mortality in the world: in 2019, almost 8% of babies died in their first year of life. After that, they are briefly better used than new: life expectancy at birth is about 62 years; however, a baby who survives the first year will live another 65 years, on average.</p>
<p class="wp-block-paragraph">Going forward, I hope we continue to reduce child mortality in every region; if we do, soon every person born will be better new than used. Or maybe we can do even better than that.</p>
<p class="wp-block-paragraph"></p>
<p>The post <a href="https://www.allendowney.com/blog/2026/03/29/attention-chinese-readers/">Attention, Chinese Readers</a> appeared first on <a href="https://www.allendowney.com/blog">Probably Overthinking It</a>.</p>
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<post-id xmlns="com-wordpress:feed-additions:1">1664</post-id>
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<item>
<title>Young Adults Are Not Very Happy</title>
<link>https://www.allendowney.com/blog/2026/03/19/young-adults-are-not-very-happy/</link>
<dc:creator><![CDATA[AllenDowney]]></dc:creator>
<pubDate>Thu, 19 Mar 2026 15:44:50 +0000</pubDate>
<category><![CDATA[Uncategorized]]></category>
<category><![CDATA[age period cohort analysis]]></category>
<category><![CDATA[bayesian statistics]]></category>
<category><![CDATA[general social survey]]></category>
<guid isPermaLink="false">https://www.allendowney.com/blog/?p=1736</guid>
<description><![CDATA[<p>Since 1972, the General Social Survey has asked respondents: “Taken all together, how would you say things are these days—would you say that you are very happy, pretty happy, or not too happy?” The following figure shows how the responses have changed over time and between birth cohorts. Each line represents one birth year. People born in 1900 were 72 years old when the survey started; at that point, about 37% said they were very happy. In 1990, the last...</p>
<p class="read-more"><a class="btn btn-default" href="https://www.allendowney.com/blog/2026/03/19/young-adults-are-not-very-happy/"> Read More<span class="screen-reader-text"> Read More</span></a></p>
<p>The post <a href="https://www.allendowney.com/blog/2026/03/19/young-adults-are-not-very-happy/">Young Adults Are Not Very Happy</a> appeared first on <a href="https://www.allendowney.com/blog">Probably Overthinking It</a>.</p>
]]></description>
<content:encoded><![CDATA[
<p class="wp-block-paragraph">Since 1972, the General Social Survey has asked respondents: “Taken all together, how would you say things are these days—would you say that you are very happy, pretty happy, or not too happy?”</p>
<p class="wp-block-paragraph">The following figure shows how the responses have changed over time and between birth cohorts. Each line represents one birth year.</p>
<figure class="wp-block-image" id="cohort-trajectories-happy"><img loading="lazy" decoding="async" width="1330" height="778" src="https://www.allendowney.com/blog/wp-content/uploads/2026/03/cohort_trajectory_ha-ee8d3c24ba4d6e9d119c114dfd0b23c3.png" alt="Cohort trajectories, percent who respond “very happy”" class="wp-image-1739" srcset="https://www.allendowney.com/blog/wp-content/uploads/2026/03/cohort_trajectory_ha-ee8d3c24ba4d6e9d119c114dfd0b23c3.png 1330w, https://www.allendowney.com/blog/wp-content/uploads/2026/03/cohort_trajectory_ha-ee8d3c24ba4d6e9d119c114dfd0b23c3-300x175.png 300w, https://www.allendowney.com/blog/wp-content/uploads/2026/03/cohort_trajectory_ha-ee8d3c24ba4d6e9d119c114dfd0b23c3-1024x599.png 1024w, https://www.allendowney.com/blog/wp-content/uploads/2026/03/cohort_trajectory_ha-ee8d3c24ba4d6e9d119c114dfd0b23c3-768x449.png 768w, https://www.allendowney.com/blog/wp-content/uploads/2026/03/cohort_trajectory_ha-ee8d3c24ba4d6e9d119c114dfd0b23c3-462x270.png 462w" sizes="auto, (max-width: 1330px) 100vw, 1330px" /></figure>
<p class="wp-block-paragraph">People born in 1900 were 72 years old when the survey started; at that point, about 37% said they were very happy. In 1990, the last year they were eligible to participate, a little more than 40% said they were very happy. So it seems like they aged well—or possibly the less happy died earlier.</p>
<p class="wp-block-paragraph">People born in 1910 were a little less happy when the survey started, but by the time they aged out, they also reached 40%. They were the last generation to reach that mark.</p>
<p class="wp-block-paragraph">Among people born between 1920 and 1950, each cohort was a little less happy than the one before (or maybe less likely to say they were happy). In these cohorts, we can see a general trend over time: increasing until about 2000, leveling off, and declining after 2010.</p>
<p class="wp-block-paragraph">The cohorts born in the 1960s and 1970s followed a similar trajectory, with only small differences from one birth year to the next.</p>
<p class="wp-block-paragraph">And then the bottom fell out. Starting with people born in the 1980s (the earliest Millennials), each successive cohort was substantially less happy than the one before.</p>
<p class="wp-block-paragraph">When people born in 1990 joined the survey in 2008 (at age 18), only 27% said they were very happy. In the most recent data, from 2024, the number had fallen to 22%.</p>
<p class="wp-block-paragraph">When people born in 2000 entered in 2018, they set a new record low at 21%, which has now fallen to 18%.</p>
<p class="wp-block-paragraph">And in the most recent cohort—born in 2006 and interviewed in 2024—only 16% said they were very happy.</p>
<p class="wp-block-paragraph">These percentages are based on a statistical model that estimates the proportion of “very happy” responses in each group at each point in time. The details of the model and its assumptions are below.</p>
<h2 class="wp-block-heading" id="the-time-trend">The Time Trend</h2>
<p class="wp-block-paragraph">With an estimated proportion for each cohort and time step, we can compute separate contributions for changes over time and between cohorts.</p>
<p class="wp-block-paragraph">To characterize the contribution of time, we have to hold the cohort effect constant, which we can do by computing the distribution of birth years across the entire dataset and simulating a population where this distribution does not change over time. The following figure shows the result.</p>
<figure class="wp-block-image" id="time-trend-happy"><img loading="lazy" decoding="async" width="1133" height="790" src="https://www.allendowney.com/blog/wp-content/uploads/2026/03/time_standardized_ha-26b65d5757264321ab30d96371b21ccf.png" alt="Standardized time trend, percent who respond “very happy”" class="wp-image-1738" srcset="https://www.allendowney.com/blog/wp-content/uploads/2026/03/time_standardized_ha-26b65d5757264321ab30d96371b21ccf.png 1133w, https://www.allendowney.com/blog/wp-content/uploads/2026/03/time_standardized_ha-26b65d5757264321ab30d96371b21ccf-300x209.png 300w, https://www.allendowney.com/blog/wp-content/uploads/2026/03/time_standardized_ha-26b65d5757264321ab30d96371b21ccf-1024x714.png 1024w, https://www.allendowney.com/blog/wp-content/uploads/2026/03/time_standardized_ha-26b65d5757264321ab30d96371b21ccf-768x535.png 768w, https://www.allendowney.com/blog/wp-content/uploads/2026/03/time_standardized_ha-26b65d5757264321ab30d96371b21ccf-387x270.png 387w" sizes="auto, (max-width: 1133px) 100vw, 1133px" /></figure>
<p class="wp-block-paragraph">The overall level of happiness increased between 1972 and 2000, leveled off, and then declined after 2010.</p>
<p class="wp-block-paragraph">Of course it is speculation to say why that happened, but we can think about large-scale economic and social patterns and how they line up with these trends.</p>
<ul class="wp-block-list">
<li>Economically, 1980 to 2000 was a period of growth and relative stability. That changed after the end of the Dot-com bubble in 2001 and, more importantly, the Global Financial Crisis in 2008, which had broad and persistent effects on employment, wealth, and economic security.</li>
<li>Geopolitically, the 1970s through the 1990s were relatively quiet compared to what followed. The September 11 attacks in 2001, and the wars in Iraq (2003–2011) and Afghanistan (2001–2021) marked a shift toward a more uncertain and conflict-oriented global environment.</li>
<li>Participation in civic organizations and religious institutions declined over the past several decades. These institutions traditionally provided social support, shared identity, and regular face-to-face interaction. Social isolation is strongly associated with lower well-being.</li>
<li>At the same time, the media environment was transformed. The rise of 24-hour news increased exposure to negative and emotionally salient events, and after 2010 the spread of smartphones and social media made that exposure continuous and personalized.</li>
<li>Finally, measures of trust in institutions and other people have generally declined over this period, while political polarization has increased. These trends may reduce people’s sense of stability and shared purpose.</li>
</ul>
<p class="wp-block-paragraph">The COVID-19 pandemic likely contributed to the most recent decline, but the downward trend was already underway before 2020.</p>
<h2 class="wp-block-heading" id="the-cohort-effect">The Cohort Effect</h2>
<p class="wp-block-paragraph">Just as we isolated the time trend by simulating a survey with a fixed distribution of cohorts, we can isolate the cohort effect by simulating a survey with a fixed distribution of times. The following figure shows the result.</p>
<figure class="wp-block-image" id="cohort-profile-happy"><img loading="lazy" decoding="async" width="1133" height="790" src="https://www.allendowney.com/blog/wp-content/uploads/2026/03/cohort_standardized_-2dbe3fdd869f5be03f0b91d2cf3b980e.png" alt="Standardized cohort effect, percent who respond “very happy”" class="wp-image-1740" srcset="https://www.allendowney.com/blog/wp-content/uploads/2026/03/cohort_standardized_-2dbe3fdd869f5be03f0b91d2cf3b980e.png 1133w, https://www.allendowney.com/blog/wp-content/uploads/2026/03/cohort_standardized_-2dbe3fdd869f5be03f0b91d2cf3b980e-300x209.png 300w, https://www.allendowney.com/blog/wp-content/uploads/2026/03/cohort_standardized_-2dbe3fdd869f5be03f0b91d2cf3b980e-1024x714.png 1024w, https://www.allendowney.com/blog/wp-content/uploads/2026/03/cohort_standardized_-2dbe3fdd869f5be03f0b91d2cf3b980e-768x535.png 768w, https://www.allendowney.com/blog/wp-content/uploads/2026/03/cohort_standardized_-2dbe3fdd869f5be03f0b91d2cf3b980e-387x270.png 387w" sizes="auto, (max-width: 1133px) 100vw, 1133px" /></figure>
<p class="wp-block-paragraph">The cohort effect is larger and more consistent than the time trend: the difference between the happiest and least happy cohorts is more than 20 percentage points.</p>
<p class="wp-block-paragraph">The decline was relatively slow for cohorts born between 1900 and 1950 and nearly zero for cohorts born in the 1950s, 1960s and 1970s (late Baby Boomers and Gen X). The steep decline begins with the Millennials and continues into Gen Z.</p>
<p class="wp-block-paragraph">Possible explanations for the recent decline include:</p>
<ul class="wp-block-list">
<li>Transformation of childhood: <a href="https://jonathanhaidt.com/anxious-generation/" target="_blank" rel="noreferrer noopener">Jonathan Haidt</a> has described childhood in recent cohorts as “overprotected in the real world and underprotected in the online world.” Increased parental monitoring, reduced independent play, and greater time spent online may affect the development of autonomy, risk tolerance, and social skills. If these early-life experiences shape long-term outlook, they could contribute to lower self-reported happiness.</li>
<li>Greater and earlier exposure to media: Younger cohorts were exposed to a media landscape characterized by continuous, personalized, and often negative content. Social media platforms amplify social comparison and negative content, while displacing in-person interaction. Increased awareness of global risks—including climate change—may contribute to a more pessimistic worldview.</li>
<li>Differential impact of economic conditions: Recent cohorts entered the labor market during periods of economic disruption, including the aftermath of the Global Financial Crisis and more recent pandemic-related shocks. These cohorts also face higher housing costs and greater student debt. Economic insecurity during the transition to adulthood may have lasting effects on well-being.</li>
<li>Extension of “liminal” adulthood: Young adults are taking longer to complete education, establish careers, form long-term partnerships, and have children. This extended unsettled period may be associated with lower life satisfaction.</li>
<li>Norms around self-reported well-being. Younger cohorts may also be less likely to say they are “very happy,” either because of changing norms around self-presentation or greater awareness of mental health.</li>
</ul>
<p class="wp-block-paragraph">It’s hard to say how much of the recent decline we can attribute to these causes. But the decline is steep, and seems to be ongoing.</p>
<h2 class="wp-block-heading" id="how-the-model-works">How the Model Works</h2>
<p class="wp-block-paragraph">One of the challenges with this kind of survey data is that the sample size is small for each birth year in each iteration of the survey. If we plot raw percentages over time, the result is noisy.</p>
<p class="wp-block-paragraph">In <a href="https://allendowney.github.io/ProbablyOverthinkingIt/simpson.html#old-optimists-young-pessimists" target="_blank" rel="noreferrer noopener"><em>Probably Overthinking It</em></a>, I addressed this problem by grouping respondents into decade-of-birth cohorts and smoothing the resulting time series. That approach works, but it has drawbacks: aggregation removes detail, introduces edge effects for the earliest and latest cohorts, and requires an arbitrary choice about the level of smoothing.</p>
<p class="wp-block-paragraph">The new model takes a more principled approach. Instead of smoothing the observed data, it models an unobserved (latent) propensity to report being “very happy” for each cohort in each year.</p>
<p class="wp-block-paragraph">We assume that the number of “very happy” responses in each group follows a binomial distribution, where the probability of a “very happy” response depends on this latent propensity. The observed responses provide noisy information about the latent factor; the model combines information across cohorts and years to estimate it.</p>
<p class="wp-block-paragraph">The latent propensity is modeled as the sum of an intercept, representing the overall level of happiness, a smooth effect of birth cohort, a smooth effect of survey year, and a year-specific random effect that captures short-term fluctuations (overdispersion).</p>
<p class="wp-block-paragraph">The cohort and period effects are modeled as second-order Gaussian random walks (RW2), which means the model assumes these effects evolve smoothly over time, with a preference for gradual changes in slope rather than abrupt jumps, unless the data provide strong evidence otherwise. The amount of smoothing is not fixed in advance; it is estimated from the data.</p>
<p class="wp-block-paragraph">The random year effect captures variation from one survey to the next that is not explained by long-term trends, like current events and topics of discussion.</p>
<p class="wp-block-paragraph">Where we have a lot of data, the estimates track the observed proportions closely. Where data are sparse, the model borrows strength from neighboring cohorts and years, providing principled smoothing and interpolation without arbitrary grouping.</p>
<p class="wp-block-paragraph">For the details of the model, see the <a href="https://allendowney.github.io/CultureWar//tech-report">Technical Report</a>.<a href="https://allendowney.github.io/CultureWar//"></a><a href="https://allendowney.github.io/CultureWar//"></a></p>
<p class="wp-block-paragraph"></p>
<p>The post <a href="https://www.allendowney.com/blog/2026/03/19/young-adults-are-not-very-happy/">Young Adults Are Not Very Happy</a> appeared first on <a href="https://www.allendowney.com/blog">Probably Overthinking It</a>.</p>
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<link>https://www.allendowney.com/blog/2026/06/12/who-is-more-trusting-liberals-or-conservatives/</link>
<dc:creator><![CDATA[AllenDowney]]></dc:creator>
<pubDate>Fri, 12 Jun 2026 13:40:20 +0000</pubDate>
<category><![CDATA[Uncategorized]]></category>
<category><![CDATA[age period cohort analysis]]></category>
<category><![CDATA[bayesian statistics]]></category>
<category><![CDATA[general social survey]]></category>
<category><![CDATA[political alignment]]></category>
<guid isPermaLink="false">https://www.allendowney.com/blog/?p=1836</guid>
<description><![CDATA[<p>When I go crawling around in data from the General Social Survey, sooner or later I run into Ryan Burge, who writes Graphs About Religion. In his most recent post, he wrote about changes in interpersonal trust, as measured by this GSS question: Generally speaking, would you say that most people can be trusted or that you can’t be too careful in dealing with people? Among other analyses, he looks at how the responses relate to self-identification as liberal, conservative,...</p>
<p class="read-more"><a class="btn btn-default" href="https://www.allendowney.com/blog/2026/06/12/who-is-more-trusting-liberals-or-conservatives/"> Read More<span class="screen-reader-text"> Read More</span></a></p>
<p>The post <a href="https://www.allendowney.com/blog/2026/06/12/who-is-more-trusting-liberals-or-conservatives/">Who Is More Trusting: Liberals or Conservatives?</a> appeared first on <a href="https://www.allendowney.com/blog">Probably Overthinking It</a>.</p>
]]></description>
<content:encoded><![CDATA[
<p class="wp-block-paragraph">When I go crawling around in data from the General Social Survey, sooner or later I run into Ryan Burge, who writes <em>Graphs About Religion</em>. In <a href="https://www.graphsaboutreligion.com/p/gen-z-doesnt-trust-anyone" target="_blank" rel="noreferrer noopener">his most recent post</a>, he wrote about changes in interpersonal trust, as measured by this GSS question:</p>
<blockquote class="wp-block-quote is-layout-flow wp-block-quote-is-layout-flow">
<p class="wp-block-paragraph">Generally speaking, would you say that most people can be trusted or that you can’t be too careful in dealing with people?</p>
</blockquote>
<p class="wp-block-paragraph">Among other analyses, he looks at how the responses relate to self-identification as liberal, conservative, or moderate. The results are … complicated. Ryan writes:</p>
<blockquote class="wp-block-quote is-layout-flow wp-block-quote-is-layout-flow">
<p class="wp-block-paragraph">Among older Americans who identify as liberal, they are more likely to trust other people. Among Gen Z liberals, it’s exactly the opposite.</p>
</blockquote>
<p class="wp-block-paragraph">To explain why older liberals are more trusting, Ryan suggests:</p>
<blockquote class="wp-block-quote is-layout-flow wp-block-quote-is-layout-flow">
<p class="wp-block-paragraph">Liberalism is based on collectivism. It embraces the idea that “together, we can achieve more.” Things like universal healthcare rely on a sense of trust among large groups of people.</p>
</blockquote>
<p class="wp-block-paragraph">But if that’s true, why does the effect go in the opposite direction with Gen Z? Ryan speculates:</p>
<blockquote class="wp-block-quote is-layout-flow wp-block-quote-is-layout-flow">
<p class="wp-block-paragraph">Well, maybe liberals feel very slighted by the fact that Donald Trump has been on the ballot for president in every election in which they’ve been eligible to vote, and he’s won twice. Or it could be that they are more impacted by the cynicism of the internet than conservatives? Or maybe it’s because they report higher rates of depression and anxiety than the rest of the ideological spectrum?</p>
</blockquote>
<p class="wp-block-paragraph">As it happened, I looked at the same GSS variable in <a href="https://www.allendowney.com/blog/2026/04/03/trust-and-well-being/" target="_blank" rel="noreferrer noopener">a recent article</a>. But I didn’t do the breakdown by political ideology, so let’s do that now.</p>
<h3 class="wp-block-heading">The Story So Far</h3>
<p class="wp-block-paragraph">First, here’s a recap of what we saw in the previous post, with the whole GSS sample. The following figure shows the percentage of respondents who said “most people can be trusted.”</p>
<figure class="wp-block-image" id="trust-recap-time-series"><img fetchpriority="high" decoding="async" width="1133" height="826" src="https://www.allendowney.com/blog/wp-content/uploads/2026/06/time_model_trust_rw2-25d010d905ca562e299e59b0e89d1713.png" alt="Time series: percent saying most people can be trusted (all respondents)" class="wp-image-1839" srcset="https://www.allendowney.com/blog/wp-content/uploads/2026/06/time_model_trust_rw2-25d010d905ca562e299e59b0e89d1713.png 1133w, https://www.allendowney.com/blog/wp-content/uploads/2026/06/time_model_trust_rw2-25d010d905ca562e299e59b0e89d1713-300x219.png 300w, https://www.allendowney.com/blog/wp-content/uploads/2026/06/time_model_trust_rw2-25d010d905ca562e299e59b0e89d1713-1024x747.png 1024w, https://www.allendowney.com/blog/wp-content/uploads/2026/06/time_model_trust_rw2-25d010d905ca562e299e59b0e89d1713-768x560.png 768w, https://www.allendowney.com/blog/wp-content/uploads/2026/06/time_model_trust_rw2-25d010d905ca562e299e59b0e89d1713-370x270.png 370w" sizes="(max-width: 1133px) 100vw, 1133px" /><figcaption class="wp-element-caption">Time series: percent saying most people can be trusted (all respondents)</figcaption></figure>
<p class="wp-block-paragraph">Interpersonal trust has declined consistently since the survey started in 1972. In the previous post, I decomposed this trend into cohort and period effects. Here’s the estimated cohort effect:</p>
<figure class="wp-block-image" id="trust-recap-cohort-effect"><img decoding="async" width="1133" height="790" src="https://www.allendowney.com/blog/wp-content/uploads/2026/06/cohort_standardized_-83920254db4863278c92f3cee792510c.png" alt="Standardized cohort effect with fixed time mix, percent saying most people can be trusted (all respondents)" class="wp-image-1840" srcset="https://www.allendowney.com/blog/wp-content/uploads/2026/06/cohort_standardized_-83920254db4863278c92f3cee792510c.png 1133w, https://www.allendowney.com/blog/wp-content/uploads/2026/06/cohort_standardized_-83920254db4863278c92f3cee792510c-300x209.png 300w, https://www.allendowney.com/blog/wp-content/uploads/2026/06/cohort_standardized_-83920254db4863278c92f3cee792510c-1024x714.png 1024w, https://www.allendowney.com/blog/wp-content/uploads/2026/06/cohort_standardized_-83920254db4863278c92f3cee792510c-768x535.png 768w, https://www.allendowney.com/blog/wp-content/uploads/2026/06/cohort_standardized_-83920254db4863278c92f3cee792510c-387x270.png 387w" sizes="(max-width: 1133px) 100vw, 1133px" /><figcaption class="wp-element-caption">Standardized cohort effect with fixed time mix, percent saying most people can be trusted (all respondents)</figcaption></figure>
<p class="wp-block-paragraph">The level of trust increased between the cohorts born in the 1900s through the 1940s, and then started a steep decline — more than 30 percentage points over 60 years. And here’s the remaining period effect, after factoring out the cohort effect.</p>
<figure class="wp-block-image" id="trust-recap-period-effect"><img decoding="async" width="1133" height="790" src="https://www.allendowney.com/blog/wp-content/uploads/2026/06/time_standardized_tr-2f029b683d9ad86a39a536e4f95c8c0f.png" alt="Standardized time trend with fixed cohort mix, percent saying most people can be trusted (all respondents)" class="wp-image-1841" srcset="https://www.allendowney.com/blog/wp-content/uploads/2026/06/time_standardized_tr-2f029b683d9ad86a39a536e4f95c8c0f.png 1133w, https://www.allendowney.com/blog/wp-content/uploads/2026/06/time_standardized_tr-2f029b683d9ad86a39a536e4f95c8c0f-300x209.png 300w, https://www.allendowney.com/blog/wp-content/uploads/2026/06/time_standardized_tr-2f029b683d9ad86a39a536e4f95c8c0f-1024x714.png 1024w, https://www.allendowney.com/blog/wp-content/uploads/2026/06/time_standardized_tr-2f029b683d9ad86a39a536e4f95c8c0f-768x535.png 768w, https://www.allendowney.com/blog/wp-content/uploads/2026/06/time_standardized_tr-2f029b683d9ad86a39a536e4f95c8c0f-387x270.png 387w" sizes="(max-width: 1133px) 100vw, 1133px" /><figcaption class="wp-element-caption">Standardized time trend with fixed cohort mix, percent saying most people can be trusted (all respondents)</figcaption></figure>
<p class="wp-block-paragraph">There is almost no period effect in the full sample.</p>
<h3 class="wp-block-heading">Breakdown by Politics</h3>
<p class="wp-block-paragraph">Now let’s get to the question we started with:</p>
<blockquote class="wp-block-quote is-layout-flow wp-block-quote-is-layout-flow">
<p class="wp-block-paragraph">Who is more trusting: liberals or conservatives?</p>
</blockquote>
<p class="wp-block-paragraph">Here’s the time series, broken down by ideology.</p>
<figure class="wp-block-image" id="trust-polviews-time-series"><img loading="lazy" decoding="async" width="1133" height="826" src="https://www.allendowney.com/blog/wp-content/uploads/2026/06/composed_trust_polvi-2191f28230cc6036ffa53c7c589783eb.png" alt="Time series: percent saying most people can be trusted, by 3-point political views" class="wp-image-1842" srcset="https://www.allendowney.com/blog/wp-content/uploads/2026/06/composed_trust_polvi-2191f28230cc6036ffa53c7c589783eb.png 1133w, https://www.allendowney.com/blog/wp-content/uploads/2026/06/composed_trust_polvi-2191f28230cc6036ffa53c7c589783eb-300x219.png 300w, https://www.allendowney.com/blog/wp-content/uploads/2026/06/composed_trust_polvi-2191f28230cc6036ffa53c7c589783eb-1024x747.png 1024w, https://www.allendowney.com/blog/wp-content/uploads/2026/06/composed_trust_polvi-2191f28230cc6036ffa53c7c589783eb-768x560.png 768w, https://www.allendowney.com/blog/wp-content/uploads/2026/06/composed_trust_polvi-2191f28230cc6036ffa53c7c589783eb-370x270.png 370w" sizes="auto, (max-width: 1133px) 100vw, 1133px" /><figcaption class="wp-element-caption">Time series: percent saying most people can be trusted, by 3-point political views</figcaption></figure>
<p class="wp-block-paragraph">Until recently, there was not much difference: liberals and conservatives were about equally likely to say people can be trusted — both a little more trusting than moderates (who are, maybe, too distrustful to join a team).</p>
<p class="wp-block-paragraph">Since the 2000s, liberals and conservatives have diverged, and now liberals are more trusting, by about 5 percentage points. But all three groups are still declining.</p>
<p class="wp-block-paragraph">Now let’s decompose those trends into cohort and period effects. Here are the cohort effects for the three groups.</p>
<figure class="wp-block-image" id="trust-polviews-cohort-effect"><img loading="lazy" decoding="async" width="1133" height="826" src="https://www.allendowney.com/blog/wp-content/uploads/2026/06/composed_trust_polvi-5e9990b3c69d8128602000b1b4e77eac.png" alt="Standardized cohort effect for generalized trust by political views (uniform weights on survey years within group)" class="wp-image-1844" srcset="https://www.allendowney.com/blog/wp-content/uploads/2026/06/composed_trust_polvi-5e9990b3c69d8128602000b1b4e77eac.png 1133w, https://www.allendowney.com/blog/wp-content/uploads/2026/06/composed_trust_polvi-5e9990b3c69d8128602000b1b4e77eac-300x219.png 300w, https://www.allendowney.com/blog/wp-content/uploads/2026/06/composed_trust_polvi-5e9990b3c69d8128602000b1b4e77eac-1024x747.png 1024w, https://www.allendowney.com/blog/wp-content/uploads/2026/06/composed_trust_polvi-5e9990b3c69d8128602000b1b4e77eac-768x560.png 768w, https://www.allendowney.com/blog/wp-content/uploads/2026/06/composed_trust_polvi-5e9990b3c69d8128602000b1b4e77eac-370x270.png 370w" sizes="auto, (max-width: 1133px) 100vw, 1133px" /><figcaption class="wp-element-caption">Standardized cohort effect for generalized trust by political views (uniform weights on survey years within group)</figcaption></figure>
<p class="wp-block-paragraph">Here we can see what Ryan reported: in most generations, liberals are more trusting than conservatives; it’s only in the most recent generation that it goes the other way. The crossover happens among people born in the mid-1990s, close to the conventional beginning of Gen Z (born 1997 to 2012).</p>
<p class="wp-block-paragraph">And here’s the period effect for the three groups.</p>
<figure class="wp-block-image" id="trust-polviews-period-effect"><img loading="lazy" decoding="async" width="1133" height="826" src="https://www.allendowney.com/blog/wp-content/uploads/2026/06/composed_trust_polvi-e873e0d24bfb4397559e322760556ee6.png" alt="Standardized period trend for generalized trust by political views (fixed within-group cohort weights)" class="wp-image-1843" srcset="https://www.allendowney.com/blog/wp-content/uploads/2026/06/composed_trust_polvi-e873e0d24bfb4397559e322760556ee6.png 1133w, https://www.allendowney.com/blog/wp-content/uploads/2026/06/composed_trust_polvi-e873e0d24bfb4397559e322760556ee6-300x219.png 300w, https://www.allendowney.com/blog/wp-content/uploads/2026/06/composed_trust_polvi-e873e0d24bfb4397559e322760556ee6-1024x747.png 1024w, https://www.allendowney.com/blog/wp-content/uploads/2026/06/composed_trust_polvi-e873e0d24bfb4397559e322760556ee6-768x560.png 768w, https://www.allendowney.com/blog/wp-content/uploads/2026/06/composed_trust_polvi-e873e0d24bfb4397559e322760556ee6-370x270.png 370w" sizes="auto, (max-width: 1133px) 100vw, 1133px" /><figcaption class="wp-element-caption">Standardized period trend for generalized trust by political views (fixed within-group cohort weights)</figcaption></figure>
<p class="wp-block-paragraph">For conservatives and moderates, the period effect is generally downward, although small. For liberals, it’s the other way around, generally increasing since about 2000.</p>
<p class="wp-block-paragraph">The cohort-period decomposition provides some hints about what’s going on:</p>
<ul class="wp-block-list">
<li>Among conservatives and moderates, the cohort and period effects are both downward, so they contributed to a steeper decline over time.</li>
<li>Among liberals, the cohort effect is also downward, but the period effect is upward, so the period effect mitigates the cohort effect.</li>
</ul>
<p class="wp-block-paragraph">To explain the cohort effect, I think Ryan’s suggestions are plausible. People born after 1995 have grown up during a discouraging time to be a liberal. Recent developments contrary to the liberal worldview include</p>
<ul class="wp-block-list">
<li>The rise of populist and nationalist movements in several countries, along with democratic backsliding or erosion of liberal norms.</li>
<li>Slow progress or reversal on climate change.</li>
<li>Increasing distrust of experts, journalists, scientists, and public institutions.</li>
<li>Declining confidence in institutions such as Congress, the media, and organized religion.</li>
<li>A series of conservative Supreme Court decisions, most notably the overturning of long-established abortion rights protections in 2022.</li>
</ul>
<p class="wp-block-paragraph">Negativity bias in the media — especially social media — is probably a contributing factor. And going to school during the pandemic probably didn’t help.</p>
<p class="wp-block-paragraph">But what about that period effect — can we think of reasons liberals would be more trusting, starting around 2005? If the recent cohort effect among young liberals is driven by the Trump era (at least in part), maybe the period effect was driven by events and trends of the Obama era that were aligned with the liberal worldview:</p>
<ul class="wp-block-list">
<li>Perception that the country was becoming more socially inclusive and diverse.</li>
<li>Greater visibility and acceptance of LGBTQ people, and growing support for same-sex marriage, culminating in nationwide legalization in 2015.</li>
<li>Expansion of health insurance coverage through the Patient Protection and Affordable Care Act.</li>
</ul>
<p class="wp-block-paragraph">And falling crime rates from the 1990s through the 2010s might have contributed more directly to increasing interpersonal trust.</p>
<p class="wp-block-paragraph">Of course these explanations are speculative, so let’s get back to what’s supported by the data:</p>
<ul class="wp-block-list">
<li>Since the 1970s, interpersonal trust has declined consistently in all three groups (liberal, conservative, and moderate).</li>
<li>Before 2005, liberals and conservatives were about equally trusting; since then, the decline among liberals has slowed, so they are now the most trusting group.</li>
<li>Among conservatives and moderates, the cohort and period effects are both downward, so they contribute to steeper decline.</li>
<li>Among liberals, the cohort effect is steeply downward in the most recent cohorts, but the decline is mitigated by a positive period effect.</li>
</ul>
<p class="wp-block-paragraph">For now, liberals are the most trusting group, but if the cohort effect persists, they might not be for long.</p>
<p class="wp-block-paragraph"></p>
<p>The post <a href="https://www.allendowney.com/blog/2026/06/12/who-is-more-trusting-liberals-or-conservatives/">Who Is More Trusting: Liberals or Conservatives?</a> appeared first on <a href="https://www.allendowney.com/blog">Probably Overthinking It</a>.</p>
]]></content:encoded>
<post-id xmlns="com-wordpress:feed-additions:1">1836</post-id> </item>
<item>
<title>The Frog Puzzle</title>
<link>https://www.allendowney.com/blog/2026/06/04/the-frog-puzzle/</link>
<dc:creator><![CDATA[AllenDowney]]></dc:creator>
<pubDate>Thu, 04 Jun 2026 19:13:19 +0000</pubDate>
<category><![CDATA[Uncategorized]]></category>
<category><![CDATA[Bayes's Theorem]]></category>
<category><![CDATA[Frog Puzzle]]></category>
<category><![CDATA[probability]]></category>
<guid isPermaLink="false">https://www.allendowney.com/blog/?p=1828</guid>
<description><![CDATA[<p>Here’s a probability puzzle from a TED-Ed video called Can you solve the frog riddle? by Derek Abbott. It came up recently in this Reddit thread: You’re stranded in a rainforest after accidentally eating a poisonous mushroom. To survive the poison, you need to lick a certain species of frog. Only female frogs produce the antidote. Male and female frogs occur in equal numbers and look identical, but male frogs have a distinctive croak. You see one frog alone on...</p>
<p class="read-more"><a class="btn btn-default" href="https://www.allendowney.com/blog/2026/06/04/the-frog-puzzle/"> Read More<span class="screen-reader-text"> Read More</span></a></p>
<p>The post <a href="https://www.allendowney.com/blog/2026/06/04/the-frog-puzzle/">The Frog Puzzle</a> appeared first on <a href="https://www.allendowney.com/blog">Probably Overthinking It</a>.</p>
]]></description>
<content:encoded><![CDATA[
<p class="wp-block-paragraph">Here’s a probability puzzle from a TED-Ed video called <a href="https://www.youtube.com/watch?v=cpwSGsb-rTs">Can you solve the frog riddle?</a> by Derek Abbott. It came up recently in this <a href="https://www.reddit.com/r/probabilitytheory/comments/1ttzcjt/frog_riddle_again/">Reddit thread</a>:</p>
<blockquote class="wp-block-quote is-layout-flow wp-block-quote-is-layout-flow">
<p class="wp-block-paragraph">You’re stranded in a rainforest after accidentally eating a poisonous mushroom. To survive the poison, you need to lick a certain species of frog. Only female frogs produce the antidote. Male and female frogs occur in equal numbers and look identical, but male frogs have a distinctive croak.</p>
<p class="wp-block-paragraph">You see one frog alone on a tree stump. In another direction, you hear the croak of a male frog coming from a clearing with two frogs. You can’t tell which one made the sound.</p>
<p class="wp-block-paragraph">You only have time to go to one place. What are your chances of survival if you go to the clearing and lick both frogs? What if you go to the lone frog?</p>
</blockquote>
<p class="wp-block-paragraph">The second question is relatively easy: if we assume that you are equally likely to see a male or female frog, the probability is 50% that the lone frog is female.</p>
<p class="wp-block-paragraph">The first question depends on how we interpret the puzzle. In particular, it hinges on the word “distinctive” – does that mean:</p>
<ul class="wp-block-list">
<li>Only male frogs croak, and the sound is distinguishable from background noises, or</li>
<li>Both male and female frogs croak, but the male croak is distinguishable from the female croak.</li>
</ul>
<p class="wp-block-paragraph">Based on the answer presented in the video, the first meaning is intended. So we’ll start by solving that version.</p>
<p class="wp-block-paragraph">But the second meaning makes the problem a little harder, so we’ll solve that one, too.</p>
<h2 class="wp-block-heading">Only Male Frogs Croak</h2>
<p class="wp-block-paragraph">To solve the intended version of the puzzle, we’ll assume</p>
<ul class="wp-block-list">
<li>Only male frogs croak, and</li>
<li>When two frogs appear together, their sexes are independent.</li>
</ul>
<p class="wp-block-paragraph">So we’ll start with a prior where all two-frog combinations are equally likely.</p>
<pre class="wp-block-preformatted">from sympy import Rational
hypo = ['FF', 'FM', 'MF', 'MM']
prior = Rational(1)
</pre>
<p class="wp-block-paragraph">Now let’s think about the likelihood of the data under each scenario. In the video, the solution is based on these assumptions:</p>
<ul class="wp-block-list">
<li>If both frogs are female, the probability of hearing the male croak is 0.</li>
<li>If either frog is male, the probability that one of them croaks is 1.</li>
</ul>
<pre class="wp-block-preformatted">likelihood = [0, 1, 1, 1]
</pre>
<p class="wp-block-paragraph">I’ll use a <code>BayesTable</code> to compute the posterior probability for each scenario.</p>
<pre class="wp-block-preformatted">import pandas as pd
import numpy as np
class BayesTable(pd.DataFrame):
def __init__(self, hypo, prior=1, **options):
columns = ['prior', 'likelihood', 'unnorm', 'posterior']
super().__init__(index=hypo, columns=columns, **options)
self.prior = prior
def update(self, likelihood):
self.likelihood = likelihood
self.unnorm = self.prior * self.likelihood
nc = self.unnorm.sum()
self.posterior = self.unnorm / nc
</pre>
<pre class="wp-block-preformatted">table = BayesTable(hypo, prior)
table.update(likelihood)
table
</pre>
<figure class="wp-block-table"><table class="has-fixed-layout"><thead><tr><th></th><th>prior</th><th>likelihood</th><th>unnorm</th><th>posterior</th></tr></thead><tbody><tr><th>FF</th><td>1</td><td>0</td><td>0</td><td>0</td></tr><tr><th>FM</th><td>1</td><td>1</td><td>1</td><td>1/3</td></tr><tr><th>MF</th><td>1</td><td>1</td><td>1</td><td>1/3</td></tr><tr><th>MM</th><td>1</td><td>1</td><td>1</td><td>1/3</td></tr></tbody></table></figure>
<p class="wp-block-paragraph">From the table, we can extract the posterior probability that both frogs are male.</p>
<pre class="wp-block-preformatted">from sympy import init_printing
init_printing(use_latex=False)
</pre>
<pre class="wp-block-preformatted">table.posterior['MM']
</pre>
<pre class="wp-block-preformatted">1/3
</pre>
<p class="wp-block-paragraph">With these assumptions, the probability 1/3 that both frogs are male (and you die), so the probability is 2/3 that at least one is female (and you live).</p>
<p class="wp-block-paragraph">And that’s the answer in the video.</p>
<h2 class="wp-block-heading">Poisson (not Poison) Frogs</h2>
<p class="wp-block-paragraph">But is that the right likelihood? Suppose frogs are equally likely to croak at any instant in time, so their croaks follow a Poisson process. If we assume that these croaking processes are independent, two frogs would be more likely to croak, during a given interval, than one.</p>
<p class="wp-block-paragraph">If the interval is much longer than the average time between croaks, the probability that either frog croaks approaches 1, which is consistent with the previous solution.</p>
<p class="wp-block-paragraph">But if the interval is short – as it might be if you were deciding whether to approach the first frog – the probability of hearing a croak would be double if there are two male frogs rather than one.</p>
<p class="wp-block-paragraph">In that case, the likelihood of the data would be:</p>
<pre class="wp-block-preformatted">half = Rational(1, 2)
likelihood = [0, half, half, 1]
</pre>
<p class="wp-block-paragraph">And here are the posterior probabilities:</p>
<pre class="wp-block-preformatted">table = BayesTable(hypo, prior)
table.update(likelihood)
table
</pre>
<figure class="wp-block-table"><table class="has-fixed-layout"><thead><tr><th></th><th>prior</th><th>likelihood</th><th>unnorm</th><th>posterior</th></tr></thead><tbody><tr><th>FF</th><td>1</td><td>0</td><td>0</td><td>0</td></tr><tr><th>FM</th><td>1</td><td>1/2</td><td>1/2</td><td>1/4</td></tr><tr><th>MF</th><td>1</td><td>1/2</td><td>1/2</td><td>1/4</td></tr><tr><th>MM</th><td>1</td><td>1</td><td>1</td><td>1/2</td></tr></tbody></table></figure>
<p class="wp-block-paragraph">With Poisson frogs and a short interval, the probability of two male frogs is 1/2, so it doesn’t matter whether you approach the lone frog or the pair of frogs.</p>
<h2 class="wp-block-heading">Female Frogs Croak, Too</h2>
<p class="wp-block-paragraph">Now let’s think about the other interpretation of the puzzle: suppose both male and female frogs croak, but we can distinguish one from the other. And suppose male and female frogs croak at different rates, but they are still independent.</p>
<p class="wp-block-paragraph">Assume that male frogs croak at a rate of 1 per time unit, and female frogs at a rate of <code>r</code> per time unit. In that case, if we start listening at a random time, the probability that we hear a male frog first is <code>1 / (r+1)</code> if there’s only one male frog, and <code>1</code> if there are two male frogs.</p>
<p class="wp-block-paragraph">So the likelihood in this case is:</p>
<pre class="wp-block-preformatted">from sympy import symbols
r = symbols('r')
likelihood = [0, 1 / (r+1), 1 / (r+1), 1]
</pre>
<p class="wp-block-paragraph">And here are the posteriors</p>
<pre class="wp-block-preformatted">table = BayesTable(hypo, prior)
table.update(likelihood)
table
</pre>
<figure class="wp-block-table"><table class="has-fixed-layout"><thead><tr><th></th><th>prior</th><th>likelihood</th><th>unnorm</th><th>posterior</th></tr></thead><tbody><tr><th>FF</th><td>1</td><td>0</td><td>0</td><td>0</td></tr><tr><th>FM</th><td>1</td><td>1/(r + 1)</td><td>1/(r + 1)</td><td>1/((1 + 2/(r + 1))*(r + 1))</td></tr><tr><th>MF</th><td>1</td><td>1/(r + 1)</td><td>1/(r + 1)</td><td>1/((1 + 2/(r + 1))*(r + 1))</td></tr><tr><th>MM</th><td>1</td><td>1</td><td>1</td><td>1/(1 + 2/(r + 1))</td></tr></tbody></table></figure>
<p class="wp-block-paragraph">In this scenario, here’s the probability you die.</p>
<pre class="wp-block-preformatted">prob_die = table.posterior['MM']
prob_die.simplify()
</pre>
<pre class="wp-block-preformatted">r + 1
─────
r + 3
</pre>
<p class="wp-block-paragraph">If female frogs don’t croak, we get the same answer as in the first scenario.</p>
<pre class="wp-block-preformatted">prob_die.subs({r: 0})
</pre>
<pre class="wp-block-preformatted">1/3
</pre>
<p class="wp-block-paragraph">If male and female frogs croak at the same rate, the probability that both frogs are male is 1/2.</p>
<pre class="wp-block-preformatted">prob_die.subs({r: 1})
</pre>
<pre class="wp-block-preformatted">1/2
</pre>
<p class="wp-block-paragraph">But if female frogs croak much more often, the fact that a male croaked first is strong evidence that both are male, so the posterior probability is close to 1.</p>
<pre class="wp-block-preformatted">prob_die.subs({r: 1000}).evalf()
</pre>
<pre class="wp-block-preformatted">0.998005982053839
</pre>
<h2 class="wp-block-heading">Assortative Mating</h2>
<p class="wp-block-paragraph">Now suppose that when we see two frogs together, their sexes are not independent; specifically, let’s assume that the probability of a same-sex pair is <code>p</code>, so the probability of a mixed-sex pair is <code>1-p</code>. In this scenario, the priors (before we hear the croak) are not equal.</p>
<pre class="wp-block-preformatted">p = symbols('p')
prior = [p, 1-p, 1-p, p]
</pre>
<p class="wp-block-paragraph">Here are the posterior probabilities, assuming again that both male and female frogs, possibly at different rates.</p>
<pre class="wp-block-preformatted">likelihood = [0, 1 / (r+1), 1 / (r+1), 1]
table = BayesTable(hypo, prior)
table.update(likelihood)
table
</pre>
<figure class="wp-block-table"><table class="has-fixed-layout"><thead><tr><th></th><th>prior</th><th>likelihood</th><th>unnorm</th><th>posterior</th></tr></thead><tbody><tr><th>FF</th><td>p</td><td>0</td><td>0</td><td>0</td></tr><tr><th>FM</th><td>1 – p</td><td>1/(r + 1)</td><td>(1 – p)/(r + 1)</td><td>(1 – p)/((p + 2*(1 – p)/(r + 1))*(r + 1))</td></tr><tr><th>MF</th><td>1 – p</td><td>1/(r + 1)</td><td>(1 – p)/(r + 1)</td><td>(1 – p)/((p + 2*(1 – p)/(r + 1))*(r + 1))</td></tr><tr><th>MM</th><td>p</td><td>1</td><td>p</td><td>p/(p + 2*(1 – p)/(r + 1))</td></tr></tbody></table></figure>
<pre class="wp-block-preformatted">table.posterior['MM'].simplify()
</pre>
<pre class="wp-block-preformatted"> p⋅(r + 1)
───────────
p⋅r - p + 2
</pre>
<p class="wp-block-paragraph">If <code>p=1/2</code>, this simplifies to the previous scenario.</p>
<pre class="wp-block-preformatted">table.posterior['MM'].subs({p: half}).simplify()
</pre>
<pre class="wp-block-preformatted">r + 1
─────
r + 3
</pre>
<p class="wp-block-paragraph">And if <code>r=0</code> (female frogs don’t croak), we get the answer presented in the video.</p>
<pre class="wp-block-preformatted">table.posterior['MM'].subs({p: half, r: 0}).simplify()
</pre>
<pre class="wp-block-preformatted">1/3
</pre>
<p class="wp-block-paragraph">But depending on the assumptions, the probability can be as low as <code>0</code></p>
<pre class="wp-block-preformatted">table.posterior['MM'].subs({p: 0, r: 1}).simplify()
</pre>
<pre class="wp-block-preformatted">0
</pre>
<p class="wp-block-paragraph">Or as high as <code>1</code>.</p>
<pre class="wp-block-preformatted">table.posterior['MM'].subs({p: 1, r: 0}).simplify()
</pre>
<pre class="wp-block-preformatted">1
</pre>
<p class="wp-block-paragraph">Or anything in between. As is often the case with problems like these, the answer depends on a precise specification of the data-generating process.</p>
<h2 class="wp-block-heading">Discussion</h2>
<p class="wp-block-paragraph">If all of this seems like more trouble than it’s worth, let me suggest a metacognitive shortcut for solving puzzles like this.</p>
<ol class="wp-block-list">
<li>Notice that in all probability puzzles, the answer is either 1/2 or 1/3.</li>
<li>Also, the answer is always counterintuitive; otherwise it wouldn’t be a puzzle.</li>
<li>Therefore, if your intuition says the answer is 1/2, it’s actually 1/3, and vice versa.</li>
</ol>
<p class="wp-block-paragraph">That might save you some time.</p>
<p class="wp-block-paragraph">This notebook uses methods and materials from <em>Think Bayes</em>, second edition. If you like this sort of thing, you can read the whole book, and more examples, at <a href="https://allendowney.github.io/ThinkBayes2/">allendowney.github.io/ThinkBayes2/</a>.</p>
<p class="wp-block-paragraph"><br><br></p>
<p class="wp-block-paragraph"></p>
<p>The post <a href="https://www.allendowney.com/blog/2026/06/04/the-frog-puzzle/">The Frog Puzzle</a> appeared first on <a href="https://www.allendowney.com/blog">Probably Overthinking It</a>.</p>
]]></content:encoded>
<post-id xmlns="com-wordpress:feed-additions:1">1828</post-id> </item>
<item>
<title>Sexual morality</title>
<link>https://www.allendowney.com/blog/2026/05/28/sexual-morality/</link>
<dc:creator><![CDATA[AllenDowney]]></dc:creator>
<pubDate>Thu, 28 May 2026 18:21:52 +0000</pubDate>
<category><![CDATA[Uncategorized]]></category>
<category><![CDATA[age period cohort analysis]]></category>
<category><![CDATA[bayesian statistics]]></category>
<category><![CDATA[general social survey]]></category>
<guid isPermaLink="false">https://www.allendowney.com/blog/?p=1818</guid>
<description><![CDATA[<p>This article is one of a series looking at changes in public opinion over the last 50 years, with a focus on culture war topics. In this installment, we’ll look at responses to four questions in the General Social Survey (GSS) related to sexual activity: As we’ll see, answers to these questions have diverged in the last 50 years. A large majority answer that extramarital and teen sex are wrong, and that has barely changed (although opposition). At the same...</p>
<p class="read-more"><a class="btn btn-default" href="https://www.allendowney.com/blog/2026/05/28/sexual-morality/"> Read More<span class="screen-reader-text"> Read More</span></a></p>
<p>The post <a href="https://www.allendowney.com/blog/2026/05/28/sexual-morality/">Sexual morality</a> appeared first on <a href="https://www.allendowney.com/blog">Probably Overthinking It</a>.</p>
]]></description>
<content:encoded><![CDATA[
<p class="wp-block-paragraph">This article is one of a series looking at changes in public opinion over the last 50 years, with a focus on culture war topics. In this installment, we’ll look at responses to four questions in the General Social Survey (GSS) related to sexual activity:</p>
<ol start="1" class="wp-block-list">
<li><strong>Premarital sex</strong> (<code>premarsx</code>): <em>There’s been a lot of discussion about the way morals and attitudes about sex are changing in this country. If a man and woman have sex relations before marriage, do you think it is always wrong, almost always wrong, wrong only sometimes, or not wrong at all?</em></li>
<li><strong>Teen premarital sex</strong> (<code>teensex</code>): <em>What if they are in their early teens, say 14 to 16 years old? In that case, do you think sex relations before marriage are always wrong, almost always wrong, wrong only sometimes, or not wrong at all?</em></li>
<li><strong>Extramarital sex</strong> (<code>xmarsex</code>): <em>What is your opinion about a married person having sexual relations with someone other than the marriage partner—is it always wrong, almost always wrong, wrong only sometimes, or not wrong at all?</em></li>
<li><strong>Same-sex relations</strong> (<code>homosex</code>): <em>What about sexual relations between two adults of the same sex—do you think it is always wrong, almost always wrong, wrong only sometimes, or not wrong at all?</em></li>
</ol>
<p class="wp-block-paragraph">As we’ll see, answers to these questions have diverged in the last 50 years. A large majority answer that extramarital and teen sex are wrong, and that has barely changed (although opposition). At the same time, opposition to premarital sex and same-sex relations has declined substantially.</p>
<p class="wp-block-paragraph">In this article, we’ll look at these trends and decompose them into cohort and period effects. In the next article, we’ll look at the relationship between these responses and religion, both affiliation and attendance.</p>
<p class="wp-block-paragraph">We’ll start with the first question, on premarital sex.</p>
<h2 class="wp-block-heading">Premarital sex</h2>
<p class="wp-block-paragraph">The following figure shows the percentage of respondents saying premarital sex is always or almost always wrong, from 1972 to 2024. The shaded area shows the results from a Bayesian model that estimates the latent trend — that is, a slowly varying underlying level of opposition to premarital sex.</p>
<figure class="wp-block-image" id="premarsx-time-model"><img loading="lazy" decoding="async" width="1145" height="826" src="https://www.allendowney.com/blog/wp-content/uploads/2026/05/time_model_premarsx_-92782a5d81ed3c322ce3a3b74a1a1525.png" alt="Time series national trend: percent saying premarital sex is always or almost always wrong (premarsx)." class="wp-image-1820" srcset="https://www.allendowney.com/blog/wp-content/uploads/2026/05/time_model_premarsx_-92782a5d81ed3c322ce3a3b74a1a1525.png 1145w, https://www.allendowney.com/blog/wp-content/uploads/2026/05/time_model_premarsx_-92782a5d81ed3c322ce3a3b74a1a1525-300x216.png 300w, https://www.allendowney.com/blog/wp-content/uploads/2026/05/time_model_premarsx_-92782a5d81ed3c322ce3a3b74a1a1525-1024x739.png 1024w, https://www.allendowney.com/blog/wp-content/uploads/2026/05/time_model_premarsx_-92782a5d81ed3c322ce3a3b74a1a1525-768x554.png 768w, https://www.allendowney.com/blog/wp-content/uploads/2026/05/time_model_premarsx_-92782a5d81ed3c322ce3a3b74a1a1525-374x270.png 374w" sizes="auto, (max-width: 1145px) 100vw, 1145px" /></figure>
<p class="wp-block-paragraph">Opposition to premarital sex has declined since 1972, from about 47% to about 20%.</p>
<p class="wp-block-paragraph">As always, when we see this kind of change over time, it might be caused by cohort or period effects, or a combination of the two. Using a Bayesian model, I estimate a cohort effect for each birth year and a period effect for each survey year. The following figure shows the resulting trajectory for each cohort over time.</p>
<figure class="wp-block-image" id="premarsx-cohort-trajectories"><img loading="lazy" decoding="async" width="1330" height="773" src="https://www.allendowney.com/blog/wp-content/uploads/2026/05/cohort_trajectory_pr-795031a5150bdfce6ad7635df8bae9d3.png" alt="Cohort trajectories: percent always or almost always wrong (premarsx), one line per birth year." class="wp-image-1826" srcset="https://www.allendowney.com/blog/wp-content/uploads/2026/05/cohort_trajectory_pr-795031a5150bdfce6ad7635df8bae9d3.png 1330w, https://www.allendowney.com/blog/wp-content/uploads/2026/05/cohort_trajectory_pr-795031a5150bdfce6ad7635df8bae9d3-300x174.png 300w, https://www.allendowney.com/blog/wp-content/uploads/2026/05/cohort_trajectory_pr-795031a5150bdfce6ad7635df8bae9d3-1024x595.png 1024w, https://www.allendowney.com/blog/wp-content/uploads/2026/05/cohort_trajectory_pr-795031a5150bdfce6ad7635df8bae9d3-768x446.png 768w, https://www.allendowney.com/blog/wp-content/uploads/2026/05/cohort_trajectory_pr-795031a5150bdfce6ad7635df8bae9d3-465x270.png 465w" sizes="auto, (max-width: 1330px) 100vw, 1330px" /></figure>
<p class="wp-block-paragraph">Each line represents a single birth year. For example, the yellow line at the top shows the fitted trajectory for people born in 1900, who were 72 when the survey started in 1972 and 90 when they aged out in 1990. The blue line in the bottom right shows responses of people born in 2000, who became eligible to participate in the survey when they turned 18 in 2018.</p>
<p class="wp-block-paragraph">One pattern is clear: each cohort is less likely than the previous cohort to say that premarital sex is wrong. Among people born in 1900, it was more than 70%. Among people born in the 2000s, it is close to 10%. So that’s a big difference.</p>
<p class="wp-block-paragraph">From these results, we can estimate the cohort and period effects separately. The following figure shows the cohort effect, standardized to control for the period effect by simulating responses as if every cohort was interviewed during every iteration of the survey.</p>
<figure class="wp-block-image" id="premarsx-cohort-standardized"><img loading="lazy" decoding="async" width="1145" height="826" src="https://www.allendowney.com/blog/wp-content/uploads/2026/05/cohort_standardized_-2ddcc0ce51962fa548b8944732f56f2c.png" alt="Standardized cohort component with uniform weights on observed survey years (premarsx)." class="wp-image-1821" srcset="https://www.allendowney.com/blog/wp-content/uploads/2026/05/cohort_standardized_-2ddcc0ce51962fa548b8944732f56f2c.png 1145w, https://www.allendowney.com/blog/wp-content/uploads/2026/05/cohort_standardized_-2ddcc0ce51962fa548b8944732f56f2c-300x216.png 300w, https://www.allendowney.com/blog/wp-content/uploads/2026/05/cohort_standardized_-2ddcc0ce51962fa548b8944732f56f2c-1024x739.png 1024w, https://www.allendowney.com/blog/wp-content/uploads/2026/05/cohort_standardized_-2ddcc0ce51962fa548b8944732f56f2c-768x554.png 768w, https://www.allendowney.com/blog/wp-content/uploads/2026/05/cohort_standardized_-2ddcc0ce51962fa548b8944732f56f2c-374x270.png 374w" sizes="auto, (max-width: 1145px) 100vw, 1145px" /></figure>
<p class="wp-block-paragraph">The decline was steepest between the cohorts born in 1900 and 1950. After that, it leveled off, then declined again among the cohorts born in the 1980s.</p>
<p class="wp-block-paragraph">Now we can estimate the period effect, standardized to control for the cohort effect, shown in the following figure.</p>
<figure class="wp-block-image" id="premarsx-period-standardized"><img loading="lazy" decoding="async" width="1145" height="826" src="https://www.allendowney.com/blog/wp-content/uploads/2026/05/time_standardized_pr-3ad2679bfedff58845cbd5c8219ec152.png" alt="Standardized period component with fixed cohort mix (premarsx)." class="wp-image-1822" srcset="https://www.allendowney.com/blog/wp-content/uploads/2026/05/time_standardized_pr-3ad2679bfedff58845cbd5c8219ec152.png 1145w, https://www.allendowney.com/blog/wp-content/uploads/2026/05/time_standardized_pr-3ad2679bfedff58845cbd5c8219ec152-300x216.png 300w, https://www.allendowney.com/blog/wp-content/uploads/2026/05/time_standardized_pr-3ad2679bfedff58845cbd5c8219ec152-1024x739.png 1024w, https://www.allendowney.com/blog/wp-content/uploads/2026/05/time_standardized_pr-3ad2679bfedff58845cbd5c8219ec152-768x554.png 768w, https://www.allendowney.com/blog/wp-content/uploads/2026/05/time_standardized_pr-3ad2679bfedff58845cbd5c8219ec152-374x270.png 374w" sizes="auto, (max-width: 1145px) 100vw, 1145px" /></figure>
<p class="wp-block-paragraph">The period effect is smaller than the cohort effect — about 8 percentage points from peak to trough — and less consistent. Opposition to premarital sex increased between 1980 and 2000, which coincides with increasing awareness of AIDS and public messaging about sexual risk, as well as the rise of the Religious Right and “family values” politics.</p>
<p class="wp-block-paragraph">But before I speculate about the causes of these patterns, it will be useful to look at the responses to the other questions.</p>
<h2 class="wp-block-heading">When is sex wrong?</h2>
<p class="wp-block-paragraph">The following figure shows the estimated percentage who think sex is wrong (always or almost always) in each of the four scenarios: premarital, teen, extramarital, and same-sex.</p>
<figure class="wp-block-image" id="sex-wrongness-composite-time-model"><img loading="lazy" decoding="async" width="1145" height="766" src="https://www.allendowney.com/blog/wp-content/uploads/2026/05/section1a_sex_wrongn-80473854b8315d2c65a20e45ee21992c.png" alt="Composite overlay: sexual-behavior wrongness scale — national time-series model (four items)." class="wp-image-1824" srcset="https://www.allendowney.com/blog/wp-content/uploads/2026/05/section1a_sex_wrongn-80473854b8315d2c65a20e45ee21992c.png 1145w, https://www.allendowney.com/blog/wp-content/uploads/2026/05/section1a_sex_wrongn-80473854b8315d2c65a20e45ee21992c-300x201.png 300w, https://www.allendowney.com/blog/wp-content/uploads/2026/05/section1a_sex_wrongn-80473854b8315d2c65a20e45ee21992c-1024x685.png 1024w, https://www.allendowney.com/blog/wp-content/uploads/2026/05/section1a_sex_wrongn-80473854b8315d2c65a20e45ee21992c-768x514.png 768w, https://www.allendowney.com/blog/wp-content/uploads/2026/05/section1a_sex_wrongn-80473854b8315d2c65a20e45ee21992c-404x270.png 404w" sizes="auto, (max-width: 1145px) 100vw, 1145px" /></figure>
<p class="wp-block-paragraph">Reading from top to bottom:</p>
<ul class="wp-block-list">
<li>Nearly everyone thinks “a married person having sexual relations with someone other than the marriage partner” is wrong, and the percentage has barely changed in more than 50 years.</li>
<li>Opposition to teen sex (the question specifies ages 14-16) is nearly as high, although it has declined since 2005 by about 15 percentage points.</li>
<li>Opposition to same-sex relations was high and mostly unchanged between 1972 and 1990. Since then it has decreased by almost 50 percentage points in 30 years, which is an astonishing speed for this kind of social change. Since 2020, opposition has increased a little.</li>
<li>Finally, as we’ve already seen, opposition to premarital sex declined substantially since the beginning of the survey.</li>
</ul>
<p class="wp-block-paragraph">For all four scenarios, we can estimate the cohort effect, controlling for the period effect, shown in the following figure.</p>
<figure class="wp-block-image" id="sex-wrongness-composite-cohort"><img loading="lazy" decoding="async" width="1145" height="766" src="https://www.allendowney.com/blog/wp-content/uploads/2026/05/section1a_sex_wrongn-f61ab0124fa6ad280ce97c7fe9addcba.png" alt="Composite overlay: standardized cohort component with uniform weights on observed years (four items)." class="wp-image-1825" srcset="https://www.allendowney.com/blog/wp-content/uploads/2026/05/section1a_sex_wrongn-f61ab0124fa6ad280ce97c7fe9addcba.png 1145w, https://www.allendowney.com/blog/wp-content/uploads/2026/05/section1a_sex_wrongn-f61ab0124fa6ad280ce97c7fe9addcba-300x201.png 300w, https://www.allendowney.com/blog/wp-content/uploads/2026/05/section1a_sex_wrongn-f61ab0124fa6ad280ce97c7fe9addcba-1024x685.png 1024w, https://www.allendowney.com/blog/wp-content/uploads/2026/05/section1a_sex_wrongn-f61ab0124fa6ad280ce97c7fe9addcba-768x514.png 768w, https://www.allendowney.com/blog/wp-content/uploads/2026/05/section1a_sex_wrongn-f61ab0124fa6ad280ce97c7fe9addcba-404x270.png 404w" sizes="auto, (max-width: 1145px) 100vw, 1145px" /></figure>
<p class="wp-block-paragraph">For all four scenarios, there is a consistent downward trend in the cohort effect, modest for extramarital and teen sex, much steeper for premarital and same-sex relations.</p>
<p class="wp-block-paragraph">The following figure shows the period effects.</p>
<figure class="wp-block-image" id="sex-wrongness-composite-period"><img loading="lazy" decoding="async" width="1145" height="766" src="https://www.allendowney.com/blog/wp-content/uploads/2026/05/section1a_sex_wrongn-f67ed5b82acbc806401f00d555e7c43e.png" alt="Composite overlay: standardized period component with fixed cohort mix (four items)." class="wp-image-1823" srcset="https://www.allendowney.com/blog/wp-content/uploads/2026/05/section1a_sex_wrongn-f67ed5b82acbc806401f00d555e7c43e.png 1145w, https://www.allendowney.com/blog/wp-content/uploads/2026/05/section1a_sex_wrongn-f67ed5b82acbc806401f00d555e7c43e-300x201.png 300w, https://www.allendowney.com/blog/wp-content/uploads/2026/05/section1a_sex_wrongn-f67ed5b82acbc806401f00d555e7c43e-1024x685.png 1024w, https://www.allendowney.com/blog/wp-content/uploads/2026/05/section1a_sex_wrongn-f67ed5b82acbc806401f00d555e7c43e-768x514.png 768w, https://www.allendowney.com/blog/wp-content/uploads/2026/05/section1a_sex_wrongn-f67ed5b82acbc806401f00d555e7c43e-404x270.png 404w" sizes="auto, (max-width: 1145px) 100vw, 1145px" /></figure>
<p class="wp-block-paragraph">After controlling for the cohort effects, the remaining period effects are more modest.</p>
<ul class="wp-block-list">
<li>Opposition to teen sex is mostly unchanged, with some decline since 2010.</li>
<li>Opposition to extramarital sex increased between 1972 and 2010, and decreased since then.</li>
<li>Opposition to same-sex relations shows by far the largest period effect, increasing between 1972 and 1990, and decreasing since then — although increasing again since 2020.</li>
<li>Opposition to premarital sex has increased and decreased modestly.</li>
</ul>
<p class="wp-block-paragraph">In most scenarios, the cohort effect accounts for more of the observed change — but for same-sex relations, the period effect also makes a substantial contribution.</p>
<h2 class="wp-block-heading">Dogma, morality, and health</h2>
<p class="wp-block-paragraph">To make sense of these patterns, let’s think about what people might mean when they say that sex is wrong.</p>
<p class="wp-block-paragraph">Taking premarital sex as an example, some people consider sex outside marriage to be contrary to spiritual values or religious teachings. Others might be concerned with sexually-transmitted disease or the social consequences of children born outside of stable families.</p>
<p class="wp-block-paragraph">And for teens specifically, some object because they see adolescence as a period of innocence that should be protected, believe sexual activity compromises purity or chastity, or think sexual restraint reflects virtues like self-discipline and respect for social norms. Also, some might think teenagers don’t have the knowledge, experience, and impulse control to avoid health consequences of sex, especially pregnancy, or the maturity to handle emotional challenges.</p>
<p class="wp-block-paragraph">Similarly, some people object to same-sex relations because they see them as contrary to religious teachings, inconsistent with traditional ideas about gender and family, or incompatible with social norms about sexuality.</p>
<p class="wp-block-paragraph">And people might object to extramarital sex because of the emotional harm it causes, because it breaks a vow, because it threatens families and social stability, or because it violates holy matrimony.</p>
<p class="wp-block-paragraph">In each scenario, objections arise from different concerns: practical risks and harms, social concerns about norms and stability, and moral or religious beliefs. Looking only at multiple-choice responses, we don’t know what respondents had in mind.</p>
<p class="wp-block-paragraph">But the differences we see — between teen and extramarital sex on one hand, and premarital sex and same-sex relations on the other — suggest a conjecture: objections rooted in immediate harms and concrete consequences might be more stable over time; objections rooted in social norms, morality, and religion might be more historically contingent.</p>
<p class="wp-block-paragraph">In the next article, we’ll test this conjecture by looking at relationships between religion and attitudes about sex — and how both have changed over time.</p>
<p class="wp-block-paragraph"><a href="https://allendowney.github.io/CultureWar//blog8-confidence"></a><a href="https://allendowney.github.io/CultureWar//blog8-confidence"></a></p>
<p class="wp-block-paragraph"></p>
<p>The post <a href="https://www.allendowney.com/blog/2026/05/28/sexual-morality/">Sexual morality</a> appeared first on <a href="https://www.allendowney.com/blog">Probably Overthinking It</a>.</p>
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<post-id xmlns="com-wordpress:feed-additions:1">1818</post-id> </item>
<item>
<title>Confidence in Institutions</title>
<link>https://www.allendowney.com/blog/2026/05/19/confidence-in-institutions/</link>
<dc:creator><![CDATA[AllenDowney]]></dc:creator>
<pubDate>Tue, 19 May 2026 15:04:04 +0000</pubDate>
<category><![CDATA[Uncategorized]]></category>
<category><![CDATA[age period cohort analysis]]></category>
<category><![CDATA[bayesian statistics]]></category>
<category><![CDATA[general social survey]]></category>
<guid isPermaLink="false">https://www.allendowney.com/blog/?p=1803</guid>
<description><![CDATA[<p>This article is one of a series exploring responses to core questions in the General Social Survey (GSS), estimating period and cohort effects, and looking for historical events that might explain the trends we see. Confidence in American institutions In this installment, we’ll look at 13 questions related to confidence in institutions. We’ll start with a detailed look at confidence in “the people running Congress”, and then summarize results from the other questions. The complete survey question is: I am...</p>
<p class="read-more"><a class="btn btn-default" href="https://www.allendowney.com/blog/2026/05/19/confidence-in-institutions/"> Read More<span class="screen-reader-text"> Read More</span></a></p>
<p>The post <a href="https://www.allendowney.com/blog/2026/05/19/confidence-in-institutions/">Confidence in Institutions</a> appeared first on <a href="https://www.allendowney.com/blog">Probably Overthinking It</a>.</p>
]]></description>
<content:encoded><![CDATA[
<p class="wp-block-paragraph">This article is one of a series exploring responses to core questions in the General Social Survey (GSS), estimating period and cohort effects, and looking for historical events that might explain the trends we see.<a href="https://github.com/AllenDowney/CultureWar" target="_blank" rel="noreferrer noopener"></a><a href="https://github.com/AllenDowney/CultureWar/edit/main/jb/blog8_confidence.md" target="_blank" rel="noreferrer noopener"></a></p>
<h2 class="wp-block-heading" id="confidence-in-american-institutions">Confidence in American institutions</h2>
<p class="wp-block-paragraph">In this installment, we’ll look at 13 questions related to confidence in institutions. We’ll start with a detailed look at confidence in “the people running Congress”, and then summarize results from the other questions. The <a href="https://gssdataexplorer.norc.org/variables/459/vshow" target="_blank" rel="noreferrer noopener">complete survey question</a> is:</p>
<blockquote class="wp-block-quote is-layout-flow wp-block-quote-is-layout-flow">
<p class="wp-block-paragraph">I am going to name some institutions in this country. As far as the people running these institutions are concerned, would you say you have a great deal of confidence, only some confidence, or hardly any confidence at all in […] Congress.</p>
</blockquote>
<p class="wp-block-paragraph">The following figure shows the fraction of people who answered “a great deal of confidence” or “only some confidence,” and a smooth line fitted to the raw percentages.</p>
<figure class="wp-block-image" id="conlegis-time-model"><img loading="lazy" decoding="async" width="1145" height="790" src="https://www.allendowney.com/blog/wp-content/uploads/2026/05/time_model_conlegis_-e47a9b867ea68609944d3abe98446e29.png" alt="Time-only model, confidence in the people running Congress." class="wp-image-1808" srcset="https://www.allendowney.com/blog/wp-content/uploads/2026/05/time_model_conlegis_-e47a9b867ea68609944d3abe98446e29.png 1145w, https://www.allendowney.com/blog/wp-content/uploads/2026/05/time_model_conlegis_-e47a9b867ea68609944d3abe98446e29-300x207.png 300w, https://www.allendowney.com/blog/wp-content/uploads/2026/05/time_model_conlegis_-e47a9b867ea68609944d3abe98446e29-1024x707.png 1024w, https://www.allendowney.com/blog/wp-content/uploads/2026/05/time_model_conlegis_-e47a9b867ea68609944d3abe98446e29-768x530.png 768w, https://www.allendowney.com/blog/wp-content/uploads/2026/05/time_model_conlegis_-e47a9b867ea68609944d3abe98446e29-391x270.png 391w" sizes="auto, (max-width: 1145px) 100vw, 1145px" /></figure>
<p class="wp-block-paragraph">The long-term trend is downward, from about 80% during the first iteration of the survey to below 50% in the most recent iterations. But there are ups and downs.</p>
<p class="wp-block-paragraph">It looks like confidence was increasing during the 1980s before collapsing in the early 1990s. Possible causes of the decline include:</p>
<ul class="wp-block-list">
<li>The <a href="https://en.wikipedia.org/wiki/House_banking_scandal" target="_blank" rel="noreferrer noopener">House banking scandal</a>, also known as Rubbergate, and the <a href="https://en.wikipedia.org/wiki/Congressional_Post_Office_scandal" target="_blank" rel="noreferrer noopener">Congressional Post Office scandal</a>.</li>
<li>Increased polarization and perception of dysfunction during the period when <a href="https://en.wikipedia.org/wiki/Newt_Gingrich#Speaker_of_the_House" target="_blank" rel="noreferrer noopener">Newt Gingrich</a> was minority whip (1989-1995).</li>
<li>An <a href="https://en.wikipedia.org/wiki/Early_1990s_recession_in_the_United_States" target="_blank" rel="noreferrer noopener">economic recession</a> from 1990 into 1991.</li>
</ul>
<p class="wp-block-paragraph">Confidence in Congress recovered between 1995 and 2005, and declined again between 2005 and 2015. A likely contributor is the <a href="https://en.wikipedia.org/wiki/Great_Recession" target="_blank" rel="noreferrer noopener">Great Recession</a> from late 2007 to mid-2009.</p>
<p class="wp-block-paragraph">This period also saw the rise of anti-establishment politics, including the <a href="https://en.wikipedia.org/wiki/Tea_Party_movement" target="_blank" rel="noreferrer noopener">Tea Party movement</a> and <a href="https://en.wikipedia.org/wiki/Ron_Paul" target="_blank" rel="noreferrer noopener">Ron Paul’s</a> presidential campaign.</p>
<p class="wp-block-paragraph">Now we’ll decompose these changes into period and cohort effects.</p>
<h3 class="wp-block-heading" id="period-and-cohort-effects">Period and cohort effects</h3>
<p class="wp-block-paragraph">Using the <a href="https://allendowney.github.io/CultureWar/tech-report/" target="_blank" rel="noreferrer noopener">Bayesian model described here</a> we can estimate a latent “confidence in Congress” factor for each birth cohort over time. The following figure shows these estimates; each line represents a single birth year.</p>
<figure class="wp-block-image" id="conlegis-cohort-trajectories"><img loading="lazy" decoding="async" width="1330" height="778" src="https://www.allendowney.com/blog/wp-content/uploads/2026/05/cohort_trajectory_co-d5cd0d30431d1f3f08bcc503ebb4d786.png" alt="Cohort trajectories, percent with a great deal or only some confidence in the people running Congress." class="wp-image-1814" srcset="https://www.allendowney.com/blog/wp-content/uploads/2026/05/cohort_trajectory_co-d5cd0d30431d1f3f08bcc503ebb4d786.png 1330w, https://www.allendowney.com/blog/wp-content/uploads/2026/05/cohort_trajectory_co-d5cd0d30431d1f3f08bcc503ebb4d786-300x175.png 300w, https://www.allendowney.com/blog/wp-content/uploads/2026/05/cohort_trajectory_co-d5cd0d30431d1f3f08bcc503ebb4d786-1024x599.png 1024w, https://www.allendowney.com/blog/wp-content/uploads/2026/05/cohort_trajectory_co-d5cd0d30431d1f3f08bcc503ebb4d786-768x449.png 768w, https://www.allendowney.com/blog/wp-content/uploads/2026/05/cohort_trajectory_co-d5cd0d30431d1f3f08bcc503ebb4d786-462x270.png 462w" sizes="auto, (max-width: 1330px) 100vw, 1330px" /></figure>
<p class="wp-block-paragraph">Those results are easier to interpret if we factor out the cohort effect (keeping the mixture of survey years constant) and the period effect (keeping the mixture of cohorts constant). The following figure shows the standardized cohort effect.</p>
<figure class="wp-block-image" id="conlegis-cohort-standardized"><img loading="lazy" decoding="async" width="1145" height="790" src="https://www.allendowney.com/blog/wp-content/uploads/2026/05/cohort_standardized_-aca7608b25112981c03dc33fffe90a93.png" alt="Standardized cohort effect with fixed time mix, confidence in Congress." class="wp-image-1812" srcset="https://www.allendowney.com/blog/wp-content/uploads/2026/05/cohort_standardized_-aca7608b25112981c03dc33fffe90a93.png 1145w, https://www.allendowney.com/blog/wp-content/uploads/2026/05/cohort_standardized_-aca7608b25112981c03dc33fffe90a93-300x207.png 300w, https://www.allendowney.com/blog/wp-content/uploads/2026/05/cohort_standardized_-aca7608b25112981c03dc33fffe90a93-1024x707.png 1024w, https://www.allendowney.com/blog/wp-content/uploads/2026/05/cohort_standardized_-aca7608b25112981c03dc33fffe90a93-768x530.png 768w, https://www.allendowney.com/blog/wp-content/uploads/2026/05/cohort_standardized_-aca7608b25112981c03dc33fffe90a93-391x270.png 391w" sizes="auto, (max-width: 1145px) 100vw, 1145px" /></figure>
<p class="wp-block-paragraph">Among people born between 1900 and 1950, there is almost no change. Then starting with people born in the 1960s, confidence in Congress has increased consistently and substantially.</p>
<p class="wp-block-paragraph">To interpret this result, it is helpful to go back to the previous figure. Starting in the upper left:</p>
<ul class="wp-block-list">
<li>Among people born in the 1960s and 1970s, about 80% reported confidence in Congress when they were surveyed as young adults.</li>
<li>Among people born in the 1980s and 1990s, it was closer to 70%.</li>
<li>And among people born in the 2000s it’s below 70%.</li>
</ul>
<p class="wp-block-paragraph">The entry point of each cohort is below the entry point of previous cohorts, but because these entry points are above the declining trend of previous generations, this <em>relative</em> optimism is interpreted as an increasing cohort effect.</p>
<p class="wp-block-paragraph">So we should not conclude that younger generations are more confident in Congress, only that when they are first surveyed, they start out above the trajectory of previous cohorts.</p>
<p class="wp-block-paragraph">As a simplification, we might imagine an 18-year-old entering adulthood with a relatively idealized understanding of American government — shaped by civics classes and maybe a school trip to Washington D.C. — before later political experiences erode some of that confidence.</p>
<p class="wp-block-paragraph">Another possibility is that younger generations have grown up with lower expectations of government, so when they say they have “some confidence”, they might be evaluating Congress against a lower standard.</p>
<p class="wp-block-paragraph">The following figure shows the estimated period effect, with the mix of cohorts held constant.</p>
<figure class="wp-block-image" id="conlegis-period-standardized"><img loading="lazy" decoding="async" width="1145" height="790" src="https://www.allendowney.com/blog/wp-content/uploads/2026/05/time_standardized_co-d65cdea9156d375abd801cc2826c9844.png" alt="Standardized period effect with fixed cohort mix, Congress." class="wp-image-1807" srcset="https://www.allendowney.com/blog/wp-content/uploads/2026/05/time_standardized_co-d65cdea9156d375abd801cc2826c9844.png 1145w, https://www.allendowney.com/blog/wp-content/uploads/2026/05/time_standardized_co-d65cdea9156d375abd801cc2826c9844-300x207.png 300w, https://www.allendowney.com/blog/wp-content/uploads/2026/05/time_standardized_co-d65cdea9156d375abd801cc2826c9844-1024x707.png 1024w, https://www.allendowney.com/blog/wp-content/uploads/2026/05/time_standardized_co-d65cdea9156d375abd801cc2826c9844-768x530.png 768w, https://www.allendowney.com/blog/wp-content/uploads/2026/05/time_standardized_co-d65cdea9156d375abd801cc2826c9844-391x270.png 391w" sizes="auto, (max-width: 1145px) 100vw, 1145px" /></figure>
<p class="wp-block-paragraph">This decline is steeper than what we saw in the time-only model, because we have factored out the mitigating effect of relative optimism in recent generations.</p>
<h3 class="wp-block-heading" id="government-institutions">Government Institutions</h3>
<p class="wp-block-paragraph">Now we’ll apply the same analysis to questions about the executive branch of the federal government, the Supreme Court, and the military (technically part of the executive branch).</p>
<p class="wp-block-paragraph">The following figure shows the estimated cohort effects for each of these institutions.</p>
<figure class="wp-block-image" id="cluster-gov-cohort"><img loading="lazy" decoding="async" width="1145" height="764" src="https://www.allendowney.com/blog/wp-content/uploads/2026/05/con_cluster_1_govern-7c461121f9363f4e9a2440f4a41ce384.png" alt="Government and security institutions, standardized cohort component (uniform survey years)." class="wp-image-1811" srcset="https://www.allendowney.com/blog/wp-content/uploads/2026/05/con_cluster_1_govern-7c461121f9363f4e9a2440f4a41ce384.png 1145w, https://www.allendowney.com/blog/wp-content/uploads/2026/05/con_cluster_1_govern-7c461121f9363f4e9a2440f4a41ce384-300x200.png 300w, https://www.allendowney.com/blog/wp-content/uploads/2026/05/con_cluster_1_govern-7c461121f9363f4e9a2440f4a41ce384-1024x683.png 1024w, https://www.allendowney.com/blog/wp-content/uploads/2026/05/con_cluster_1_govern-7c461121f9363f4e9a2440f4a41ce384-768x512.png 768w, https://www.allendowney.com/blog/wp-content/uploads/2026/05/con_cluster_1_govern-7c461121f9363f4e9a2440f4a41ce384-405x270.png 405w" sizes="auto, (max-width: 1145px) 100vw, 1145px" /></figure>
<p class="wp-block-paragraph">And the following figure shows the period effect, after factoring out the cohort effect.</p>
<figure class="wp-block-image" id="cluster-gov-standardized-period"><img loading="lazy" decoding="async" width="1145" height="764" src="https://www.allendowney.com/blog/wp-content/uploads/2026/05/con_cluster_1_govern-b24ed098d4d8b3b779b1face8e1cd0be.png" alt="Government and security institutions, standardized period component (fixed cohort mix)." class="wp-image-1813" srcset="https://www.allendowney.com/blog/wp-content/uploads/2026/05/con_cluster_1_govern-b24ed098d4d8b3b779b1face8e1cd0be.png 1145w, https://www.allendowney.com/blog/wp-content/uploads/2026/05/con_cluster_1_govern-b24ed098d4d8b3b779b1face8e1cd0be-300x200.png 300w, https://www.allendowney.com/blog/wp-content/uploads/2026/05/con_cluster_1_govern-b24ed098d4d8b3b779b1face8e1cd0be-1024x683.png 1024w, https://www.allendowney.com/blog/wp-content/uploads/2026/05/con_cluster_1_govern-b24ed098d4d8b3b779b1face8e1cd0be-768x512.png 768w, https://www.allendowney.com/blog/wp-content/uploads/2026/05/con_cluster_1_govern-b24ed098d4d8b3b779b1face8e1cd0be-405x270.png 405w" sizes="auto, (max-width: 1145px) 100vw, 1145px" /></figure>
<p class="wp-block-paragraph">The results for the executive branch are similar to the results for Congress.</p>
<ul class="wp-block-list">
<li>The cohort effect is flat between people born in the 1900s and 1950s, and increasing after that.</li>
<li>The period effect declines substantially and consistently — without the ups and downs of confidence in Congress.</li>
</ul>
<p class="wp-block-paragraph">When respondents are asked about the “executive branch”, it’s not clear whether they think primarily about the president, federal agencies, or the federal government in general.</p>
<p class="wp-block-paragraph">The patterns for the military and Supreme Court are different.</p>
<ul class="wp-block-list">
<li>Confidence in the military is generally high. The cohort effect declined gradually, and possibly more steeply among people born after 1980. The period effect gradually increased.</li>
<li>Confidence in the Supreme Court is higher than confidence in other branches, although the period effect has dropped steeply since 2015. The cohort effect increased among people born between 1900 and 1960; among more recent generations it is gradually declining.</li>
</ul>
<p class="wp-block-paragraph">Historically, the Court cultivated an image of being above politics; that perception weakened substantially in the 2010s. In March 2016, Merrick Garland was nominated to the Supreme Court after the death of Antonin Scalia. The Republican majority in the Senate refused to hold a hearing or vote on his nomination. The seat remained empty until Donald Trump nominated, and the Senate confirmed, Neil Gorsuch, who is considered to be more conservative. To many liberals, the Senate’s 293-day blockade undermined the legitimacy of the Court.</p>
<p class="wp-block-paragraph">Then when Ruth Bader Ginsburg died in September 2020, Donald Trump nominated Amy Coney Barrett and the Senate confirmed her 8 days before the 2020 presidential election, in a process criticized by Democratic leaders as illegitimate.</p>
<p class="wp-block-paragraph">These appointments, along with the confirmation of Brett Kavanaugh in 2018, shifted the composition of the Court toward conservatives, forming what is now described as a 6-3 supermajority of conservative justices.</p>
<p class="wp-block-paragraph">Since then, the Supreme Court has issued several decisions contrary to majority public opinion, most notably the 2022 decision overturning <em>Roe v. Wade</em>. Other unpopular decisions weakened gun control and limited federal regulatory authority, especially over environmental policy. Many of these decisions have been perceived, especially on the left, to be motivated by politics rather than constitutional principles and precedent.</p>
<p class="wp-block-paragraph">The slope of the cohort effect might reflect a generational change in associations with the Supreme Court. Older cohorts may associate the Supreme Court with landmark decisions like Brown v. Board of Education and the expansion of civil rights. Younger cohorts may instead associate it with partisan conflict, blocked reforms, and ideological polarization. Older generations might also have been more deferential toward the institution itself. Younger generations, exposed to more adversarial and partisan media coverage, might be less inclined to deference.</p>
<h3 class="wp-block-heading" id="economic-institutions">Economic institutions</h3>
<p class="wp-block-paragraph">The following figures show the cohort and period effects for confidence in economic institutions: banks, major companies, and organized labor.</p>
<figure class="wp-block-image" id="cluster-econ-cohort"><img loading="lazy" decoding="async" width="1145" height="764" src="https://www.allendowney.com/blog/wp-content/uploads/2026/05/con_cluster_2_econom-b4cf1eea3eb5290377d151bac981fdaf.png" alt="Economic institutions, standardized cohort component." class="wp-image-1809" srcset="https://www.allendowney.com/blog/wp-content/uploads/2026/05/con_cluster_2_econom-b4cf1eea3eb5290377d151bac981fdaf.png 1145w, https://www.allendowney.com/blog/wp-content/uploads/2026/05/con_cluster_2_econom-b4cf1eea3eb5290377d151bac981fdaf-300x200.png 300w, https://www.allendowney.com/blog/wp-content/uploads/2026/05/con_cluster_2_econom-b4cf1eea3eb5290377d151bac981fdaf-1024x683.png 1024w, https://www.allendowney.com/blog/wp-content/uploads/2026/05/con_cluster_2_econom-b4cf1eea3eb5290377d151bac981fdaf-768x512.png 768w, https://www.allendowney.com/blog/wp-content/uploads/2026/05/con_cluster_2_econom-b4cf1eea3eb5290377d151bac981fdaf-405x270.png 405w" sizes="auto, (max-width: 1145px) 100vw, 1145px" /></figure>
<p class="wp-block-paragraph"></p>
<figure class="wp-block-image" id="cluster-econ-standardized-period"><img loading="lazy" decoding="async" width="1145" height="764" src="https://www.allendowney.com/blog/wp-content/uploads/2026/05/con_cluster_2_econom-76a4be0f163f28d139a677ac90cfd0e5.png" alt="Economic institutions, standardized period component." class="wp-image-1806" srcset="https://www.allendowney.com/blog/wp-content/uploads/2026/05/con_cluster_2_econom-76a4be0f163f28d139a677ac90cfd0e5.png 1145w, https://www.allendowney.com/blog/wp-content/uploads/2026/05/con_cluster_2_econom-76a4be0f163f28d139a677ac90cfd0e5-300x200.png 300w, https://www.allendowney.com/blog/wp-content/uploads/2026/05/con_cluster_2_econom-76a4be0f163f28d139a677ac90cfd0e5-1024x683.png 1024w, https://www.allendowney.com/blog/wp-content/uploads/2026/05/con_cluster_2_econom-76a4be0f163f28d139a677ac90cfd0e5-768x512.png 768w, https://www.allendowney.com/blog/wp-content/uploads/2026/05/con_cluster_2_econom-76a4be0f163f28d139a677ac90cfd0e5-405x270.png 405w" sizes="auto, (max-width: 1145px) 100vw, 1145px" /></figure>
<p class="wp-block-paragraph">Confidence in these institutions is generally high. Looking at the cohort effects, the most salient feature is increased confidence in organized labor among people born after 1940.</p>
<p class="wp-block-paragraph">A possible explanation is that younger cohorts have less exposure to organized labor. Older generations were more likely to be affected by strikes and related economic disruption, and more likely to be aware of corruption in labor unions. As union membership has declined and the gig economy has expanded, younger cohorts are less aware of the negative aspects of organized labor, including dues, and more likely to perceive their lack of negotiating power in the labor market. Also, anti-labor ideology has declined since the end of the Cold War, as the framing has shifted from “labor versus management” to “workers versus corporations”.</p>
<p class="wp-block-paragraph">By comparison with the cohort effects, the period effects are modest:</p>
<ul class="wp-block-list">
<li>The period effect on organized labor is almost unchanged since the 1980s — the change we see over time is almost entirely due to generational replacement.</li>
<li>The period effect on confidence in major companies has declined somewhat.</li>
<li>The trend for banks and financial institutions is more complicated — arguably driven by shorter-term period effects like scandals and financial crises. The first notable downturn, in the 1980s, coincides with the <a href="https://en.wikipedia.org/wiki/Savings_and_loan_crisis" target="_blank" rel="noreferrer noopener">savings and loan crisis</a>, when hundreds of financial institutions failed and taxpayers absorbed large bailout costs, followed by an <a href="https://en.wikipedia.org/wiki/Early_1990s_recession_in_the_United_States" target="_blank" rel="noreferrer noopener">economic recession</a> from 1990 into 1991. The larger downturn around 2008 coincides with the <a href="https://en.wikipedia.org/wiki/2008_financial_crisis" target="_blank" rel="noreferrer noopener">2008 global financial crisis</a>, when taxpayers were hit with even larger bailout costs, and public anger at “private gains, public losses” came to a focus in the <a href="https://en.wikipedia.org/wiki/Occupy_Wall_Street" target="_blank" rel="noreferrer noopener">Occupy Wall Street protests</a>.</li>
</ul>
<h3 class="wp-block-heading" id="professions-knowledge-and-religion">Professions, knowledge, and religion</h3>
<p class="wp-block-paragraph">The following figures show estimated cohort and period effects for confidence in education, medicine, the scientific community, and organized religion.</p>
<figure class="wp-block-image" id="cluster-prof-cohort"><img loading="lazy" decoding="async" width="1145" height="764" src="https://www.allendowney.com/blog/wp-content/uploads/2026/05/con_cluster_3_profes-14bdbff63efcff6380045908aa3157ab.png" alt="Professions and knowledge institutions, standardized cohort component." class="wp-image-1816" srcset="https://www.allendowney.com/blog/wp-content/uploads/2026/05/con_cluster_3_profes-14bdbff63efcff6380045908aa3157ab.png 1145w, https://www.allendowney.com/blog/wp-content/uploads/2026/05/con_cluster_3_profes-14bdbff63efcff6380045908aa3157ab-300x200.png 300w, https://www.allendowney.com/blog/wp-content/uploads/2026/05/con_cluster_3_profes-14bdbff63efcff6380045908aa3157ab-1024x683.png 1024w, https://www.allendowney.com/blog/wp-content/uploads/2026/05/con_cluster_3_profes-14bdbff63efcff6380045908aa3157ab-768x512.png 768w, https://www.allendowney.com/blog/wp-content/uploads/2026/05/con_cluster_3_profes-14bdbff63efcff6380045908aa3157ab-405x270.png 405w" sizes="auto, (max-width: 1145px) 100vw, 1145px" /></figure>
<p class="wp-block-paragraph"></p>
<figure class="wp-block-image" id="cluster-prof-standardized-period"><img loading="lazy" decoding="async" width="1145" height="764" src="https://www.allendowney.com/blog/wp-content/uploads/2026/05/con_cluster_3_profes-f5418c000cfe9c18849ed481e1182500.png" alt="Professions and knowledge institutions, standardized period component." class="wp-image-1805" srcset="https://www.allendowney.com/blog/wp-content/uploads/2026/05/con_cluster_3_profes-f5418c000cfe9c18849ed481e1182500.png 1145w, https://www.allendowney.com/blog/wp-content/uploads/2026/05/con_cluster_3_profes-f5418c000cfe9c18849ed481e1182500-300x200.png 300w, https://www.allendowney.com/blog/wp-content/uploads/2026/05/con_cluster_3_profes-f5418c000cfe9c18849ed481e1182500-1024x683.png 1024w, https://www.allendowney.com/blog/wp-content/uploads/2026/05/con_cluster_3_profes-f5418c000cfe9c18849ed481e1182500-768x512.png 768w, https://www.allendowney.com/blog/wp-content/uploads/2026/05/con_cluster_3_profes-f5418c000cfe9c18849ed481e1182500-405x270.png 405w" sizes="auto, (max-width: 1145px) 100vw, 1145px" /></figure>
<p class="wp-block-paragraph">Confidence in these institutions is highest for science and medicine, lower for education and religion.</p>
<p class="wp-block-paragraph">Looking at the period effects, they are all in decline. Confidence in education declined most steeply; confidence in the scientific community is relatively stable, although it declines after 2020.</p>
<p class="wp-block-paragraph">Thinking about confidence in education, it might be useful to separate colleges and universities from K-12 schools.</p>
<ul class="wp-block-list">
<li>In higher education, the decline might be due to increasing tuition and student debt, credential inflation, and increasing uncertainty about the economic return on a college degree, especially among majors in the arts and humanities. More recently, confidence in universities has decreased steeply, especially among conservatives, due to the perception of ideological bias.</li>
<li>In K-12 education, declining confidence might be related to anxiety about standardized testing, international competition, and especially around the <a href="https://en.wikipedia.org/wiki/No_Child_Left_Behind_Act" target="_blank" rel="noreferrer noopener">No Child Left Behind Act</a> in 2001, the framing of public schools as underperforming institutions requiring accountability reforms and federal intervention. Also, public schools have increasingly become focal points for political conflicts about curriculum, race, gender, religion, and parental authority.</li>
</ul>
<p class="wp-block-paragraph">Most of the cohort effects have increased modestly; in particular confidence in education is higher among people born after 1980, compared to previous generations observed at the same time. But for these institutions, the interaction of the period and cohort effect is similar to what we saw for Congress — it’s not that recent generations have <em>more</em> confidence, it’s just that when they are surveyed as young adults, they come in at entry points above the declining trend of previous generations.</p>
<p class="wp-block-paragraph">Confidence in organized religion is the exception — the period and cohort effects both trend downward, so the decline is additive. A likely contributor to the period effect is growing public awareness of <a href="https://en.wikipedia.org/wiki/Catholic_Church_sex_abuse_cases_in_the_United_States" target="_blank" rel="noreferrer noopener">sexual abuse and institutional coverups in the Catholic Church</a>, which received national attention beginning in the 1980s, escalated after the <a href="https://en.wikipedia.org/wiki/Sexual_abuse_scandal_in_the_Archdiocese_of_Boston" target="_blank" rel="noreferrer noopener">Boston Globe investigations</a> published in 2002, and continues to the present with additional revelations in the United States and other countries. But the decline is not limited to the Catholic Church, and it began before these scandals were widely known.</p>
<p class="wp-block-paragraph">The cohort effect likely reflects broader secularization trends, including declining religious affiliation, lower church attendance, and weakening institutional authority among younger generations.</p>
<h3 class="wp-block-heading" id="media">Media</h3>
<p class="wp-block-paragraph">Finally, the following figures show estimated cohort and period effects for confidence in television and the press.</p>
<figure class="wp-block-image" id="cluster-media-cohort"><img loading="lazy" decoding="async" width="1145" height="764" src="https://www.allendowney.com/blog/wp-content/uploads/2026/05/con_cluster_4_media_-8bf3f75d17ac4f1f8991025f1051ce52.png" alt="Media, standardized cohort component." class="wp-image-1815" srcset="https://www.allendowney.com/blog/wp-content/uploads/2026/05/con_cluster_4_media_-8bf3f75d17ac4f1f8991025f1051ce52.png 1145w, https://www.allendowney.com/blog/wp-content/uploads/2026/05/con_cluster_4_media_-8bf3f75d17ac4f1f8991025f1051ce52-300x200.png 300w, https://www.allendowney.com/blog/wp-content/uploads/2026/05/con_cluster_4_media_-8bf3f75d17ac4f1f8991025f1051ce52-1024x683.png 1024w, https://www.allendowney.com/blog/wp-content/uploads/2026/05/con_cluster_4_media_-8bf3f75d17ac4f1f8991025f1051ce52-768x512.png 768w, https://www.allendowney.com/blog/wp-content/uploads/2026/05/con_cluster_4_media_-8bf3f75d17ac4f1f8991025f1051ce52-405x270.png 405w" sizes="auto, (max-width: 1145px) 100vw, 1145px" /></figure>
<p class="wp-block-paragraph"></p>
<figure class="wp-block-image" id="cluster-media-standardized-period"><img loading="lazy" decoding="async" width="1145" height="764" src="https://www.allendowney.com/blog/wp-content/uploads/2026/05/con_cluster_4_media_-db77e283c289a556c23c800a199f1ce9.png" alt="Media, standardized period component." class="wp-image-1810" srcset="https://www.allendowney.com/blog/wp-content/uploads/2026/05/con_cluster_4_media_-db77e283c289a556c23c800a199f1ce9.png 1145w, https://www.allendowney.com/blog/wp-content/uploads/2026/05/con_cluster_4_media_-db77e283c289a556c23c800a199f1ce9-300x200.png 300w, https://www.allendowney.com/blog/wp-content/uploads/2026/05/con_cluster_4_media_-db77e283c289a556c23c800a199f1ce9-1024x683.png 1024w, https://www.allendowney.com/blog/wp-content/uploads/2026/05/con_cluster_4_media_-db77e283c289a556c23c800a199f1ce9-768x512.png 768w, https://www.allendowney.com/blog/wp-content/uploads/2026/05/con_cluster_4_media_-db77e283c289a556c23c800a199f1ce9-405x270.png 405w" sizes="auto, (max-width: 1145px) 100vw, 1145px" /></figure>
<p class="wp-block-paragraph">There is almost no cohort effect, although the most recent cohorts might have a little more confidence in television.</p>
<p class="wp-block-paragraph">The headline here is the period effect, which is consistently downward, and steeper for the press than television. The steepest part of the decline for both media started around 1990, shortly after the 1987 abolition of the <a href="https://en.wikipedia.org/wiki/Fairness_doctrine" target="_blank" rel="noreferrer noopener">fairness doctrine</a>, which required broadcast coverage of controversial topics to be “fair in the sense that it provides an opportunity for the presentation of contrasting points of view,” as described in the <a href="https://www.fcc.gov/document/editorializing-broadcast-licensees" target="_blank" rel="noreferrer noopener">1949 FCC report</a> that established the doctrine.</p>
<p class="wp-block-paragraph">The end of the fairness doctrine coincided with the rise of talk radio programs with explicit political viewpoints, including <a href="https://en.wikipedia.org/wiki/The_Rush_Limbaugh_Show" target="_blank" rel="noreferrer noopener">The Rush Limbaugh Show</a>, which was nationally syndicated in 1988.</p>
<p class="wp-block-paragraph">Cable television news followed, including <a href="https://en.wikipedia.org/wiki/Fox_News" target="_blank" rel="noreferrer noopener">Fox News Channel</a> in 1996, with an explicit conservative orientation, and <a href="https://en.wikipedia.org/wiki/MSNBC" target="_blank" rel="noreferrer noopener">MSNBC</a>, which developed a more liberal identity in the 2000s.</p>
<p class="wp-block-paragraph">During this period, more generally, media audiences became more fragmented. Prior to 1980, most Americans were exposed to a small number of shared news sources, notably the three major television networks. Talk radio and cable television offered more options and less common experience.</p>
<p class="wp-block-paragraph">And then the internet happened, starting in the 1990s with online news and political blogs, including the <a href="https://en.wikipedia.org/wiki/Drudge_Report" target="_blank" rel="noreferrer noopener">Drudge Report</a> which started as a weekly email newsletter in 1995, and rose to national prominence when it broke the <a href="https://en.wikipedia.org/wiki/Clinton%E2%80%93Lewinsky_scandal" target="_blank" rel="noreferrer noopener">Clinton-Lewinsky scandal</a> in 1998.</p>
<p class="wp-block-paragraph">Social media followed. YouTube was founded in 2005; Facebook and Twitter launched in 2006. While these platforms have become important sources of news for many Americans, engagement-driven algorithms often promote emotionally provocative and polarizing content over careful reporting. The rise of the internet contributed to the decline of local newspapers, and eventually national newspapers as well.</p>
<p class="wp-block-paragraph">Ownership of television stations became increasingly consolidated following the <a href="https://en.wikipedia.org/wiki/Telecommunications_Act_of_1996" target="_blank" rel="noreferrer noopener">1996 Telecommunications Act</a>, allowing a small number of national media companies to control larger shares of local news programming. The effect of this consolidation is explained in <a href="https://www.vox.com/policy-and-politics/2018/4/2/17189302/sinclair-broadcast-fake-news-biased-trump-viral-video" target="_blank" rel="noreferrer noopener">this Vox article</a> and memorably demonstrated in <a href="https://www.youtube.com/watch?v=hWLjYJ4BzvI" target="_blank" rel="noreferrer noopener">this Deadspin compilation</a> showing dozens of TV news anchors reading nearly identical scripts provided by the <a href="https://en.wikipedia.org/wiki/Sinclair_Broadcast_Group" target="_blank" rel="noreferrer noopener">Sinclair Broadcast Group</a>, which requires the channels it owns to air segments called <a href="https://www.nytimes.com/2017/05/12/business/media/sinclair-broadcast-komo-conservative-media.html" target="_blank" rel="noreferrer noopener">“must-runs”</a> — many of them presenting conservative talking points.</p>
<p class="wp-block-paragraph">Finally, since the beginning of his presidential campaign in 2015, Donald Trump has repeatedly denigrated television and print media, frequently describing unfavorable coverage as “fake news” and labeling journalists “enemies of the people.” These attacks likely contribute to declining confidence in the press, especially among Republicans.</p>
<h3 class="wp-block-heading" id="negativity-bias">Negativity Bias</h3>
<p class="wp-block-paragraph">In the previous examples, you might notice that I offer explanations for the downturns, but no explanation for the upturns. That’s because bad things, like scandals and economic crises, often happen quickly and they get a lot of coverage; good things often happen slowly and continue without comment.</p>
<p class="wp-block-paragraph">For many institutions, no news is good news. When they do their jobs, they don’t get much attention, and public confidence drifts higher, even without specific positive events or coverage.</p>
<p class="wp-block-paragraph">So I want to end this article by highlighting some of the positive results we see in this data:</p>
<ul class="wp-block-list">
<li>Confidence in education, science, and medicine is high and although the period effects are negative, the cohort effects are positive, which bodes well for the future.</li>
<li>Confidence in financial institutions and organized labor is high.</li>
<li>Confidence in government is lower and declining, but as each generation of young adults starts out more optimistic than their elders, there is hope for a turnaround.</li>
</ul>
<p class="wp-block-paragraph">But the recent steep decline of confidence in the Supreme Court is a concern, as is the loss of confidence in the media. It’s hard to find a positive take on those trends.</p>
<p class="wp-block-paragraph"><a href="https://allendowney.github.io/CultureWar//blog7-hapgen"></a><a href="https://allendowney.github.io/CultureWar//blog7-hapgen"></a></p>
<p class="wp-block-paragraph"></p>
<p>The post <a href="https://www.allendowney.com/blog/2026/05/19/confidence-in-institutions/">Confidence in Institutions</a> appeared first on <a href="https://www.allendowney.com/blog">Probably Overthinking It</a>.</p>
]]></content:encoded>
<post-id xmlns="com-wordpress:feed-additions:1">1803</post-id> </item>
<item>
<title>Planning for your midlife crisis</title>
<link>https://www.allendowney.com/blog/2026/05/01/planning-for-your-midlife-crisis/</link>
<dc:creator><![CDATA[AllenDowney]]></dc:creator>
<pubDate>Fri, 01 May 2026 19:34:53 +0000</pubDate>
<category><![CDATA[Uncategorized]]></category>
<category><![CDATA[life expectancy]]></category>
<category><![CDATA[mortality]]></category>
<category><![CDATA[ODSC]]></category>
<guid isPermaLink="false">https://www.allendowney.com/blog/?p=1794</guid>
<description><![CDATA[<p>Yesterday I presented a talk at ODSC East 2026, called “Counterfactual Analysis with Bayesian Models: What Drives the Life Expectancy Gap?” Here’s the abstract Across nearly every country in the world, women live longer than men—but the size of this gap varies from about two years in some countries to more than twelve in others. What explains these differences, and how much of the gap can be closed? In this talk, I present a practical approach to counterfactual analysis using...</p>
<p class="read-more"><a class="btn btn-default" href="https://www.allendowney.com/blog/2026/05/01/planning-for-your-midlife-crisis/"> Read More<span class="screen-reader-text"> Read More</span></a></p>
<p>The post <a href="https://www.allendowney.com/blog/2026/05/01/planning-for-your-midlife-crisis/">Planning for your midlife crisis</a> appeared first on <a href="https://www.allendowney.com/blog">Probably Overthinking It</a>.</p>
]]></description>
<content:encoded><![CDATA[
<p class="wp-block-paragraph">Yesterday I presented a talk at ODSC East 2026, called “Counterfactual Analysis with Bayesian Models: What Drives the Life Expectancy Gap?” Here’s the abstract</p>
<blockquote class="wp-block-quote is-layout-flow wp-block-quote-is-layout-flow">
<p class="wp-block-paragraph">Across nearly every country in the world, women live longer than men—but the size of this gap varies from about two years in some countries to more than twelve in others. What explains these differences, and how much of the gap can be closed?</p>
<p class="wp-block-paragraph">In this talk, I present a practical approach to counterfactual analysis using Bayesian regression models. Using publicly available mortality data, we build a model that relates the life expectancy gap between men and women to differences in cause-specific death rates, including homicide, drug overdoses, traffic fatalities, smoking-related disease, and chronic illness.</p>
<p class="wp-block-paragraph">The model generates posterior simulations that answer “what-if” questions. For example: How much smaller would the U.S. life expectancy gap be if homicide rates matched those in Western Europe?</p>
<p class="wp-block-paragraph">The talk presents the workflow—from assembling global datasets to fitting interpretable Bayesian models with PyMC and generating counterfactual simulations. Attendees will learn how Bayesian models can support explainable modeling and analysis under uncertainty.</p>
</blockquote>
<p class="wp-block-paragraph">I think the talk went well, and we got some good questions at the end. There’s no recording, unfortunately, <a href="https://docs.google.com/presentation/d/e/2PACX-1vSiwjA6Mi95poqGQJiXw7Mdy0BgPa-aEmVhJHXwP35QRjt2dduEEN53yZi4fnpAReVaS-EDWS3CwMt1/pub?start=false&loop=false&delayms=3000">but my slides are here</a>. And if you want to know more, I have a series of blog posts on Substack</p>
<ul class="wp-block-list">
<li><a href="https://allendowney.substack.com/p/the-gender-gap-in-life-expectancy">The Gender Gap in Life Expectancy</a></li>
<li><a href="https://allendowney.substack.com/p/what-drives-the-life-expectancy-gender">What Drives the Life Expectancy Gender Gap?</a></li>
<li><a href="https://allendowney.substack.com/p/how-much-of-the-life-expectancy-gap">How Much of the Life Expectancy Gap Could We Close?</a></li>
<li><a href="https://allendowney.substack.com/p/international-patterns-in-the-life">International Patterns in the Life Expectancy Gap</a></li>
</ul>
<p class="wp-block-paragraph">The fifth and final post is on the way. In the meantime, here’s a quick post on a related topic.</p>
<h2 class="wp-block-heading">Are you middle-aged?</h2>
<p class="wp-block-paragraph">Here’s a question from Reddit’s <a href="https://www.reddit.com/r/stupidquestions/comments/1sxesux/what_age_is_actually_considered_middle_age/">Stupid Questions forum</a>:</p>
<blockquote class="wp-block-quote is-layout-flow wp-block-quote-is-layout-flow">
<p class="wp-block-paragraph">I always thought middle age was in your 40s but since life expectancy is around 75 or so, wouldn’t it be about 35?</p>
</blockquote>
<p class="wp-block-paragraph">If life expectancy is 75, you might think the midpoint is half that, which is 37.5. But if 75 is life expectancy <em>at birth</em> and you survive to age 37.5, your life expectancy <em>at that age</em> is higher than 75. So 37.5 is not halfway!</p>
<p class="wp-block-paragraph">If we really want to find the midpoint – and it wouldn’t be <em>Probably Overthinking It</em> if we didn’t – we have to find the age where your expected remaining lifetime equals your current age.</p>
<p class="wp-block-paragraph">Let’s do it.</p>
<h2 class="wp-block-heading">Data</h2>
<p class="wp-block-paragraph">From the <a href="https://www.mortality.org/Country/Country?cntr=USA">Human Mortality Database</a> I downloaded life tables for the United States, combined and broken down for men and women. The following function reads and cleans a table.</p>
<pre id="codecell1" class="wp-block-preformatted">def read_life_table(filename):
lt = pd.read_fwf(filename, skiprows=2, infer_nrows=200)
lt['Age'] = lt['Age'].str.replace('+', '', regex=False).astype(int)
return lt
</pre>
<p class="wp-block-paragraph">Here are the first few rows of the combined table (see notes below for details).</p>
<pre id="codecell2" class="wp-block-preformatted">blt = read_life_table('../data/bltper_1x1.txt')
blt.head()
</pre>
<figure class="wp-block-table"><table class="has-fixed-layout"><thead><tr><th></th><th>Year</th><th>Age</th><th>mx</th><th>qx</th><th>ax</th><th>lx</th><th>dx</th><th>Lx</th><th>Tx</th><th>ex</th></tr></thead><tbody><tr><th>0</th><td>1933</td><td>0</td><td>0.06129</td><td>0.05861</td><td>0.25</td><td>100000</td><td>5861</td><td>95624</td><td>6089609</td><td>60.90</td></tr><tr><th>1</th><td>1933</td><td>1</td><td>0.00946</td><td>0.00941</td><td>0.50</td><td>94139</td><td>886</td><td>93696</td><td>5993985</td><td>63.67</td></tr><tr><th>2</th><td>1933</td><td>2</td><td>0.00435</td><td>0.00434</td><td>0.50</td><td>93253</td><td>405</td><td>93050</td><td>5900289</td><td>63.27</td></tr><tr><th>3</th><td>1933</td><td>3</td><td>0.00310</td><td>0.00310</td><td>0.50</td><td>92848</td><td>288</td><td>92704</td><td>5807239</td><td>62.55</td></tr><tr><th>4</th><td>1933</td><td>4</td><td>0.00239</td><td>0.00238</td><td>0.50</td><td>92560</td><td>221</td><td>92450</td><td>5714535</td><td>61.74</td></tr></tbody></table></figure>
<p class="wp-block-paragraph">We’ll also read the female and male tables.</p>
<pre id="codecell3" class="wp-block-preformatted">flt = read_life_table('../data/fltper_1x1.txt')
</pre>
<pre id="codecell4" class="wp-block-preformatted">mlt = read_life_table('../data/mltper_1x1.txt')
</pre>
<p class="wp-block-paragraph">The tables include data from 1933 to 2024, so we’ll select the most recent data.</p>
<pre id="codecell5" class="wp-block-preformatted">year = blt['Year'].unique()[-1]
table = blt.query('Year == @year').set_index('Age')
</pre>
<p class="wp-block-paragraph">The column we’ll use is <code>ex</code>, which is life expectancy as a function of age.</p>
<pre id="codecell6" class="wp-block-preformatted">age = table.index.to_series()
ex = table['ex']
</pre>
<p class="wp-block-paragraph">Life expectancy at birth is 79 years, so the naive midpoint is 39.5.</p>
<pre id="codecell7" class="wp-block-preformatted">ex[0], ex[0] / 2
</pre>
<pre id="codecell8" class="wp-block-preformatted">(79.08, 39.54)
</pre>
<p class="wp-block-paragraph">But at age 40, expected remaining lifetime is 41.1, so 39.5 is not the midpoint.</p>
<pre id="codecell9" class="wp-block-preformatted">ex[39], ex[40]
</pre>
<pre id="codecell10" class="wp-block-preformatted">(42.04, 41.12)
</pre>
<p class="wp-block-paragraph">This plot shows life expectancy at each age, compared to age.</p>
<pre id="codecell11" class="wp-block-preformatted">ex.plot(label='Remaining life expectancy')
age.plot(label='Age')
decorate(ylabel='Years',
title='Remaining life expectancy vs age, United States 2024')
</pre>
<figure class="wp-block-image"><img loading="lazy" decoding="async" width="438" height="250" src="https://www.allendowney.com/blog/wp-content/uploads/2026/05/a55e9cbde25b36d9c42e2ede2a78a827460d537f230b5cc4e7dfcb519a44bbc6.png" alt="_images/a55e9cbde25b36d9c42e2ede2a78a827460d537f230b5cc4e7dfcb519a44bbc6.png" class="wp-image-1797" srcset="https://www.allendowney.com/blog/wp-content/uploads/2026/05/a55e9cbde25b36d9c42e2ede2a78a827460d537f230b5cc4e7dfcb519a44bbc6.png 438w, https://www.allendowney.com/blog/wp-content/uploads/2026/05/a55e9cbde25b36d9c42e2ede2a78a827460d537f230b5cc4e7dfcb519a44bbc6-300x171.png 300w" sizes="auto, (max-width: 438px) 100vw, 438px" /></figure>
<p class="wp-block-paragraph">“Middle age” is where the lines cross, which we can compute by linear interpolation.</p>
<pre id="codecell12" class="wp-block-preformatted">from scipy.interpolate import interp1d
inverse = interp1d(ex - age, age)
inverse(0)
</pre>
<pre id="codecell13" class="wp-block-preformatted">array(40.58638743)
</pre>
<p class="wp-block-paragraph">So the overall midpoint is 40.6 years. But as you might expect, it’s different for men and women. Let’s put the analysis we did in a function.</p>
<pre id="codecell14" class="wp-block-preformatted">def get_midpoint(filename):
lt = read_life_table(filename)
year = lt['Year'].unique()[-1]
table = lt.query('Year == @year').set_index('Age')
age = pd.Series(table.index)
ex = table['ex']
inverse = interp1d(ex - age, age)
return inverse(0)
</pre>
<p class="wp-block-paragraph">And run it for men.</p>
<pre id="codecell15" class="wp-block-preformatted">get_midpoint('../data/mltper_1x1.txt')
</pre>
<pre id="codecell16" class="wp-block-preformatted">array(39.57142857)
</pre>
<p class="wp-block-paragraph">And women.</p>
<pre id="codecell17" class="wp-block-preformatted">get_midpoint('../data/fltper_1x1.txt')
</pre>
<pre id="codecell18" class="wp-block-preformatted">array(41.56185567)
</pre>
<p class="wp-block-paragraph">Men hit middle age at 39.6, women at 41.6.</p>
<h2 class="wp-block-heading">The Gender Gap and Age</h2>
<p class="wp-block-paragraph">Finally, let’s see how the gender gap in life expectancy changes as a function of age.</p>
<pre id="codecell19" class="wp-block-preformatted">ex_male = mlt.query('Year == @year').set_index('Age')['ex']
ex_female = flt.query('Year == @year').set_index('Age')['ex']
gap = ex_female - ex_male
</pre>
<pre id="codecell20" class="wp-block-preformatted">gap.plot(label='')
decorate(ylabel='Years',
title='Life expectancy gender gap vs age')
</pre>
<figure class="wp-block-image"><img loading="lazy" decoding="async" width="438" height="250" src="https://www.allendowney.com/blog/wp-content/uploads/2026/05/2cf48be5acc971ad8f6973506c224767a25ef2e38bcf53c5b12b0f895c26ed11.png" alt="_images/2cf48be5acc971ad8f6973506c224767a25ef2e38bcf53c5b12b0f895c26ed11.png" class="wp-image-1796" srcset="https://www.allendowney.com/blog/wp-content/uploads/2026/05/2cf48be5acc971ad8f6973506c224767a25ef2e38bcf53c5b12b0f895c26ed11.png 438w, https://www.allendowney.com/blog/wp-content/uploads/2026/05/2cf48be5acc971ad8f6973506c224767a25ef2e38bcf53c5b12b0f895c26ed11-300x171.png 300w" sizes="auto, (max-width: 438px) 100vw, 438px" /></figure>
<p class="wp-block-paragraph">At birth the life expectancy gap is close to five years. At age 100, it is close to zero.</p>
<p class="wp-block-paragraph">But just looking at the gap might be misleading. For a more complete picture let’s also look at the ratio.</p>
<pre id="codecell21" class="wp-block-preformatted">ratio = ex_female / ex_male
ratio.plot(label='')
decorate(ylabel='Ratio',
title='Life expectancy gender ratio (female / male)')
</pre>
<figure class="wp-block-image"><img loading="lazy" decoding="async" width="446" height="250" src="https://www.allendowney.com/blog/wp-content/uploads/2026/05/1a514d22895c3e18a767184700d6edf467975abb4b302afe044fd42c002ae21c.png" alt="_images/1a514d22895c3e18a767184700d6edf467975abb4b302afe044fd42c002ae21c.png" class="wp-image-1798" srcset="https://www.allendowney.com/blog/wp-content/uploads/2026/05/1a514d22895c3e18a767184700d6edf467975abb4b302afe044fd42c002ae21c.png 446w, https://www.allendowney.com/blog/wp-content/uploads/2026/05/1a514d22895c3e18a767184700d6edf467975abb4b302afe044fd42c002ae21c-300x168.png 300w" sizes="auto, (max-width: 446px) 100vw, 446px" /></figure>
<p class="wp-block-paragraph">The life expectancy ratio tells a more complicated story.</p>
<ul class="wp-block-list">
<li>At birth, the ratio is 1.06, which means female babies live 6% longer, on average.</li>
<li>Around age 80, the ratio peaks at nearly 1.14 – so between female and male octogenarians, we expect the women to live 14% longer.</li>
<li>At advanced ages, the ratio declines steeply and actually crosses over after age 100 – although the crossover is minimal and might not be statistically valid.</li>
</ul>
<p class="wp-block-paragraph">To interpret these results, we can think about the causes of death that contribute to age-specific death rates at different stages of life.</p>
<ul class="wp-block-list">
<li>In young adulthood, the causes of death that contribute most to gender gaps include road traffic, homicide, accidental injury, drug use disorders.</li>
<li>In advanced adulthood, they include cancer, cardiovascular disease, respiratory disease, liver disease, diabetes, and suicide.</li>
</ul>
<p class="wp-block-paragraph">The causes that affect younger people have large gender gaps, but relatively low death rates. As people get older, these low-rate causes contribute less to age-specific death rates, and the higher-rate causes contribute more.</p>
<p class="wp-block-paragraph">I think that’s a plausible explanation for the increasing ratio from age 0 to 80. For the decline that follows, I can only speculate that there is a selection effect: people who get to these advanced ages are likely to have better-than-average lifestyle histories (less smoking and drinking, better diet, more exercise) – and among people with better lifestyles, the gender gap is small.</p>
<h2 class="wp-block-heading">Notes</h2>
<p class="wp-block-paragraph">Data credit: HMD. Human Mortality Database. Max Planck Institute for Demographic Research (Germany), University of California, Berkeley (USA), and French Institute for Demographic Studies (France). Available at [<a href="http://www.mortality.org">www.mortality.org</a>].</p>
<p class="wp-block-paragraph">Here are the columns of the 1×1 Period Life Tables:</p>
<ul class="wp-block-list">
<li><strong>Year</strong>: Calendar year to which the period life table refers.</li>
<li><strong>Age</strong>: Exact age (x), in years, at the beginning of the interval ([x, x+1)).</li>
<li><strong>mx</strong>: Central death rate at age (x):</li>
</ul>
<ul class="wp-block-list">
<li><strong>qx</strong>: Probability of dying between ages (x) and (x+1):</li>
</ul>
<ul class="wp-block-list">
<li><strong>ax</strong>: Average fraction of the interval lived by those who die in ([x, x+1)). Typically around 0.5 for most ages, lower for infants (reflecting higher early mortality within the year).</li>
<li><strong>lx</strong>: Number of survivors at exact age (x), out of a radix (usually 100,000 births).</li>
<li><strong>dx</strong>: Number of deaths between ages (x) and (x+1):</li>
</ul>
<ul class="wp-block-list">
<li><strong>Lx</strong>: Person-years lived between ages (x) and (x+1), approximately</li>
</ul>
<ul class="wp-block-list">
<li><strong>Tx</strong>: Total person-years remaining above age (x):</li>
</ul>
<ul class="wp-block-list">
<li><strong>ex</strong>: Life expectancy at age (x):</li>
</ul>
<p class="wp-block-paragraph">The details are in<a href="https://github.com/AllenDowney/ProbablyOverthinkingIt/blob/book/examples/midlife.ipynb"> this Jupyter notebook</a>.</p>
<p>The post <a href="https://www.allendowney.com/blog/2026/05/01/planning-for-your-midlife-crisis/">Planning for your midlife crisis</a> appeared first on <a href="https://www.allendowney.com/blog">Probably Overthinking It</a>.</p>
]]></content:encoded>
<post-id xmlns="com-wordpress:feed-additions:1">1794</post-id> </item>
<item>
<title>Changing Opinions on Assisted Suicide</title>
<link>https://www.allendowney.com/blog/2026/04/16/changing-opinions-on-assisted-suicide/</link>
<dc:creator><![CDATA[AllenDowney]]></dc:creator>
<pubDate>Thu, 16 Apr 2026 20:01:37 +0000</pubDate>
<category><![CDATA[Uncategorized]]></category>
<category><![CDATA[age period cohort analysis]]></category>
<category><![CDATA[bayesian statistics]]></category>
<category><![CDATA[general social survey]]></category>
<guid isPermaLink="false">https://www.allendowney.com/blog/?p=1782</guid>
<description><![CDATA[<p>In Graphs About Religion, Ryan Burge recently wrote about changing opinions about assisted suicide and how they relate to religion. As always, when I see survey responses changing over time, I wonder whether it is driven primarily by period or cohort effects. And if you’ve read my last few posts, you know I’ve been working on a Bayesian model to answer that question. Ryan’s analysis is based on four questions from the General Social Survey (GSS): In addition, we’ll look...</p>
<p class="read-more"><a class="btn btn-default" href="https://www.allendowney.com/blog/2026/04/16/changing-opinions-on-assisted-suicide/"> Read More<span class="screen-reader-text"> Read More</span></a></p>
<p>The post <a href="https://www.allendowney.com/blog/2026/04/16/changing-opinions-on-assisted-suicide/">Changing Opinions on Assisted Suicide</a> appeared first on <a href="https://www.allendowney.com/blog">Probably Overthinking It</a>.</p>
]]></description>
<content:encoded><![CDATA[
<p class="wp-block-paragraph">In <a href="https://www.graphsaboutreligion.com/p/god-death-and-the-right-to-choose" target="_blank" rel="noreferrer noopener">Graphs About Religion</a>, Ryan Burge recently wrote about changing opinions about assisted suicide and how they relate to religion.</p>
<p class="wp-block-paragraph">As always, when I see survey responses changing over time, I wonder whether it is driven primarily by period or cohort effects. And if you’ve read my last few posts, you know I’ve been working on a Bayesian model to answer that question.</p>
<p class="wp-block-paragraph">Ryan’s analysis is based on four questions from the General Social Survey (GSS):</p>
<blockquote class="wp-block-quote is-layout-flow wp-block-quote-is-layout-flow">
<p class="wp-block-paragraph">Do you think a person has the right to end his or her own life if this person:</p>
<ul class="wp-block-list">
<li>Has an incurable disease? (<code>suicide1</code>)</li>
<li>Has gone bankrupt? (<code>suicide2</code>)</li>
<li>Has dishonored his or her family? (<code>suicide3</code>)</li>
<li>Is tired of living and ready to die? (<code>suicide4</code>)</li>
</ul>
</blockquote>
<p class="wp-block-paragraph">In addition, we’ll look at results from a related question (<code>letdie1</code>):</p>
<blockquote class="wp-block-quote is-layout-flow wp-block-quote-is-layout-flow">
<p class="wp-block-paragraph">When a person has a disease that cannot be cured, do you think doctors should be allowed by law to end the patient’s life by some painless means if the patient and his family request it?</p>
</blockquote>
<p class="wp-block-paragraph">The framing of the questions is different: the first four are about the right to end one’s life and the last is about the legality of doctor-assisted suicide.</p>
<p class="wp-block-paragraph">Before we look at the breakdown of period and cohort effects, here are the results from a model that estimates latent opposition to each proposition as a smooth function over time.</p>
<figure class="wp-block-image" id="letdie-single-time"><img loading="lazy" decoding="async" width="1108" height="704" src="https://www.allendowney.com/blog/wp-content/uploads/2026/04/letdie_compare_time_-340f828df36b2086971ded6f63293cf6.png" alt="Time-only trends." class="wp-image-1784" srcset="https://www.allendowney.com/blog/wp-content/uploads/2026/04/letdie_compare_time_-340f828df36b2086971ded6f63293cf6.png 1108w, https://www.allendowney.com/blog/wp-content/uploads/2026/04/letdie_compare_time_-340f828df36b2086971ded6f63293cf6-300x191.png 300w, https://www.allendowney.com/blog/wp-content/uploads/2026/04/letdie_compare_time_-340f828df36b2086971ded6f63293cf6-1024x651.png 1024w, https://www.allendowney.com/blog/wp-content/uploads/2026/04/letdie_compare_time_-340f828df36b2086971ded6f63293cf6-768x488.png 768w, https://www.allendowney.com/blog/wp-content/uploads/2026/04/letdie_compare_time_-340f828df36b2086971ded6f63293cf6-425x270.png 425w" sizes="auto, (max-width: 1108px) 100vw, 1108px" /></figure>
<p class="wp-block-paragraph">Opposition to suicide is high in three of the scenarios — bankrupt, dishonored family, and tired of living — and lower in the incurable disease scenarios.</p>
<p class="wp-block-paragraph">In all five questions, opposition has declined over time, although for the incurable disease scenarios, it might have leveled off after 1990.</p>
<h2 class="wp-block-heading" id="doctor-assisted-death">Doctor-assisted death</h2>
<p class="wp-block-paragraph">Now let’s see if we can decompose these changes into period and cohort effects. We’ll start with the question about doctor-assisted death when the patient has an incurable disease.</p>
<p class="wp-block-paragraph">As in the previous posts, I used a Bayesian model to estimate a trajectory over time for each birth cohort, shown in the following figure.</p>
<figure class="wp-block-image" id="letdie1-cohort-trajectories"><img loading="lazy" decoding="async" width="1330" height="778" src="https://www.allendowney.com/blog/wp-content/uploads/2026/04/cohort_trajectory_le-28df4a8cc3e21cad9b463f53ddf9a3ef.png" alt="Cohort trajectories: letdie1." class="wp-image-1785" srcset="https://www.allendowney.com/blog/wp-content/uploads/2026/04/cohort_trajectory_le-28df4a8cc3e21cad9b463f53ddf9a3ef.png 1330w, https://www.allendowney.com/blog/wp-content/uploads/2026/04/cohort_trajectory_le-28df4a8cc3e21cad9b463f53ddf9a3ef-300x175.png 300w, https://www.allendowney.com/blog/wp-content/uploads/2026/04/cohort_trajectory_le-28df4a8cc3e21cad9b463f53ddf9a3ef-1024x599.png 1024w, https://www.allendowney.com/blog/wp-content/uploads/2026/04/cohort_trajectory_le-28df4a8cc3e21cad9b463f53ddf9a3ef-768x449.png 768w, https://www.allendowney.com/blog/wp-content/uploads/2026/04/cohort_trajectory_le-28df4a8cc3e21cad9b463f53ddf9a3ef-462x270.png 462w" sizes="auto, (max-width: 1330px) 100vw, 1330px" /></figure>
<p class="wp-block-paragraph">Reading from top to bottom, we can see that opposition has declined from one cohort to the next, and reading from left to right, we can see that opposition has varied over time within each cohort.</p>
<p class="wp-block-paragraph">The following figure shows the cohort component alone, standardized to factor out the period effect.</p>
<figure class="wp-block-image" id="letdie1-cohort-component"><img loading="lazy" decoding="async" width="1166" height="790" src="https://www.allendowney.com/blog/wp-content/uploads/2026/04/cohort_standardized_-d780162e3521c3e8c568d864d1d04042.png" alt="Cohort component (uniform years): letdie1." class="wp-image-1786" srcset="https://www.allendowney.com/blog/wp-content/uploads/2026/04/cohort_standardized_-d780162e3521c3e8c568d864d1d04042.png 1166w, https://www.allendowney.com/blog/wp-content/uploads/2026/04/cohort_standardized_-d780162e3521c3e8c568d864d1d04042-300x203.png 300w, https://www.allendowney.com/blog/wp-content/uploads/2026/04/cohort_standardized_-d780162e3521c3e8c568d864d1d04042-1024x694.png 1024w, https://www.allendowney.com/blog/wp-content/uploads/2026/04/cohort_standardized_-d780162e3521c3e8c568d864d1d04042-768x520.png 768w, https://www.allendowney.com/blog/wp-content/uploads/2026/04/cohort_standardized_-d780162e3521c3e8c568d864d1d04042-399x270.png 399w" sizes="auto, (max-width: 1166px) 100vw, 1166px" /></figure>
<p class="wp-block-paragraph">Opposition to doctor-assisted suicide has declined from more than 40% in the earliest cohorts to 20% among people born in 2006.</p>
<p class="wp-block-paragraph">A possible explanation for the cohort pattern is that people anchor their moral judgments to the legal environment they encounter when they are young. During the “impressionable years” of late adolescence and early adulthood, existing laws can establish a moral baseline, so that what is illegal is inferred to be wrong, and therefore should remain illegal. As a result, gradual legalization can generate long-run attitudinal change through cohort replacement: people who grow up after a practice becomes legal are less likely to see it as morally problematic.</p>
<p class="wp-block-paragraph">The following figure shows the period effect alone, along with the results from the time model (which includes both period and cohort effects).</p>
<figure class="wp-block-image" id="letdie1-period-time"><img loading="lazy" decoding="async" width="1166" height="790" src="https://www.allendowney.com/blog/wp-content/uploads/2026/04/time_standardized_le-c7580a12cc292dbce6e525849d0e6220.png" alt="Standardized period component with time model: letdie1." class="wp-image-1788" srcset="https://www.allendowney.com/blog/wp-content/uploads/2026/04/time_standardized_le-c7580a12cc292dbce6e525849d0e6220.png 1166w, https://www.allendowney.com/blog/wp-content/uploads/2026/04/time_standardized_le-c7580a12cc292dbce6e525849d0e6220-300x203.png 300w, https://www.allendowney.com/blog/wp-content/uploads/2026/04/time_standardized_le-c7580a12cc292dbce6e525849d0e6220-1024x694.png 1024w, https://www.allendowney.com/blog/wp-content/uploads/2026/04/time_standardized_le-c7580a12cc292dbce6e525849d0e6220-768x520.png 768w, https://www.allendowney.com/blog/wp-content/uploads/2026/04/time_standardized_le-c7580a12cc292dbce6e525849d0e6220-399x270.png 399w" sizes="auto, (max-width: 1166px) 100vw, 1166px" /></figure>
<p class="wp-block-paragraph">Comparing the two lines, we can conclude that the decline we see over time is entirely due to the cohort effect — when we control for generational replacement, the estimated period effect has generally <em>increased</em> since 1990.</p>
<p class="wp-block-paragraph">The increase between 1990 and 2005 might reflect increasing moral concern due to advances in life-sustaining medical technology, high-profile legal disputes like the <a href="https://en.wikipedia.org/wiki/Terri_Schiavo_case" target="_blank" rel="noreferrer noopener">Terri Schiavo case</a>, and broader discussions of the sanctity of life.</p>
<p class="wp-block-paragraph">The decline between 2005 to 2015 might reflect normalization of assisted dying following legalization in several states (Oregon in 1997, Washington in 2008, and Montana in 2009, Vermont in 2013), along with a shift in public discourse toward autonomy, dignity, and patient choice, reinforced by high-profile cases like <a href="https://en.wikipedia.org/wiki/Brittany_Maynard" target="_blank" rel="noreferrer noopener">Brittany Maynard</a>.</p>
<h2 class="wp-block-heading" id="other-scenarios">Other Scenarios</h2>
<p class="wp-block-paragraph">The following figure shows the estimated cohort effects for all five questions.</p>
<figure class="wp-block-image" id="letdie-single-cohort"><img loading="lazy" decoding="async" width="1108" height="704" src="https://www.allendowney.com/blog/wp-content/uploads/2026/04/letdie_compare_cohor-ca0769cc27ba5266de2e551bbf9f7ec3.png" alt="Cohort margins, single panel." class="wp-image-1789" srcset="https://www.allendowney.com/blog/wp-content/uploads/2026/04/letdie_compare_cohor-ca0769cc27ba5266de2e551bbf9f7ec3.png 1108w, https://www.allendowney.com/blog/wp-content/uploads/2026/04/letdie_compare_cohor-ca0769cc27ba5266de2e551bbf9f7ec3-300x191.png 300w, https://www.allendowney.com/blog/wp-content/uploads/2026/04/letdie_compare_cohor-ca0769cc27ba5266de2e551bbf9f7ec3-1024x651.png 1024w, https://www.allendowney.com/blog/wp-content/uploads/2026/04/letdie_compare_cohor-ca0769cc27ba5266de2e551bbf9f7ec3-768x488.png 768w, https://www.allendowney.com/blog/wp-content/uploads/2026/04/letdie_compare_cohor-ca0769cc27ba5266de2e551bbf9f7ec3-425x270.png 425w" sizes="auto, (max-width: 1108px) 100vw, 1108px" /></figure>
<p class="wp-block-paragraph">For the incurable disease scenario, opposition has declined from more than 60% in the earliest cohorts to less than 40% among cohorts born after 1950 — although it might have leveled off since then.</p>
<p class="wp-block-paragraph">In the other scenarios, opposition has also declined from one cohort to the next, but the size of the effect is smaller.</p>
<p class="wp-block-paragraph">The following figure shows the estimated period effects, controlling for generational replacement.</p>
<figure class="wp-block-image" id="letdie-single-period"><img loading="lazy" decoding="async" width="1108" height="704" src="https://www.allendowney.com/blog/wp-content/uploads/2026/04/letdie_compare_perio-76fe4f16ad277fcdde3a47797ddbb13e.png" alt="Period margins, single panel." class="wp-image-1787" srcset="https://www.allendowney.com/blog/wp-content/uploads/2026/04/letdie_compare_perio-76fe4f16ad277fcdde3a47797ddbb13e.png 1108w, https://www.allendowney.com/blog/wp-content/uploads/2026/04/letdie_compare_perio-76fe4f16ad277fcdde3a47797ddbb13e-300x191.png 300w, https://www.allendowney.com/blog/wp-content/uploads/2026/04/letdie_compare_perio-76fe4f16ad277fcdde3a47797ddbb13e-1024x651.png 1024w, https://www.allendowney.com/blog/wp-content/uploads/2026/04/letdie_compare_perio-76fe4f16ad277fcdde3a47797ddbb13e-768x488.png 768w, https://www.allendowney.com/blog/wp-content/uploads/2026/04/letdie_compare_perio-76fe4f16ad277fcdde3a47797ddbb13e-425x270.png 425w" sizes="auto, (max-width: 1108px) 100vw, 1108px" /></figure>
<p class="wp-block-paragraph">Since 1990, most of the period effects are small. The only exception is the “tired of living” scenario, where there is some decline over time, independent of generational replacement.</p>
<p class="wp-block-paragraph">In the next post, we’ll do the same analysis with questions about abortion and the situations where it should be legal or not.</p>
<p class="wp-block-paragraph"></p>
<p>The post <a href="https://www.allendowney.com/blog/2026/04/16/changing-opinions-on-assisted-suicide/">Changing Opinions on Assisted Suicide</a> appeared first on <a href="https://www.allendowney.com/blog">Probably Overthinking It</a>.</p>
]]></content:encoded>
<post-id xmlns="com-wordpress:feed-additions:1">1782</post-id> </item>
<item>
<title>Trust and Well-Being</title>
<link>https://www.allendowney.com/blog/2026/04/03/trust-and-well-being/</link>
<dc:creator><![CDATA[AllenDowney]]></dc:creator>
<pubDate>Fri, 03 Apr 2026 14:48:45 +0000</pubDate>
<category><![CDATA[Uncategorized]]></category>
<category><![CDATA[age period cohort analysis]]></category>
<category><![CDATA[general social survey]]></category>
<category><![CDATA[happiness]]></category>
<category><![CDATA[logistic regression]]></category>
<guid isPermaLink="false">https://www.allendowney.com/blog/?p=1766</guid>
<description><![CDATA[<p>In a previous article, I claimed that Young adults are not very happy. Now the World Happiness Report 2026 has confirmed that young people in North America and Western Europe are less happy than they were fifteen years ago, and less happy than previous generations. In this article, we’ll look at results from three related questions in the General Social Survey (GSS): As we’ll see, young adults in the United States have a more negative outlook than previous generations: they...</p>
<p class="read-more"><a class="btn btn-default" href="https://www.allendowney.com/blog/2026/04/03/trust-and-well-being/"> Read More<span class="screen-reader-text"> Read More</span></a></p>
<p>The post <a href="https://www.allendowney.com/blog/2026/04/03/trust-and-well-being/">Trust and Well-Being</a> appeared first on <a href="https://www.allendowney.com/blog">Probably Overthinking It</a>.</p>
]]></description>
<content:encoded><![CDATA[
<p class="wp-block-paragraph">In a previous article, I claimed that <a href="https://www.allendowney.com/blog/2026/03/19/young-adults-are-not-very-happy/" target="_blank" rel="noreferrer noopener">Young adults are not very happy</a>. Now the <a href="https://worldhappiness.report/ed/2026/" target="_blank" rel="noreferrer noopener">World Happiness Report 2026</a> has confirmed that young people in North America and Western Europe are less happy than they were fifteen years ago, and less happy than previous generations.</p>
<p class="wp-block-paragraph">In this article, we’ll look at results from three related questions in the General Social Survey (GSS):</p>
<ul class="wp-block-list">
<li><strong>Trust:</strong> “Generally speaking, would you say that most people can be trusted or that you can’t be too careful in dealing with people?”</li>
<li><strong>Fair:</strong> “Do you think most people would try to take advantage of you if they got a chance, or would they try to be fair?”</li>
<li><strong>Helpful:</strong> “Would you say that most of the time people try to be helpful, or that they are mostly just looking out for themselves?”</li>
</ul>
<p class="wp-block-paragraph">As we’ll see, young adults in the United States have a more negative outlook than previous generations: they are less likely to say that people can be trusted, that they are fair, or that they are helpful. And we’ll consider connections between this bleak outlook and unhappiness.</p>
<h2 class="wp-block-heading" id="trust">Trust</h2>
<p class="wp-block-paragraph">Using the same model from the previous articles, I estimated the percentage who say people can be trusted, following each birth year over time.</p>
<figure class="wp-block-image" id="cohort-trajectories-trust"><img loading="lazy" decoding="async" width="1330" height="778" src="https://www.allendowney.com/blog/wp-content/uploads/2026/04/cohort_trajectory_tr-5809c4884f70b4b9b75cfe97047f2fe8.png" alt="Cohort trajectories, percent saying most people can be trusted" class="wp-image-1769" srcset="https://www.allendowney.com/blog/wp-content/uploads/2026/04/cohort_trajectory_tr-5809c4884f70b4b9b75cfe97047f2fe8.png 1330w, https://www.allendowney.com/blog/wp-content/uploads/2026/04/cohort_trajectory_tr-5809c4884f70b4b9b75cfe97047f2fe8-300x175.png 300w, https://www.allendowney.com/blog/wp-content/uploads/2026/04/cohort_trajectory_tr-5809c4884f70b4b9b75cfe97047f2fe8-1024x599.png 1024w, https://www.allendowney.com/blog/wp-content/uploads/2026/04/cohort_trajectory_tr-5809c4884f70b4b9b75cfe97047f2fe8-768x449.png 768w, https://www.allendowney.com/blog/wp-content/uploads/2026/04/cohort_trajectory_tr-5809c4884f70b4b9b75cfe97047f2fe8-462x270.png 462w" sizes="auto, (max-width: 1330px) 100vw, 1330px" /></figure>
<p class="wp-block-paragraph"><em>Cohort trajectories, percent saying most people can be trusted</em></p>
<p class="wp-block-paragraph">With these trajectories, we can decompose the cohort and period effects. The following figure shows the cohort effect, standardized by holding the period effect constant.</p>
<figure class="wp-block-image" id="cohort-profile-trust"><img loading="lazy" decoding="async" width="1133" height="790" src="https://www.allendowney.com/blog/wp-content/uploads/2026/04/cohort_standardized_-83920254db4863278c92f3cee792510c.png" alt="Standardized cohort effect with fixed time mix, percent saying most people can be trusted" class="wp-image-1772" srcset="https://www.allendowney.com/blog/wp-content/uploads/2026/04/cohort_standardized_-83920254db4863278c92f3cee792510c.png 1133w, https://www.allendowney.com/blog/wp-content/uploads/2026/04/cohort_standardized_-83920254db4863278c92f3cee792510c-300x209.png 300w, https://www.allendowney.com/blog/wp-content/uploads/2026/04/cohort_standardized_-83920254db4863278c92f3cee792510c-1024x714.png 1024w, https://www.allendowney.com/blog/wp-content/uploads/2026/04/cohort_standardized_-83920254db4863278c92f3cee792510c-768x535.png 768w, https://www.allendowney.com/blog/wp-content/uploads/2026/04/cohort_standardized_-83920254db4863278c92f3cee792510c-387x270.png 387w" sizes="auto, (max-width: 1133px) 100vw, 1133px" /></figure>
<p class="wp-block-paragraph">Standardized cohort effect with fixed time mix, percent saying most people can be trusted</p>
<p class="wp-block-paragraph">The level of trust increased between the cohorts born in the 1900s through the 1940s, and then started a steep decline. This is a large cohort effect, dropping about 30 percentage points over 60 years.</p>
<p class="wp-block-paragraph">The following figure shows the period effect, standardized by holding the cohort mix constant.</p>
<figure class="wp-block-image" id="time-trend-trust"><img loading="lazy" decoding="async" width="1133" height="790" src="https://www.allendowney.com/blog/wp-content/uploads/2026/04/time_standardized_tr-2f029b683d9ad86a39a536e4f95c8c0f.png" alt="Standardized time trend with fixed cohort mix, percent saying most people can be trusted" class="wp-image-1773" srcset="https://www.allendowney.com/blog/wp-content/uploads/2026/04/time_standardized_tr-2f029b683d9ad86a39a536e4f95c8c0f.png 1133w, https://www.allendowney.com/blog/wp-content/uploads/2026/04/time_standardized_tr-2f029b683d9ad86a39a536e4f95c8c0f-300x209.png 300w, https://www.allendowney.com/blog/wp-content/uploads/2026/04/time_standardized_tr-2f029b683d9ad86a39a536e4f95c8c0f-1024x714.png 1024w, https://www.allendowney.com/blog/wp-content/uploads/2026/04/time_standardized_tr-2f029b683d9ad86a39a536e4f95c8c0f-768x535.png 768w, https://www.allendowney.com/blog/wp-content/uploads/2026/04/time_standardized_tr-2f029b683d9ad86a39a536e4f95c8c0f-387x270.png 387w" sizes="auto, (max-width: 1133px) 100vw, 1133px" /></figure>
<p class="wp-block-paragraph"><em>Standardized time trend with fixed cohort mix, percent saying most people can be trusted</em></p>
<p class="wp-block-paragraph">In contrast, there is almost no period effect.</p>
<h2 class="wp-block-heading" id="the-conjecture-part">The conjecture part</h2>
<p class="wp-block-paragraph">About my previous article, one of my former colleagues said he appreciated my attempt to offer explanations, but reminded me that with this kind of data alone, it is hard to say what causes what with any confidence. That’s true, and it’s a good reminder — but we can get some clues:</p>
<ul class="wp-block-list">
<li>When we see a strong cohort effect and almost no period effect, that’s evidence that we’re seeing patterns set in childhood.</li>
<li>When we see period effects, we should look for events that affected all cohorts at the same time.</li>
</ul>
<p class="wp-block-paragraph">So let’s think about what was happening in the formative years of these cohorts, starting with the 1940 cohort, which was the high point in trust, before the decline:</p>
<ul class="wp-block-list">
<li>Cohort 1940 (childhood: 1940–1960): dense local communities, strong civic and religious institutions, frequent face-to-face interaction, and shared media environment.</li>
<li>Cohort 1950 (1950–1970): suburbanization expands, some weakening of community density, television becomes widespread but still shared.</li>
<li>Cohort 1960 (1960–1980): civil rights conflict, Vietnam War, Watergate scandal, rising crime.</li>
<li>Cohort 1970 (1970–1990): reduced civic participation, rising inequality, more cautious parenting, less unstructured social interaction.</li>
<li>Cohort 1980 (1980–2000): increasing inequality, more segregation by class and education, early internet exposure, continued decline in shared institutions.</li>
</ul>
<p class="wp-block-paragraph">At this point a multi-generational effect comes into play — the parents of Cohort 1980, born in the 1950s and 1960s, were less trusting than previous generations of parents.</p>
<ul class="wp-block-list">
<li>Cohort 1990 (1990–2010): widespread internet use, early social media, more structured childhood, increasing awareness of global risks.</li>
<li>Cohort 2000 (2000–2020): smartphones and social media throughout formative years, algorithmic content, reduced in-person interaction.</li>
</ul>
<p class="wp-block-paragraph">If trust is largely set early in life, then differences between cohorts reflect the environments they experienced during their first two decades.</p>
<p class="wp-block-paragraph">In addition to this question about trust, the GSS includes related questions about fairness and mutual assistance.</p>
<h2 class="wp-block-heading" id="fair">Fair</h2>
<p class="wp-block-paragraph">Do you think most people would try to take advantage of you if they got a chance, or would they try to be fair? The following figure shows the percentage who thought people would be fair.</p>
<figure class="wp-block-image" id="cohort-trajectories-fair"><img loading="lazy" decoding="async" width="1330" height="783" src="https://www.allendowney.com/blog/wp-content/uploads/2026/04/cohort_trajectory_fa-941da70cb9e1fdb60ecd622a8e79f682.png" alt="Cohort trajectories, percent saying people would try to be fair" class="wp-image-1771" srcset="https://www.allendowney.com/blog/wp-content/uploads/2026/04/cohort_trajectory_fa-941da70cb9e1fdb60ecd622a8e79f682.png 1330w, https://www.allendowney.com/blog/wp-content/uploads/2026/04/cohort_trajectory_fa-941da70cb9e1fdb60ecd622a8e79f682-300x177.png 300w, https://www.allendowney.com/blog/wp-content/uploads/2026/04/cohort_trajectory_fa-941da70cb9e1fdb60ecd622a8e79f682-1024x603.png 1024w, https://www.allendowney.com/blog/wp-content/uploads/2026/04/cohort_trajectory_fa-941da70cb9e1fdb60ecd622a8e79f682-768x452.png 768w, https://www.allendowney.com/blog/wp-content/uploads/2026/04/cohort_trajectory_fa-941da70cb9e1fdb60ecd622a8e79f682-459x270.png 459w" sizes="auto, (max-width: 1330px) 100vw, 1330px" /></figure>
<p class="wp-block-paragraph"><em>Cohort trajectories, percent saying people would try to be fair</em></p>
<p class="wp-block-paragraph">And here’s the cohort effect.</p>
<figure class="wp-block-image" id="cohort-profile-fair"><img loading="lazy" decoding="async" width="1266" height="764" src="https://www.allendowney.com/blog/wp-content/uploads/2026/04/cohort_standardized_-e471d5b01144d15bbf17ba11755d7731.png" alt="Standardized cohort effect with fixed time mix, percent saying people would try to be fair" class="wp-image-1774" srcset="https://www.allendowney.com/blog/wp-content/uploads/2026/04/cohort_standardized_-e471d5b01144d15bbf17ba11755d7731.png 1266w, https://www.allendowney.com/blog/wp-content/uploads/2026/04/cohort_standardized_-e471d5b01144d15bbf17ba11755d7731-300x181.png 300w, https://www.allendowney.com/blog/wp-content/uploads/2026/04/cohort_standardized_-e471d5b01144d15bbf17ba11755d7731-1024x618.png 1024w, https://www.allendowney.com/blog/wp-content/uploads/2026/04/cohort_standardized_-e471d5b01144d15bbf17ba11755d7731-768x463.png 768w, https://www.allendowney.com/blog/wp-content/uploads/2026/04/cohort_standardized_-e471d5b01144d15bbf17ba11755d7731-447x270.png 447w" sizes="auto, (max-width: 1266px) 100vw, 1266px" /></figure>
<p class="wp-block-paragraph"><em>Standardized cohort effect with fixed time mix, percent saying people would try to be fair</em></p>
<p class="wp-block-paragraph">And the period effect.</p>
<figure class="wp-block-image" id="time-trend-fair"><img loading="lazy" decoding="async" width="1266" height="764" src="https://www.allendowney.com/blog/wp-content/uploads/2026/04/time_standardized_fa-c4e6dd0e53f81bd5148e3461a47a3664.png" alt="Standardized time trend with fixed cohort mix, percent saying people would try to be fair" class="wp-image-1775" srcset="https://www.allendowney.com/blog/wp-content/uploads/2026/04/time_standardized_fa-c4e6dd0e53f81bd5148e3461a47a3664.png 1266w, https://www.allendowney.com/blog/wp-content/uploads/2026/04/time_standardized_fa-c4e6dd0e53f81bd5148e3461a47a3664-300x181.png 300w, https://www.allendowney.com/blog/wp-content/uploads/2026/04/time_standardized_fa-c4e6dd0e53f81bd5148e3461a47a3664-1024x618.png 1024w, https://www.allendowney.com/blog/wp-content/uploads/2026/04/time_standardized_fa-c4e6dd0e53f81bd5148e3461a47a3664-768x463.png 768w, https://www.allendowney.com/blog/wp-content/uploads/2026/04/time_standardized_fa-c4e6dd0e53f81bd5148e3461a47a3664-447x270.png 447w" sizes="auto, (max-width: 1266px) 100vw, 1266px" /></figure>
<p class="wp-block-paragraph"><em>Standardized time trend with fixed cohort mix, percent saying people would try to be fair</em></p>
<p class="wp-block-paragraph">The cohort pattern is similar to what we saw in trust: small changes between the 1900s and 1940s cohorts, and then a steep decline — almost 40 percentage points over 60 years.</p>
<p class="wp-block-paragraph">The period effect is relatively small, varying by only 10 percentage points from lowest to highest point, but it was generally positive until about 2015 (the onset of the Trump Era?).</p>
<h2 class="wp-block-heading" id="helpful">Helpful</h2>
<p class="wp-block-paragraph">Would you say that most of the time people try to be helpful, or that they are mostly just looking out for themselves?</p>
<p class="wp-block-paragraph">Here is a period–cohort fingerprint of the responses, showing the percentage who thought people try to be helpful.</p>
<figure class="wp-block-image" id="cohort-trajectories-helpful"><img loading="lazy" decoding="async" width="1330" height="783" src="https://www.allendowney.com/blog/wp-content/uploads/2026/04/cohort_trajectory_he-73b3c2f2b5af024ffd374acb439b3ec8.png" alt="Cohort trajectories, percent saying people try to be helpful" class="wp-image-1770" srcset="https://www.allendowney.com/blog/wp-content/uploads/2026/04/cohort_trajectory_he-73b3c2f2b5af024ffd374acb439b3ec8.png 1330w, https://www.allendowney.com/blog/wp-content/uploads/2026/04/cohort_trajectory_he-73b3c2f2b5af024ffd374acb439b3ec8-300x177.png 300w, https://www.allendowney.com/blog/wp-content/uploads/2026/04/cohort_trajectory_he-73b3c2f2b5af024ffd374acb439b3ec8-1024x603.png 1024w, https://www.allendowney.com/blog/wp-content/uploads/2026/04/cohort_trajectory_he-73b3c2f2b5af024ffd374acb439b3ec8-768x452.png 768w, https://www.allendowney.com/blog/wp-content/uploads/2026/04/cohort_trajectory_he-73b3c2f2b5af024ffd374acb439b3ec8-459x270.png 459w" sizes="auto, (max-width: 1330px) 100vw, 1330px" /></figure>
<p class="wp-block-paragraph"><em>Cohort trajectories, percent saying people try to be helpful</em></p>
<p class="wp-block-paragraph">Here’s the cohort effect:</p>
<figure class="wp-block-image" id="cohort-profile-helpful"><img loading="lazy" decoding="async" width="1337" height="764" src="https://www.allendowney.com/blog/wp-content/uploads/2026/04/cohort_standardized_-24a4cd718ef72385d57fbc3eb0dbc47d.png" alt="Standardized cohort effect with fixed time mix, percent saying people try to be helpful" class="wp-image-1777" srcset="https://www.allendowney.com/blog/wp-content/uploads/2026/04/cohort_standardized_-24a4cd718ef72385d57fbc3eb0dbc47d.png 1337w, https://www.allendowney.com/blog/wp-content/uploads/2026/04/cohort_standardized_-24a4cd718ef72385d57fbc3eb0dbc47d-300x171.png 300w, https://www.allendowney.com/blog/wp-content/uploads/2026/04/cohort_standardized_-24a4cd718ef72385d57fbc3eb0dbc47d-1024x585.png 1024w, https://www.allendowney.com/blog/wp-content/uploads/2026/04/cohort_standardized_-24a4cd718ef72385d57fbc3eb0dbc47d-768x439.png 768w, https://www.allendowney.com/blog/wp-content/uploads/2026/04/cohort_standardized_-24a4cd718ef72385d57fbc3eb0dbc47d-473x270.png 473w" sizes="auto, (max-width: 1337px) 100vw, 1337px" /></figure>
<p class="wp-block-paragraph"><em>Standardized cohort effect with fixed time mix, percent saying people try to be helpful</em></p>
<p class="wp-block-paragraph">And the period effect.</p>
<figure class="wp-block-image" id="time-trend-helpful"><img loading="lazy" decoding="async" width="1337" height="764" src="https://www.allendowney.com/blog/wp-content/uploads/2026/04/time_standardized_he-28e70c9d0a1b012cf525b854897416f2.png" alt="Standardized time trend with fixed cohort mix, percent saying people try to be helpful" class="wp-image-1776" srcset="https://www.allendowney.com/blog/wp-content/uploads/2026/04/time_standardized_he-28e70c9d0a1b012cf525b854897416f2.png 1337w, https://www.allendowney.com/blog/wp-content/uploads/2026/04/time_standardized_he-28e70c9d0a1b012cf525b854897416f2-300x171.png 300w, https://www.allendowney.com/blog/wp-content/uploads/2026/04/time_standardized_he-28e70c9d0a1b012cf525b854897416f2-1024x585.png 1024w, https://www.allendowney.com/blog/wp-content/uploads/2026/04/time_standardized_he-28e70c9d0a1b012cf525b854897416f2-768x439.png 768w, https://www.allendowney.com/blog/wp-content/uploads/2026/04/time_standardized_he-28e70c9d0a1b012cf525b854897416f2-473x270.png 473w" sizes="auto, (max-width: 1337px) 100vw, 1337px" /></figure>
<p class="wp-block-paragraph"><em>Standardized time trend with fixed cohort mix, percent saying people try to be helpful</em></p>
<p class="wp-block-paragraph">Again we see the same pattern: little change between the cohorts born between 1900 and 1940, and then a decline of more than 30 percentage points over 60 years.</p>
<p class="wp-block-paragraph">And again, the period effect is comparatively small and generally increasing — but possibly declining in the most recent cycles of the survey.</p>
<h2 class="wp-block-heading" id="cause-and-effect">Cause and Effect?</h2>
<p class="wp-block-paragraph">It is plausible that the decline in trust is a contributing factor to the decline in happiness. If you believe that people are out to get you, and 80% of your friends agree, that’s not a worldview conducive to a sense of well-being. And generational decline in trust precedes the decline in happiness, so it is at least a potential cause.</p>
<p class="wp-block-paragraph">The decline in trust-related beliefs also supports the interpretation that recent cohorts are <em>actually</em> unhappy, rather than interpreting the question differently, or being more willing than previous generations to say they are unhappy.</p>
<p class="wp-block-paragraph">I haven’t done full-on causal modeling to quantify these relationships, but I ran a few regression models to explore. To reduce the number of researcher degrees of freedom, I asked ChatGPT to interpret the results:</p>
<blockquote class="wp-block-quote is-layout-flow wp-block-quote-is-layout-flow">
<p class="wp-block-paragraph">Differences in happiness across cohorts appear to be partly explained by differences in social outlook (trust, fairness, helpfulness), and these outlook variables behave like stable, cohort-structured traits rather than period-driven fluctuations.</p>
</blockquote>
<p class="wp-block-paragraph">The AI-generated summary of the experiments follows.</p>
<h3 class="wp-block-heading" id="model-1-cross-sectional-association-complete-cases">Model 1: Cross-sectional association (complete cases)</h3>
<p class="wp-block-paragraph"><strong>Specification:</strong></p>
<ul class="wp-block-list">
<li>Outcome: <code>very_happy</code> (binary)</li>
<li>Predictors: <code>trust</code>, <code>fair</code>, <code>helpful</code> (all binary)</li>
<li>Sample: complete cases with all variables observed</li>
</ul>
<p class="wp-block-paragraph"><strong>Purpose:</strong></p>
<ul class="wp-block-list">
<li>Estimate the <strong>cross-sectional relationship</strong> between social outlook and happiness.</li>
<li>Provides baseline associations without accounting for cohort or period effects.</li>
</ul>
<p class="wp-block-paragraph"><strong>Interpretation:</strong></p>
<ul class="wp-block-list">
<li>Coefficients represent <strong>conditional associations</strong> among individuals at a point in time.</li>
<li>Answers: <em>Are people with a more positive outlook more likely to be very happy?</em></li>
</ul>
<hr class="wp-block-separator has-alpha-channel-opacity"/>
<h3 class="wp-block-heading" id="model-2-outlook-cohort-period-restricted-sample">Model 2: Outlook + cohort + period (restricted sample)</h3>
<p class="wp-block-paragraph"><strong>Specification:</strong></p>
<ul class="wp-block-list">
<li>Outcome: <code>very_happy</code></li>
<li>Predictors:
<ul class="wp-block-list">
<li><code>trust</code>, <code>fair</code>, <code>helpful</code></li>
<li><code>cohort_c</code> (mean-centered birth year)</li>
<li><code>year_c</code> (mean-centered survey year)</li>
</ul>
</li>
<li>Sample: respondents born ≥ 1940 with complete data</li>
</ul>
<p class="wp-block-paragraph"><strong>Purpose:</strong></p>
<ul class="wp-block-list">
<li>Assess whether the outlook–happiness relationship persists after accounting for:
<ul class="wp-block-list">
<li><strong>Cohort effects</strong> (differences across birth cohorts)</li>
<li><strong>Period effects</strong> (changes over survey years)</li>
</ul>
</li>
</ul>
<p class="wp-block-paragraph"><strong>Interpretation:</strong></p>
<ul class="wp-block-list">
<li>Coefficients for outlook variables reflect <strong>within-cohort, within-period associations</strong>.</li>
<li>Cohort and year coefficients capture <strong>linear trends</strong> in happiness after controlling for outlook.</li>
<li>Answers:
<ul class="wp-block-list">
<li><em>Are outlook variables still associated with happiness after adjusting for historical context?</em></li>
<li><em>Is there an independent cohort or period trend?</em></li>
</ul>
</li>
</ul>
<hr class="wp-block-separator has-alpha-channel-opacity"/>
<h3 class="wp-block-heading" id="model-3-cohort-period-only-no-outlook-variables">Model 3: Cohort + period only (no outlook variables)</h3>
<p class="wp-block-paragraph"><strong>Specification:</strong></p>
<ul class="wp-block-list">
<li>Outcome: <code>very_happy</code></li>
<li>Predictors:
<ul class="wp-block-list">
<li><code>cohort_c</code></li>
<li><code>year_c</code></li>
</ul>
</li>
<li>Sample: respondents born > 1940 (larger sample since outlook variables not required)</li>
</ul>
<p class="wp-block-paragraph"><strong>Purpose:</strong></p>
<ul class="wp-block-list">
<li>Estimate <strong>total cohort and period effects</strong> on happiness without controlling for outlook.</li>
<li>Provides a baseline for comparison with Model 2.</li>
</ul>
<p class="wp-block-paragraph"><strong>Interpretation:</strong></p>
<ul class="wp-block-list">
<li>Cohort and year coefficients reflect <strong>combined (direct + indirect) effects</strong>.</li>
<li>Comparing to Model 2 shows how much of these effects are <strong>accounted for by outlook variables</strong>.</li>
<li>Answers:
<ul class="wp-block-list">
<li><em>How does happiness vary across cohorts and over time in aggregate?</em></li>
<li><em>How much do these patterns change when outlook is included?</em></li>
</ul>
</li>
</ul>
<h3 class="wp-block-heading" id="key-findings">Key Findings</h3>
<ul class="wp-block-list">
<li><strong>Positive social outlook is associated with higher happiness.</strong>
<ul class="wp-block-list">
<li>Trust, fairness, and helpfulness all have positive and statistically significant associations with being “very happy.”</li>
<li>Estimated odds ratios:
<ul class="wp-block-list">
<li>Trust: ~1.25</li>
<li>Fairness: ~1.36 (strongest)</li>
<li>Helpfulness: ~1.29</li>
</ul>
</li>
<li>These effects are modest in size and explain a small fraction of overall variation (Pseudo R² ≈ 0.016).</li>
</ul>
</li>
<li><strong>These relationships are stable across cohorts and time.</strong>
<ul class="wp-block-list">
<li>Adding cohort and survey year controls has little effect on the coefficients.</li>
<li>This suggests the outlook–happiness relationship is primarily cross-sectional, not driven by historical shifts.</li>
</ul>
</li>
</ul>
<hr class="wp-block-separator has-alpha-channel-opacity"/>
<h3 class="wp-block-heading" id="cohort-and-period-effects">Cohort and Period Effects</h3>
<ul class="wp-block-list">
<li><strong>Without controlling for outlook:</strong>
<ul class="wp-block-list">
<li>Later cohorts are less likely to report being very happy.</li>
<li>There is also a negative period trend (declining happiness over time).</li>
</ul>
</li>
<li><strong>With outlook variables included:</strong>
<ul class="wp-block-list">
<li>The cohort effect becomes small and statistically insignificant.</li>
<li>The period effect remains negative and significant.</li>
</ul>
</li>
</ul>
<hr class="wp-block-separator has-alpha-channel-opacity"/>
<h3 class="wp-block-heading" id="interpretation">Interpretation</h3>
<ul class="wp-block-list">
<li><strong>Outlook variables appear to mediate cohort differences in happiness.</strong>
<ul class="wp-block-list">
<li>Later cohorts tend to report lower trust, fairness, and helpfulness.</li>
<li>These differences account for much of the observed cohort decline in happiness.</li>
</ul>
</li>
<li><strong>Period effects persist independently.</strong>
<ul class="wp-block-list">
<li>There is a modest downward trend in happiness over time that is not explained by outlook variables.</li>
</ul>
</li>
</ul>
<hr class="wp-block-separator has-alpha-channel-opacity"/>
<h3 class="wp-block-heading" id="data-considerations">Data Considerations</h3>
<ul class="wp-block-list">
<li>Approximately <strong>40% of observations are missing at least one outlook variable</strong>, reducing the complete-case sample.</li>
<li>This raises the possibility of <strong>selection bias</strong> in the estimates.</li>
</ul>
<hr class="wp-block-separator has-alpha-channel-opacity"/>
<h3 class="wp-block-heading" id="bottom-line">Bottom Line</h3>
<ul class="wp-block-list">
<li>A more positive view of others (trust, fairness, helpfulness) is consistently associated with higher happiness.</li>
<li>Differences in these outlook measures help explain why later cohorts report lower happiness.</li>
<li>However, there is also an independent downward trend in happiness over time.</li>
</ul>
<p class="wp-block-paragraph"><a href="https://allendowney.github.io/CultureWar//blog1-happy"></a><a href="https://allendowney.github.io/CultureWar//blog1-happy"></a></p>
<p>The post <a href="https://www.allendowney.com/blog/2026/04/03/trust-and-well-being/">Trust and Well-Being</a> appeared first on <a href="https://www.allendowney.com/blog">Probably Overthinking It</a>.</p>
]]></content:encoded>
<post-id xmlns="com-wordpress:feed-additions:1">1766</post-id> </item>
<item>
<title>Have the Nones hit a ceiling?</title>
<link>https://www.allendowney.com/blog/2026/03/30/have-the-nones-hit-a-ceiling/</link>
<dc:creator><![CDATA[AllenDowney]]></dc:creator>
<pubDate>Mon, 30 Mar 2026 15:51:55 +0000</pubDate>
<category><![CDATA[Uncategorized]]></category>
<category><![CDATA[bayesian statistics]]></category>
<category><![CDATA[general social survey]]></category>
<category><![CDATA[religion]]></category>
<guid isPermaLink="false">https://www.allendowney.com/blog/?p=1756</guid>
<description><![CDATA[<p>Someone asked me recently why I stopped writing about religion, and I said there were two reasons: One is that the primary dataset I was following stopped updating; the other is that Ryan Burge is doing such a good job, I felt redundant. His most recent article presents evidence that the Nones have hit a ceiling — that is, that the percentage of people in the U.S. with no religious affiliation, which has consistently increased for several decades, has either...</p>
<p class="read-more"><a class="btn btn-default" href="https://www.allendowney.com/blog/2026/03/30/have-the-nones-hit-a-ceiling/"> Read More<span class="screen-reader-text"> Read More</span></a></p>
<p>The post <a href="https://www.allendowney.com/blog/2026/03/30/have-the-nones-hit-a-ceiling/">Have the Nones hit a ceiling?</a> appeared first on <a href="https://www.allendowney.com/blog">Probably Overthinking It</a>.</p>
]]></description>
<content:encoded><![CDATA[
<p class="wp-block-paragraph">Someone asked me recently why I stopped writing about religion, and I said there were two reasons: One is that the <a href="https://heri.ucla.edu/publications-tfs/" target="_blank" rel="noreferrer noopener">primary dataset I was following</a> stopped updating; the other is that <a href="https://en.wikipedia.org/wiki/Ryan_Burge_(political_scientist)" target="_blank" rel="noreferrer noopener">Ryan Burge</a> is doing such a good job, I felt redundant.</p>
<p class="wp-block-paragraph">His <a href="https://substack.com/home/post/p-192339927" target="_blank" rel="noreferrer noopener">most recent article</a> presents evidence that the Nones have hit a ceiling — that is, that the percentage of people in the U.S. with no religious affiliation, which has consistently increased for several decades, has either leveled off or started to reverse.</p>
<p class="wp-block-paragraph">He reports on new data from the Cooperative Election Study and the 2024 General Social Survey, including this figure based on the GSS.</p>
<figure class="wp-block-image" id="relig-burge-gss"><img loading="lazy" decoding="async" width="2048" height="1365" src="https://www.allendowney.com/blog/wp-content/uploads/2026/03/gss_relig_raw_data_s-2320d07fdfaaf7f3e756fbec933e265b.png" alt="The percentage of “Nones” from Ryan Burge’s Graphs About Religion." class="wp-image-1761" srcset="https://www.allendowney.com/blog/wp-content/uploads/2026/03/gss_relig_raw_data_s-2320d07fdfaaf7f3e756fbec933e265b.png 2048w, https://www.allendowney.com/blog/wp-content/uploads/2026/03/gss_relig_raw_data_s-2320d07fdfaaf7f3e756fbec933e265b-300x200.png 300w, https://www.allendowney.com/blog/wp-content/uploads/2026/03/gss_relig_raw_data_s-2320d07fdfaaf7f3e756fbec933e265b-1024x683.png 1024w, https://www.allendowney.com/blog/wp-content/uploads/2026/03/gss_relig_raw_data_s-2320d07fdfaaf7f3e756fbec933e265b-768x512.png 768w, https://www.allendowney.com/blog/wp-content/uploads/2026/03/gss_relig_raw_data_s-2320d07fdfaaf7f3e756fbec933e265b-1536x1024.png 1536w, https://www.allendowney.com/blog/wp-content/uploads/2026/03/gss_relig_raw_data_s-2320d07fdfaaf7f3e756fbec933e265b-405x270.png 405w" sizes="auto, (max-width: 2048px) 100vw, 2048px" /></figure>
<p class="wp-block-paragraph">The percentage of “Nones” from Ryan Burge’s <a target="_blank" rel="noreferrer noopener" href="https://www.graphsaboutreligion.com/">Graphs About Religion</a></p>
<p class="wp-block-paragraph">The observed percentage of Nones peaked in the 2021 survey and has dropped in the last two cycles. The CES data show a similar pattern, with a much larger sample size. So I’m not going to disagree with Ryan: it sure looks like the rise of the Nones has stalled or even reversed.</p>
<p class="wp-block-paragraph">However, since I am developing a model that decomposes trends like this into cohort and period effects, we can use it to check whether the turnaround is a cohort or a period effect. It turns out to be both.</p>
<h2 class="wp-block-heading" id="the-model">The Model</h2>
<p class="wp-block-paragraph">The model assumes that each cohort in each year has an unobserved (latent) propensity to report a religious affiliation or none.</p>
<p class="wp-block-paragraph">The cohort and period effects are modeled as second-order Gaussian random walks, which means the model assumes these effects evolve smoothly over time, unless the data provide strong evidence otherwise. The amount of smoothing is estimated from the data.</p>
<p class="wp-block-paragraph">An additional random year effect captures variation from one survey to the next that is not explained by long-term trends, like current events and topics of discussion.</p>
<p class="wp-block-paragraph">The “time only” version of the model estimates a latent propensity for each cycle of the survey, so the result is a smooth curve through the raw proportions.</p>
<p class="wp-block-paragraph">The “time-cohort” version estimates a latent propensity for each cohort during each cycle, so the result is a trajectory over time for each birth year.</p>
<h2 class="wp-block-heading" id="results">Results</h2>
<p class="wp-block-paragraph">Here are the results for the time-only model, showing the posterior mean and a 94% credible interval.</p>
<figure class="wp-block-image" id="time-model-relig"><img loading="lazy" decoding="async" width="1133" height="764" src="https://www.allendowney.com/blog/wp-content/uploads/2026/03/time_model_relig_rw2-ab3b53dbf72feed6f35a356232032396.png" alt="Time-only model, percent with no religious preference" class="wp-image-1759" srcset="https://www.allendowney.com/blog/wp-content/uploads/2026/03/time_model_relig_rw2-ab3b53dbf72feed6f35a356232032396.png 1133w, https://www.allendowney.com/blog/wp-content/uploads/2026/03/time_model_relig_rw2-ab3b53dbf72feed6f35a356232032396-300x202.png 300w, https://www.allendowney.com/blog/wp-content/uploads/2026/03/time_model_relig_rw2-ab3b53dbf72feed6f35a356232032396-1024x690.png 1024w, https://www.allendowney.com/blog/wp-content/uploads/2026/03/time_model_relig_rw2-ab3b53dbf72feed6f35a356232032396-768x518.png 768w, https://www.allendowney.com/blog/wp-content/uploads/2026/03/time_model_relig_rw2-ab3b53dbf72feed6f35a356232032396-400x270.png 400w" sizes="auto, (max-width: 1133px) 100vw, 1133px" /></figure>
<p class="wp-block-paragraph">The posterior mean indicates that the trend in the latent factor has probably slowed; the credible interval indicates that it might have leveled off or reversed.</p>
<p class="wp-block-paragraph">And here are the trajectories for each cohort:</p>
<figure class="wp-block-image" id="cohort-trajectories-relig"><img loading="lazy" decoding="async" width="1330" height="783" src="https://www.allendowney.com/blog/wp-content/uploads/2026/03/cohort_trajectory_re-2dd48c8df781b26e84647025ea5891b6.png" alt="Cohort trajectories, percent with no religious preference" class="wp-image-1762" srcset="https://www.allendowney.com/blog/wp-content/uploads/2026/03/cohort_trajectory_re-2dd48c8df781b26e84647025ea5891b6.png 1330w, https://www.allendowney.com/blog/wp-content/uploads/2026/03/cohort_trajectory_re-2dd48c8df781b26e84647025ea5891b6-300x177.png 300w, https://www.allendowney.com/blog/wp-content/uploads/2026/03/cohort_trajectory_re-2dd48c8df781b26e84647025ea5891b6-1024x603.png 1024w, https://www.allendowney.com/blog/wp-content/uploads/2026/03/cohort_trajectory_re-2dd48c8df781b26e84647025ea5891b6-768x452.png 768w, https://www.allendowney.com/blog/wp-content/uploads/2026/03/cohort_trajectory_re-2dd48c8df781b26e84647025ea5891b6-459x270.png 459w" sizes="auto, (max-width: 1330px) 100vw, 1330px" /></figure>
<p class="wp-block-paragraph">Starting at the bottom, we can see that cohorts born between 1900 and 1930 were not very different — fewer than 10% of them were Nones.</p>
<p class="wp-block-paragraph">People born in the 1940s were increasingly non-religious, but this first wave of secularization stalled in the cohorts born in the 1950s. The second wave got started with people born in the 1960s, and continued until the 2000s cohorts, where it seems to have stalled again.</p>
<h2 class="wp-block-heading" id="decomposition">Decomposition</h2>
<p class="wp-block-paragraph">With these trajectories, we can decompose the cohort and period effects. The following figure shows the cohort effect, standardized by holding the period effect constant.</p>
<figure class="wp-block-image" id="cohort-profile-relig"><img loading="lazy" decoding="async" width="1133" height="764" src="https://www.allendowney.com/blog/wp-content/uploads/2026/03/cohort_standardized_-8a992073e7d82ea3a375589a5651bb5d.png" alt="Standardized cohort effect with fixed time mix, percent with no religious preference" class="wp-image-1760" srcset="https://www.allendowney.com/blog/wp-content/uploads/2026/03/cohort_standardized_-8a992073e7d82ea3a375589a5651bb5d.png 1133w, https://www.allendowney.com/blog/wp-content/uploads/2026/03/cohort_standardized_-8a992073e7d82ea3a375589a5651bb5d-300x202.png 300w, https://www.allendowney.com/blog/wp-content/uploads/2026/03/cohort_standardized_-8a992073e7d82ea3a375589a5651bb5d-1024x690.png 1024w, https://www.allendowney.com/blog/wp-content/uploads/2026/03/cohort_standardized_-8a992073e7d82ea3a375589a5651bb5d-768x518.png 768w, https://www.allendowney.com/blog/wp-content/uploads/2026/03/cohort_standardized_-8a992073e7d82ea3a375589a5651bb5d-400x270.png 400w" sizes="auto, (max-width: 1133px) 100vw, 1133px" /></figure>
<p class="wp-block-paragraph">As we saw in the previous figure, there was a period of relatively fast change in the 1940s cohorts that stalled among people born in the 1950s and then resumed among people born in the 1960s through the 1980s (primarily Gen X).</p>
<p class="wp-block-paragraph">Again, it looks like the most recent cohorts have leveled off, but with the width of the credible interval, it’s possible that the trend has continued or reversed.</p>
<p class="wp-block-paragraph">The following figure shows the period effect, standardized by holding the cohort mix constant.</p>
<figure class="wp-block-image" id="time-trend-relig"><img loading="lazy" decoding="async" width="1133" height="764" src="https://www.allendowney.com/blog/wp-content/uploads/2026/03/time_standardized_re-748498d5f8212df060fbdbfffbe5f356.png" alt="Standardized time trend with fixed cohort mix, percent with no religious preference" class="wp-image-1757" srcset="https://www.allendowney.com/blog/wp-content/uploads/2026/03/time_standardized_re-748498d5f8212df060fbdbfffbe5f356.png 1133w, https://www.allendowney.com/blog/wp-content/uploads/2026/03/time_standardized_re-748498d5f8212df060fbdbfffbe5f356-300x202.png 300w, https://www.allendowney.com/blog/wp-content/uploads/2026/03/time_standardized_re-748498d5f8212df060fbdbfffbe5f356-1024x690.png 1024w, https://www.allendowney.com/blog/wp-content/uploads/2026/03/time_standardized_re-748498d5f8212df060fbdbfffbe5f356-768x518.png 768w, https://www.allendowney.com/blog/wp-content/uploads/2026/03/time_standardized_re-748498d5f8212df060fbdbfffbe5f356-400x270.png 400w" sizes="auto, (max-width: 1133px) 100vw, 1133px" /></figure>
<p class="wp-block-paragraph">The period effect was generally increasing from 1990 to 2020, but seems to have leveled off or rolled over.</p>
<p class="wp-block-paragraph">So, if the rise of the Nones has stalled, at least temporarily, it seems to be a combination of a cohort effect among people born after 2000 and a period effect starting around 2020. This decomposition suggests we should look for at least two kinds of explanations:</p>
<ul class="wp-block-list">
<li>Differences in the childhood of people born after 2000 that might make them more likely to have a religious affiliation as young adults, and</li>
<li>Events since 2020 that have affected all cohorts in ways that might make them more religious.</li>
</ul>
<p class="wp-block-paragraph">I’ll hold off on speculating.</p>
<p class="wp-block-paragraph">For purposes of comparison, here is the trend from the time-only model (blue) and the standardized time trend from the time-cohort model (purple).</p>
<figure class="wp-block-image" id="time-trend-relig-comparison"><img loading="lazy" decoding="async" width="1133" height="764" src="https://www.allendowney.com/blog/wp-content/uploads/2026/03/time_standardized_re-251c2eac1b194a6d2418a92654e81829.png" alt="Time-only trend (blue) and standardized time trend from the cohort–period model (purple), percent with no religious preference" class="wp-image-1758" srcset="https://www.allendowney.com/blog/wp-content/uploads/2026/03/time_standardized_re-251c2eac1b194a6d2418a92654e81829.png 1133w, https://www.allendowney.com/blog/wp-content/uploads/2026/03/time_standardized_re-251c2eac1b194a6d2418a92654e81829-300x202.png 300w, https://www.allendowney.com/blog/wp-content/uploads/2026/03/time_standardized_re-251c2eac1b194a6d2418a92654e81829-1024x690.png 1024w, https://www.allendowney.com/blog/wp-content/uploads/2026/03/time_standardized_re-251c2eac1b194a6d2418a92654e81829-768x518.png 768w, https://www.allendowney.com/blog/wp-content/uploads/2026/03/time_standardized_re-251c2eac1b194a6d2418a92654e81829-400x270.png 400w" sizes="auto, (max-width: 1133px) 100vw, 1133px" /></figure>
<p class="wp-block-paragraph">The difference between these lines is the part of the change due to the cohort effect. So we can see that most of the change over this interval is due to generational replacement rather than disaffiliation.</p>
<p class="wp-block-paragraph"><strong>Methods</strong>: Details about the model are in the <a href="https://allendowney.github.io/CultureWar//tech-report">Technical Report</a>.</p>
<p class="wp-block-paragraph"></p>
<p>The post <a href="https://www.allendowney.com/blog/2026/03/30/have-the-nones-hit-a-ceiling/">Have the Nones hit a ceiling?</a> appeared first on <a href="https://www.allendowney.com/blog">Probably Overthinking It</a>.</p>
]]></content:encoded>
<post-id xmlns="com-wordpress:feed-additions:1">1756</post-id> </item>
<item>
<title>Attention, Chinese Readers</title>
<link>https://www.allendowney.com/blog/2026/03/29/attention-chinese-readers/</link>
<dc:creator><![CDATA[AllenDowney]]></dc:creator>
<pubDate>Sun, 29 Mar 2026 00:31:52 +0000</pubDate>
<category><![CDATA[Uncategorized]]></category>
<category><![CDATA[book]]></category>
<category><![CDATA[censorship]]></category>
<category><![CDATA[chinese]]></category>
<guid isPermaLink="false">https://www.allendowney.com/blog/?p=1664</guid>
<description><![CDATA[<p>The Chinese edition of Probably Overthinking It is available now (also here)! If you have the Chinese edition, there are two sections you won’t get to read — so I am including them here. Here is an excerpt from Chapter 3, including the deleted paragraph: In the Present The women surveyed in 1990 rejected the childbearing example of their mothers emphatically. On average, each woman had 2.3 fewer children than her mother. If that pattern had continued for another generation,...</p>
<p class="read-more"><a class="btn btn-default" href="https://www.allendowney.com/blog/2026/03/29/attention-chinese-readers/"> Read More<span class="screen-reader-text"> Read More</span></a></p>
<p>The post <a href="https://www.allendowney.com/blog/2026/03/29/attention-chinese-readers/">Attention, Chinese Readers</a> appeared first on <a href="https://www.allendowney.com/blog">Probably Overthinking It</a>.</p>
]]></description>
<content:encoded><![CDATA[
<p class="wp-block-paragraph">The Chinese edition of <em>Probably Overthinking It</em> is <a href="https://www.books.com.tw/products/CN17947121">available now</a> (also <a href="https://product.dangdang.com/12469358967.html">here</a>)!</p>
<figure class="wp-block-image size-full"><img loading="lazy" decoding="async" width="246" height="346" src="https://www.allendowney.com/blog/wp-content/uploads/2026/03/image-1.png" alt="" class="wp-image-1750" srcset="https://www.allendowney.com/blog/wp-content/uploads/2026/03/image-1.png 246w, https://www.allendowney.com/blog/wp-content/uploads/2026/03/image-1-213x300.png 213w, https://www.allendowney.com/blog/wp-content/uploads/2026/03/image-1-192x270.png 192w" sizes="auto, (max-width: 246px) 100vw, 246px" /></figure>
<p class="wp-block-paragraph">If you have the Chinese edition, there are two sections you won’t get to read — so I am including them here.</p>
<blockquote class="wp-block-quote is-layout-flow wp-block-quote-is-layout-flow">
<p class="wp-block-paragraph">Here is an excerpt from <a href="https://allendowney.github.io/ProbablyOverthinkingBook/preston.html#in-the-present">Chapter 3</a>, including the deleted paragraph:</p>
</blockquote>
<h2 class="wp-block-heading">In the Present</h2>
<p class="wp-block-paragraph">The women surveyed in 1990 rejected the childbearing example of their mothers emphatically. On average, each woman had 2.3 fewer children than her mother. If that pattern had continued for another generation, the average family size in 2018 would have been about 0.8. But it wasn’t.</p>
<p class="wp-block-paragraph">In fact, the average family size in 2018 was very close to 2, just as in 1990. So how did that happen?</p>
<p class="wp-block-paragraph">As it turns out, this is close to what we would expect if every woman had one child fewer than her mother. The following distribution shows the actual distribution in 2018, compared to the result if we start with the 1990 distribution and simulate the “one child fewer” scenario.</p>
<figure class="wp-block-image"><img loading="lazy" decoding="async" width="438" height="250" src="https://www.allendowney.com/blog/wp-content/uploads/2026/03/ddb1f82d657fad8171d5c400c9a539aead9ac1a4f85b7460f3a4ae7f7cb00237.png" alt="_images/ddb1f82d657fad8171d5c400c9a539aead9ac1a4f85b7460f3a4ae7f7cb00237.png" class="wp-image-1752" srcset="https://www.allendowney.com/blog/wp-content/uploads/2026/03/ddb1f82d657fad8171d5c400c9a539aead9ac1a4f85b7460f3a4ae7f7cb00237.png 438w, https://www.allendowney.com/blog/wp-content/uploads/2026/03/ddb1f82d657fad8171d5c400c9a539aead9ac1a4f85b7460f3a4ae7f7cb00237-300x171.png 300w" sizes="auto, (max-width: 438px) 100vw, 438px" /></figure>
<p class="wp-block-paragraph">The means of the two distributions are almost the same, but the shapes are different. In reality, there were more zero- and two-child families in 1990 than the simulation predicts, and fewer one-child families. But at least on average, it seems like women in the U.S. have been following the “one child fewer” policy for the last 30 years.</p>
<p class="wp-block-paragraph">The scenario at the beginning of this chapter is meant to be light-hearted, but in reality governments in many places and times have enacted policies meant to control family sizes and population growth. <strong>Most famously, China implemented a one-child policy in 1980 that imposed severe penalties on families with more than one child. Of course, this policy is objectionable to anyone who considers reproductive freedom a fundamental human right. But even as a practical matter, the unintended consequences were profound.</strong></p>
<p class="wp-block-paragraph"><strong>Rather than catalog them, I will mention one that is particularly ironic: while this policy was in effect, economic and social forces reduced the average <em>desired</em> family size so much that, when the policy was relaxed in 2015 and again in 2021, average lifetime fertility increased to only 1.3, far below the level needed to keep the population constant, near 2.1. Since then, China has implemented new policies intended to <em>increase</em> family sizes, but it is not clear whether they will have much effect. Demographers predict that by the time you read this, the population of China will probably be shrinking </strong>[UPDATE: It is.]<strong>. The consequences of the one-child policy are widespread and will affect China and the rest of the world for a long time.</strong></p>
<blockquote class="wp-block-quote is-layout-flow wp-block-quote-is-layout-flow">
<p class="wp-block-paragraph">And here is an excerpt from <a href="https://allendowney.github.io/ProbablyOverthinkingBook/nbue.html#child-mortality">Chapter 5</a>, including the deleted explanation.</p>
</blockquote>
<h2 class="wp-block-heading">Child mortality</h2>
<p class="wp-block-paragraph">Fortunately, child mortality has decreased since 1900. The following figure shows the percentage of children who die before age 5 for four geographical regions, from 1900 to 2019. These data were combined from several sources by Gapminder, a foundation based in Sweden that “promotes sustainable global development […] by increased use and understanding of statistics.”</p>
<figure class="wp-block-image"><img loading="lazy" decoding="async" width="436" height="250" src="https://www.allendowney.com/blog/wp-content/uploads/2026/03/220c5c7e411ef012b610deab7f65ab6dbd0a010aa40d46318a9a14823f2a268e.png" alt="_images/220c5c7e411ef012b610deab7f65ab6dbd0a010aa40d46318a9a14823f2a268e.png" class="wp-image-1754" srcset="https://www.allendowney.com/blog/wp-content/uploads/2026/03/220c5c7e411ef012b610deab7f65ab6dbd0a010aa40d46318a9a14823f2a268e.png 436w, https://www.allendowney.com/blog/wp-content/uploads/2026/03/220c5c7e411ef012b610deab7f65ab6dbd0a010aa40d46318a9a14823f2a268e-300x172.png 300w" sizes="auto, (max-width: 436px) 100vw, 436px" /></figure>
<p class="wp-block-paragraph">In every region, child mortality has decreased consistently and substantially. The only exceptions are indicated by the vertical lines: the 1918 influenza pandemic, which visibly affected Asia, the Americas, and Europe; World War II in Europe (1939-1945); <strong>and the Great Leap Forward in China (1958-1962)</strong>. In every case, these exceptions did not affect the long-term trend.</p>
<blockquote class="wp-block-quote is-layout-flow wp-block-quote-is-layout-flow">
<p class="wp-block-paragraph">[COMMENT: I thought I was being diplomatic by referring generally to the <a href="https://en.wikipedia.org/wiki/Great_Leap_Forward">Great Leap Forward</a> — rather than the <a href="https://en.wikipedia.org/wiki/Great_Chinese_Famine">Great Chinese Famine</a> or “Three Years of Great Famine” (三年大饥荒) — but apparently that was not enough.]</p>
</blockquote>
<p class="wp-block-paragraph">Although there is more work to do, especially in Africa, child mortality is substantially lower now, in every region of the world, than in 1900. As a result most people now are better new than used.</p>
<p class="wp-block-paragraph">To demonstrate this change, I collected recent mortality data from the Global Health Observatory of the World Health Organization (WHO). For people born in 2019, we don’t know what their future lifetimes will be, but we can estimate it if we assume that the mortality rate in each age group will not change over their lifetimes.</p>
<p class="wp-block-paragraph">Based on that simplification, the following figure shows average remaining lifetime as a function of age for Sweden and Nigeria in 2019, compared to Sweden in 1905.</p>
<figure class="wp-block-image"><img loading="lazy" decoding="async" width="438" height="250" src="https://www.allendowney.com/blog/wp-content/uploads/2026/03/6a45a65e6a7b3201af0f74c7b7df4d57ce5c5976972ce0e69538a1914fa5cc5b.png" alt="_images/6a45a65e6a7b3201af0f74c7b7df4d57ce5c5976972ce0e69538a1914fa5cc5b.png" class="wp-image-1753" srcset="https://www.allendowney.com/blog/wp-content/uploads/2026/03/6a45a65e6a7b3201af0f74c7b7df4d57ce5c5976972ce0e69538a1914fa5cc5b.png 438w, https://www.allendowney.com/blog/wp-content/uploads/2026/03/6a45a65e6a7b3201af0f74c7b7df4d57ce5c5976972ce0e69538a1914fa5cc5b-300x171.png 300w" sizes="auto, (max-width: 438px) 100vw, 438px" /></figure>
<p class="wp-block-paragraph">Since 1905, Sweden has continued to make progress; life expectancy at every age is higher in 2019 than in 1905. And Swedes now have the new-better-than-used property. Their life expectancy at birth is about 82 years, and it declines consistently over their lives, just like a light bulb.</p>
<p class="wp-block-paragraph">Unfortunately, Nigeria has one of the highest rates of child mortality in the world: in 2019, almost 8% of babies died in their first year of life. After that, they are briefly better used than new: life expectancy at birth is about 62 years; however, a baby who survives the first year will live another 65 years, on average.</p>
<p class="wp-block-paragraph">Going forward, I hope we continue to reduce child mortality in every region; if we do, soon every person born will be better new than used. Or maybe we can do even better than that.</p>
<p class="wp-block-paragraph"></p>
<p>The post <a href="https://www.allendowney.com/blog/2026/03/29/attention-chinese-readers/">Attention, Chinese Readers</a> appeared first on <a href="https://www.allendowney.com/blog">Probably Overthinking It</a>.</p>
]]></content:encoded>
<post-id xmlns="com-wordpress:feed-additions:1">1664</post-id> </item>
<item>
<title>Young Adults Are Not Very Happy</title>
<link>https://www.allendowney.com/blog/2026/03/19/young-adults-are-not-very-happy/</link>
<dc:creator><![CDATA[AllenDowney]]></dc:creator>
<pubDate>Thu, 19 Mar 2026 15:44:50 +0000</pubDate>
<category><![CDATA[Uncategorized]]></category>
<category><![CDATA[age period cohort analysis]]></category>
<category><![CDATA[bayesian statistics]]></category>
<category><![CDATA[general social survey]]></category>
<guid isPermaLink="false">https://www.allendowney.com/blog/?p=1736</guid>
<description><![CDATA[<p>Since 1972, the General Social Survey has asked respondents: “Taken all together, how would you say things are these days—would you say that you are very happy, pretty happy, or not too happy?” The following figure shows how the responses have changed over time and between birth cohorts. Each line represents one birth year. People born in 1900 were 72 years old when the survey started; at that point, about 37% said they were very happy. In 1990, the last...</p>
<p class="read-more"><a class="btn btn-default" href="https://www.allendowney.com/blog/2026/03/19/young-adults-are-not-very-happy/"> Read More<span class="screen-reader-text"> Read More</span></a></p>
<p>The post <a href="https://www.allendowney.com/blog/2026/03/19/young-adults-are-not-very-happy/">Young Adults Are Not Very Happy</a> appeared first on <a href="https://www.allendowney.com/blog">Probably Overthinking It</a>.</p>
]]></description>
<content:encoded><![CDATA[
<p class="wp-block-paragraph">Since 1972, the General Social Survey has asked respondents: “Taken all together, how would you say things are these days—would you say that you are very happy, pretty happy, or not too happy?”</p>
<p class="wp-block-paragraph">The following figure shows how the responses have changed over time and between birth cohorts. Each line represents one birth year.</p>
<figure class="wp-block-image" id="cohort-trajectories-happy"><img loading="lazy" decoding="async" width="1330" height="778" src="https://www.allendowney.com/blog/wp-content/uploads/2026/03/cohort_trajectory_ha-ee8d3c24ba4d6e9d119c114dfd0b23c3.png" alt="Cohort trajectories, percent who respond “very happy”" class="wp-image-1739" srcset="https://www.allendowney.com/blog/wp-content/uploads/2026/03/cohort_trajectory_ha-ee8d3c24ba4d6e9d119c114dfd0b23c3.png 1330w, https://www.allendowney.com/blog/wp-content/uploads/2026/03/cohort_trajectory_ha-ee8d3c24ba4d6e9d119c114dfd0b23c3-300x175.png 300w, https://www.allendowney.com/blog/wp-content/uploads/2026/03/cohort_trajectory_ha-ee8d3c24ba4d6e9d119c114dfd0b23c3-1024x599.png 1024w, https://www.allendowney.com/blog/wp-content/uploads/2026/03/cohort_trajectory_ha-ee8d3c24ba4d6e9d119c114dfd0b23c3-768x449.png 768w, https://www.allendowney.com/blog/wp-content/uploads/2026/03/cohort_trajectory_ha-ee8d3c24ba4d6e9d119c114dfd0b23c3-462x270.png 462w" sizes="auto, (max-width: 1330px) 100vw, 1330px" /></figure>
<p class="wp-block-paragraph">People born in 1900 were 72 years old when the survey started; at that point, about 37% said they were very happy. In 1990, the last year they were eligible to participate, a little more than 40% said they were very happy. So it seems like they aged well—or possibly the less happy died earlier.</p>
<p class="wp-block-paragraph">People born in 1910 were a little less happy when the survey started, but by the time they aged out, they also reached 40%. They were the last generation to reach that mark.</p>
<p class="wp-block-paragraph">Among people born between 1920 and 1950, each cohort was a little less happy than the one before (or maybe less likely to say they were happy). In these cohorts, we can see a general trend over time: increasing until about 2000, leveling off, and declining after 2010.</p>
<p class="wp-block-paragraph">The cohorts born in the 1960s and 1970s followed a similar trajectory, with only small differences from one birth year to the next.</p>
<p class="wp-block-paragraph">And then the bottom fell out. Starting with people born in the 1980s (the earliest Millennials), each successive cohort was substantially less happy than the one before.</p>
<p class="wp-block-paragraph">When people born in 1990 joined the survey in 2008 (at age 18), only 27% said they were very happy. In the most recent data, from 2024, the number had fallen to 22%.</p>
<p class="wp-block-paragraph">When people born in 2000 entered in 2018, they set a new record low at 21%, which has now fallen to 18%.</p>
<p class="wp-block-paragraph">And in the most recent cohort—born in 2006 and interviewed in 2024—only 16% said they were very happy.</p>
<p class="wp-block-paragraph">These percentages are based on a statistical model that estimates the proportion of “very happy” responses in each group at each point in time. The details of the model and its assumptions are below.</p>
<h2 class="wp-block-heading" id="the-time-trend">The Time Trend</h2>
<p class="wp-block-paragraph">With an estimated proportion for each cohort and time step, we can compute separate contributions for changes over time and between cohorts.</p>
<p class="wp-block-paragraph">To characterize the contribution of time, we have to hold the cohort effect constant, which we can do by computing the distribution of birth years across the entire dataset and simulating a population where this distribution does not change over time. The following figure shows the result.</p>
<figure class="wp-block-image" id="time-trend-happy"><img loading="lazy" decoding="async" width="1133" height="790" src="https://www.allendowney.com/blog/wp-content/uploads/2026/03/time_standardized_ha-26b65d5757264321ab30d96371b21ccf.png" alt="Standardized time trend, percent who respond “very happy”" class="wp-image-1738" srcset="https://www.allendowney.com/blog/wp-content/uploads/2026/03/time_standardized_ha-26b65d5757264321ab30d96371b21ccf.png 1133w, https://www.allendowney.com/blog/wp-content/uploads/2026/03/time_standardized_ha-26b65d5757264321ab30d96371b21ccf-300x209.png 300w, https://www.allendowney.com/blog/wp-content/uploads/2026/03/time_standardized_ha-26b65d5757264321ab30d96371b21ccf-1024x714.png 1024w, https://www.allendowney.com/blog/wp-content/uploads/2026/03/time_standardized_ha-26b65d5757264321ab30d96371b21ccf-768x535.png 768w, https://www.allendowney.com/blog/wp-content/uploads/2026/03/time_standardized_ha-26b65d5757264321ab30d96371b21ccf-387x270.png 387w" sizes="auto, (max-width: 1133px) 100vw, 1133px" /></figure>
<p class="wp-block-paragraph">The overall level of happiness increased between 1972 and 2000, leveled off, and then declined after 2010.</p>
<p class="wp-block-paragraph">Of course it is speculation to say why that happened, but we can think about large-scale economic and social patterns and how they line up with these trends.</p>
<ul class="wp-block-list">
<li>Economically, 1980 to 2000 was a period of growth and relative stability. That changed after the end of the Dot-com bubble in 2001 and, more importantly, the Global Financial Crisis in 2008, which had broad and persistent effects on employment, wealth, and economic security.</li>
<li>Geopolitically, the 1970s through the 1990s were relatively quiet compared to what followed. The September 11 attacks in 2001, and the wars in Iraq (2003–2011) and Afghanistan (2001–2021) marked a shift toward a more uncertain and conflict-oriented global environment.</li>
<li>Participation in civic organizations and religious institutions declined over the past several decades. These institutions traditionally provided social support, shared identity, and regular face-to-face interaction. Social isolation is strongly associated with lower well-being.</li>
<li>At the same time, the media environment was transformed. The rise of 24-hour news increased exposure to negative and emotionally salient events, and after 2010 the spread of smartphones and social media made that exposure continuous and personalized.</li>
<li>Finally, measures of trust in institutions and other people have generally declined over this period, while political polarization has increased. These trends may reduce people’s sense of stability and shared purpose.</li>
</ul>
<p class="wp-block-paragraph">The COVID-19 pandemic likely contributed to the most recent decline, but the downward trend was already underway before 2020.</p>
<h2 class="wp-block-heading" id="the-cohort-effect">The Cohort Effect</h2>
<p class="wp-block-paragraph">Just as we isolated the time trend by simulating a survey with a fixed distribution of cohorts, we can isolate the cohort effect by simulating a survey with a fixed distribution of times. The following figure shows the result.</p>
<figure class="wp-block-image" id="cohort-profile-happy"><img loading="lazy" decoding="async" width="1133" height="790" src="https://www.allendowney.com/blog/wp-content/uploads/2026/03/cohort_standardized_-2dbe3fdd869f5be03f0b91d2cf3b980e.png" alt="Standardized cohort effect, percent who respond “very happy”" class="wp-image-1740" srcset="https://www.allendowney.com/blog/wp-content/uploads/2026/03/cohort_standardized_-2dbe3fdd869f5be03f0b91d2cf3b980e.png 1133w, https://www.allendowney.com/blog/wp-content/uploads/2026/03/cohort_standardized_-2dbe3fdd869f5be03f0b91d2cf3b980e-300x209.png 300w, https://www.allendowney.com/blog/wp-content/uploads/2026/03/cohort_standardized_-2dbe3fdd869f5be03f0b91d2cf3b980e-1024x714.png 1024w, https://www.allendowney.com/blog/wp-content/uploads/2026/03/cohort_standardized_-2dbe3fdd869f5be03f0b91d2cf3b980e-768x535.png 768w, https://www.allendowney.com/blog/wp-content/uploads/2026/03/cohort_standardized_-2dbe3fdd869f5be03f0b91d2cf3b980e-387x270.png 387w" sizes="auto, (max-width: 1133px) 100vw, 1133px" /></figure>
<p class="wp-block-paragraph">The cohort effect is larger and more consistent than the time trend: the difference between the happiest and least happy cohorts is more than 20 percentage points.</p>
<p class="wp-block-paragraph">The decline was relatively slow for cohorts born between 1900 and 1950 and nearly zero for cohorts born in the 1950s, 1960s and 1970s (late Baby Boomers and Gen X). The steep decline begins with the Millennials and continues into Gen Z.</p>
<p class="wp-block-paragraph">Possible explanations for the recent decline include:</p>
<ul class="wp-block-list">
<li>Transformation of childhood: <a href="https://jonathanhaidt.com/anxious-generation/" target="_blank" rel="noreferrer noopener">Jonathan Haidt</a> has described childhood in recent cohorts as “overprotected in the real world and underprotected in the online world.” Increased parental monitoring, reduced independent play, and greater time spent online may affect the development of autonomy, risk tolerance, and social skills. If these early-life experiences shape long-term outlook, they could contribute to lower self-reported happiness.</li>
<li>Greater and earlier exposure to media: Younger cohorts were exposed to a media landscape characterized by continuous, personalized, and often negative content. Social media platforms amplify social comparison and negative content, while displacing in-person interaction. Increased awareness of global risks—including climate change—may contribute to a more pessimistic worldview.</li>
<li>Differential impact of economic conditions: Recent cohorts entered the labor market during periods of economic disruption, including the aftermath of the Global Financial Crisis and more recent pandemic-related shocks. These cohorts also face higher housing costs and greater student debt. Economic insecurity during the transition to adulthood may have lasting effects on well-being.</li>
<li>Extension of “liminal” adulthood: Young adults are taking longer to complete education, establish careers, form long-term partnerships, and have children. This extended unsettled period may be associated with lower life satisfaction.</li>
<li>Norms around self-reported well-being. Younger cohorts may also be less likely to say they are “very happy,” either because of changing norms around self-presentation or greater awareness of mental health.</li>
</ul>
<p class="wp-block-paragraph">It’s hard to say how much of the recent decline we can attribute to these causes. But the decline is steep, and seems to be ongoing.</p>
<h2 class="wp-block-heading" id="how-the-model-works">How the Model Works</h2>
<p class="wp-block-paragraph">One of the challenges with this kind of survey data is that the sample size is small for each birth year in each iteration of the survey. If we plot raw percentages over time, the result is noisy.</p>
<p class="wp-block-paragraph">In <a href="https://allendowney.github.io/ProbablyOverthinkingIt/simpson.html#old-optimists-young-pessimists" target="_blank" rel="noreferrer noopener"><em>Probably Overthinking It</em></a>, I addressed this problem by grouping respondents into decade-of-birth cohorts and smoothing the resulting time series. That approach works, but it has drawbacks: aggregation removes detail, introduces edge effects for the earliest and latest cohorts, and requires an arbitrary choice about the level of smoothing.</p>
<p class="wp-block-paragraph">The new model takes a more principled approach. Instead of smoothing the observed data, it models an unobserved (latent) propensity to report being “very happy” for each cohort in each year.</p>
<p class="wp-block-paragraph">We assume that the number of “very happy” responses in each group follows a binomial distribution, where the probability of a “very happy” response depends on this latent propensity. The observed responses provide noisy information about the latent factor; the model combines information across cohorts and years to estimate it.</p>
<p class="wp-block-paragraph">The latent propensity is modeled as the sum of an intercept, representing the overall level of happiness, a smooth effect of birth cohort, a smooth effect of survey year, and a year-specific random effect that captures short-term fluctuations (overdispersion).</p>
<p class="wp-block-paragraph">The cohort and period effects are modeled as second-order Gaussian random walks (RW2), which means the model assumes these effects evolve smoothly over time, with a preference for gradual changes in slope rather than abrupt jumps, unless the data provide strong evidence otherwise. The amount of smoothing is not fixed in advance; it is estimated from the data.</p>
<p class="wp-block-paragraph">The random year effect captures variation from one survey to the next that is not explained by long-term trends, like current events and topics of discussion.</p>
<p class="wp-block-paragraph">Where we have a lot of data, the estimates track the observed proportions closely. Where data are sparse, the model borrows strength from neighboring cohorts and years, providing principled smoothing and interpolation without arbitrary grouping.</p>
<p class="wp-block-paragraph">For the details of the model, see the <a href="https://allendowney.github.io/CultureWar//tech-report">Technical Report</a>.<a href="https://allendowney.github.io/CultureWar//"></a><a href="https://allendowney.github.io/CultureWar//"></a></p>
<p class="wp-block-paragraph"></p>
<p>The post <a href="https://www.allendowney.com/blog/2026/03/19/young-adults-are-not-very-happy/">Young Adults Are Not Very Happy</a> appeared first on <a href="https://www.allendowney.com/blog">Probably Overthinking It</a>.</p>
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"id": "https://www.allendowney.com/blog/?p=1836",
"title": "Who Is More Trusting: Liberals or Conservatives?",
"description": "<p>When I go crawling around in data from the General Social Survey, sooner or later I run into Ryan Burge, who writes Graphs About Religion. In his most recent post, he wrote about changes in interpersonal trust, as measured by this GSS question: Generally speaking, would you say that most people can be trusted or that you can’t be too careful in dealing with people? Among other analyses, he looks at how the responses relate to self-identification as liberal, conservative,...</p>\n<p class=\"read-more\"><a class=\"btn btn-default\" href=\"https://www.allendowney.com/blog/2026/06/12/who-is-more-trusting-liberals-or-conservatives/\"> Read More<span class=\"screen-reader-text\"> Read More</span></a></p>\n<p>The post <a href=\"https://www.allendowney.com/blog/2026/06/12/who-is-more-trusting-liberals-or-conservatives/\">Who Is More Trusting: Liberals or Conservatives?</a> appeared first on <a href=\"https://www.allendowney.com/blog\">Probably Overthinking It</a>.</p>",
"url": "https://www.allendowney.com/blog/2026/06/12/who-is-more-trusting-liberals-or-conservatives/",
"published": "2026-06-12T13:40:20.000Z",
"updated": "2026-06-12T13:40:20.000Z",
"content": "<p class=\"wp-block-paragraph\">When I go crawling around in data from the General Social Survey, sooner or later I run into Ryan Burge, who writes <em>Graphs About Religion</em>. In <a href=\"https://www.graphsaboutreligion.com/p/gen-z-doesnt-trust-anyone\" target=\"_blank\" rel=\"noreferrer noopener\">his most recent post</a>, he wrote about changes in interpersonal trust, as measured by this GSS question:</p>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\">\n<p class=\"wp-block-paragraph\">Generally speaking, would you say that most people can be trusted or that you can’t be too careful in dealing with people?</p>\n</blockquote>\n\n\n\n<p class=\"wp-block-paragraph\">Among other analyses, he looks at how the responses relate to self-identification as liberal, conservative, or moderate. The results are … complicated. Ryan writes:</p>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\">\n<p class=\"wp-block-paragraph\">Among older Americans who identify as liberal, they are more likely to trust other people. Among Gen Z liberals, it’s exactly the opposite.</p>\n</blockquote>\n\n\n\n<p class=\"wp-block-paragraph\">To explain why older liberals are more trusting, Ryan suggests:</p>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\">\n<p class=\"wp-block-paragraph\">Liberalism is based on collectivism. It embraces the idea that “together, we can achieve more.” Things like universal healthcare rely on a sense of trust among large groups of people.</p>\n</blockquote>\n\n\n\n<p class=\"wp-block-paragraph\">But if that’s true, why does the effect go in the opposite direction with Gen Z? Ryan speculates:</p>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\">\n<p class=\"wp-block-paragraph\">Well, maybe liberals feel very slighted by the fact that Donald Trump has been on the ballot for president in every election in which they’ve been eligible to vote, and he’s won twice. Or it could be that they are more impacted by the cynicism of the internet than conservatives? Or maybe it’s because they report higher rates of depression and anxiety than the rest of the ideological spectrum?</p>\n</blockquote>\n\n\n\n<p class=\"wp-block-paragraph\">As it happened, I looked at the same GSS variable in <a href=\"https://www.allendowney.com/blog/2026/04/03/trust-and-well-being/\" target=\"_blank\" rel=\"noreferrer noopener\">a recent article</a>. But I didn’t do the breakdown by political ideology, so let’s do that now.</p>\n\n\n\n<h3 class=\"wp-block-heading\">The Story So Far</h3>\n\n\n\n<p class=\"wp-block-paragraph\">First, here’s a recap of what we saw in the previous post, with the whole GSS sample. The following figure shows the percentage of respondents who said “most people can be trusted.”</p>\n\n\n\n<figure class=\"wp-block-image\" id=\"trust-recap-time-series\"><img fetchpriority=\"high\" decoding=\"async\" width=\"1133\" height=\"826\" src=\"https://www.allendowney.com/blog/wp-content/uploads/2026/06/time_model_trust_rw2-25d010d905ca562e299e59b0e89d1713.png\" alt=\"Time series: percent saying most people can be trusted (all respondents)\" class=\"wp-image-1839\" srcset=\"https://www.allendowney.com/blog/wp-content/uploads/2026/06/time_model_trust_rw2-25d010d905ca562e299e59b0e89d1713.png 1133w, https://www.allendowney.com/blog/wp-content/uploads/2026/06/time_model_trust_rw2-25d010d905ca562e299e59b0e89d1713-300x219.png 300w, https://www.allendowney.com/blog/wp-content/uploads/2026/06/time_model_trust_rw2-25d010d905ca562e299e59b0e89d1713-1024x747.png 1024w, https://www.allendowney.com/blog/wp-content/uploads/2026/06/time_model_trust_rw2-25d010d905ca562e299e59b0e89d1713-768x560.png 768w, https://www.allendowney.com/blog/wp-content/uploads/2026/06/time_model_trust_rw2-25d010d905ca562e299e59b0e89d1713-370x270.png 370w\" sizes=\"(max-width: 1133px) 100vw, 1133px\" /><figcaption class=\"wp-element-caption\">Time series: percent saying most people can be trusted (all respondents)</figcaption></figure>\n\n\n\n<p class=\"wp-block-paragraph\">Interpersonal trust has declined consistently since the survey started in 1972. In the previous post, I decomposed this trend into cohort and period effects. Here’s the estimated cohort effect:</p>\n\n\n\n<figure class=\"wp-block-image\" id=\"trust-recap-cohort-effect\"><img decoding=\"async\" width=\"1133\" height=\"790\" src=\"https://www.allendowney.com/blog/wp-content/uploads/2026/06/cohort_standardized_-83920254db4863278c92f3cee792510c.png\" alt=\"Standardized cohort effect with fixed time mix, percent saying most people can be trusted (all respondents)\" class=\"wp-image-1840\" srcset=\"https://www.allendowney.com/blog/wp-content/uploads/2026/06/cohort_standardized_-83920254db4863278c92f3cee792510c.png 1133w, https://www.allendowney.com/blog/wp-content/uploads/2026/06/cohort_standardized_-83920254db4863278c92f3cee792510c-300x209.png 300w, https://www.allendowney.com/blog/wp-content/uploads/2026/06/cohort_standardized_-83920254db4863278c92f3cee792510c-1024x714.png 1024w, https://www.allendowney.com/blog/wp-content/uploads/2026/06/cohort_standardized_-83920254db4863278c92f3cee792510c-768x535.png 768w, https://www.allendowney.com/blog/wp-content/uploads/2026/06/cohort_standardized_-83920254db4863278c92f3cee792510c-387x270.png 387w\" sizes=\"(max-width: 1133px) 100vw, 1133px\" /><figcaption class=\"wp-element-caption\">Standardized cohort effect with fixed time mix, percent saying most people can be trusted (all respondents)</figcaption></figure>\n\n\n\n<p class=\"wp-block-paragraph\">The level of trust increased between the cohorts born in the 1900s through the 1940s, and then started a steep decline — more than 30 percentage points over 60 years. And here’s the remaining period effect, after factoring out the cohort effect.</p>\n\n\n\n<figure class=\"wp-block-image\" id=\"trust-recap-period-effect\"><img decoding=\"async\" width=\"1133\" height=\"790\" src=\"https://www.allendowney.com/blog/wp-content/uploads/2026/06/time_standardized_tr-2f029b683d9ad86a39a536e4f95c8c0f.png\" alt=\"Standardized time trend with fixed cohort mix, percent saying most people can be trusted (all respondents)\" class=\"wp-image-1841\" srcset=\"https://www.allendowney.com/blog/wp-content/uploads/2026/06/time_standardized_tr-2f029b683d9ad86a39a536e4f95c8c0f.png 1133w, https://www.allendowney.com/blog/wp-content/uploads/2026/06/time_standardized_tr-2f029b683d9ad86a39a536e4f95c8c0f-300x209.png 300w, https://www.allendowney.com/blog/wp-content/uploads/2026/06/time_standardized_tr-2f029b683d9ad86a39a536e4f95c8c0f-1024x714.png 1024w, https://www.allendowney.com/blog/wp-content/uploads/2026/06/time_standardized_tr-2f029b683d9ad86a39a536e4f95c8c0f-768x535.png 768w, https://www.allendowney.com/blog/wp-content/uploads/2026/06/time_standardized_tr-2f029b683d9ad86a39a536e4f95c8c0f-387x270.png 387w\" sizes=\"(max-width: 1133px) 100vw, 1133px\" /><figcaption class=\"wp-element-caption\">Standardized time trend with fixed cohort mix, percent saying most people can be trusted (all respondents)</figcaption></figure>\n\n\n\n<p class=\"wp-block-paragraph\">There is almost no period effect in the full sample.</p>\n\n\n\n<h3 class=\"wp-block-heading\">Breakdown by Politics</h3>\n\n\n\n<p class=\"wp-block-paragraph\">Now let’s get to the question we started with:</p>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\">\n<p class=\"wp-block-paragraph\">Who is more trusting: liberals or conservatives?</p>\n</blockquote>\n\n\n\n<p class=\"wp-block-paragraph\">Here’s the time series, broken down by ideology.</p>\n\n\n\n<figure class=\"wp-block-image\" id=\"trust-polviews-time-series\"><img loading=\"lazy\" decoding=\"async\" width=\"1133\" height=\"826\" src=\"https://www.allendowney.com/blog/wp-content/uploads/2026/06/composed_trust_polvi-2191f28230cc6036ffa53c7c589783eb.png\" alt=\"Time series: percent saying most people can be trusted, by 3-point political views\" class=\"wp-image-1842\" srcset=\"https://www.allendowney.com/blog/wp-content/uploads/2026/06/composed_trust_polvi-2191f28230cc6036ffa53c7c589783eb.png 1133w, https://www.allendowney.com/blog/wp-content/uploads/2026/06/composed_trust_polvi-2191f28230cc6036ffa53c7c589783eb-300x219.png 300w, https://www.allendowney.com/blog/wp-content/uploads/2026/06/composed_trust_polvi-2191f28230cc6036ffa53c7c589783eb-1024x747.png 1024w, https://www.allendowney.com/blog/wp-content/uploads/2026/06/composed_trust_polvi-2191f28230cc6036ffa53c7c589783eb-768x560.png 768w, https://www.allendowney.com/blog/wp-content/uploads/2026/06/composed_trust_polvi-2191f28230cc6036ffa53c7c589783eb-370x270.png 370w\" sizes=\"auto, (max-width: 1133px) 100vw, 1133px\" /><figcaption class=\"wp-element-caption\">Time series: percent saying most people can be trusted, by 3-point political views</figcaption></figure>\n\n\n\n<p class=\"wp-block-paragraph\">Until recently, there was not much difference: liberals and conservatives were about equally likely to say people can be trusted — both a little more trusting than moderates (who are, maybe, too distrustful to join a team).</p>\n\n\n\n<p class=\"wp-block-paragraph\">Since the 2000s, liberals and conservatives have diverged, and now liberals are more trusting, by about 5 percentage points. But all three groups are still declining.</p>\n\n\n\n<p class=\"wp-block-paragraph\">Now let’s decompose those trends into cohort and period effects. Here are the cohort effects for the three groups.</p>\n\n\n\n<figure class=\"wp-block-image\" id=\"trust-polviews-cohort-effect\"><img loading=\"lazy\" decoding=\"async\" width=\"1133\" height=\"826\" src=\"https://www.allendowney.com/blog/wp-content/uploads/2026/06/composed_trust_polvi-5e9990b3c69d8128602000b1b4e77eac.png\" alt=\"Standardized cohort effect for generalized trust by political views (uniform weights on survey years within group)\" class=\"wp-image-1844\" srcset=\"https://www.allendowney.com/blog/wp-content/uploads/2026/06/composed_trust_polvi-5e9990b3c69d8128602000b1b4e77eac.png 1133w, https://www.allendowney.com/blog/wp-content/uploads/2026/06/composed_trust_polvi-5e9990b3c69d8128602000b1b4e77eac-300x219.png 300w, https://www.allendowney.com/blog/wp-content/uploads/2026/06/composed_trust_polvi-5e9990b3c69d8128602000b1b4e77eac-1024x747.png 1024w, https://www.allendowney.com/blog/wp-content/uploads/2026/06/composed_trust_polvi-5e9990b3c69d8128602000b1b4e77eac-768x560.png 768w, https://www.allendowney.com/blog/wp-content/uploads/2026/06/composed_trust_polvi-5e9990b3c69d8128602000b1b4e77eac-370x270.png 370w\" sizes=\"auto, (max-width: 1133px) 100vw, 1133px\" /><figcaption class=\"wp-element-caption\">Standardized cohort effect for generalized trust by political views (uniform weights on survey years within group)</figcaption></figure>\n\n\n\n<p class=\"wp-block-paragraph\">Here we can see what Ryan reported: in most generations, liberals are more trusting than conservatives; it’s only in the most recent generation that it goes the other way. The crossover happens among people born in the mid-1990s, close to the conventional beginning of Gen Z (born 1997 to 2012).</p>\n\n\n\n<p class=\"wp-block-paragraph\">And here’s the period effect for the three groups.</p>\n\n\n\n<figure class=\"wp-block-image\" id=\"trust-polviews-period-effect\"><img loading=\"lazy\" decoding=\"async\" width=\"1133\" height=\"826\" src=\"https://www.allendowney.com/blog/wp-content/uploads/2026/06/composed_trust_polvi-e873e0d24bfb4397559e322760556ee6.png\" alt=\"Standardized period trend for generalized trust by political views (fixed within-group cohort weights)\" class=\"wp-image-1843\" srcset=\"https://www.allendowney.com/blog/wp-content/uploads/2026/06/composed_trust_polvi-e873e0d24bfb4397559e322760556ee6.png 1133w, https://www.allendowney.com/blog/wp-content/uploads/2026/06/composed_trust_polvi-e873e0d24bfb4397559e322760556ee6-300x219.png 300w, https://www.allendowney.com/blog/wp-content/uploads/2026/06/composed_trust_polvi-e873e0d24bfb4397559e322760556ee6-1024x747.png 1024w, https://www.allendowney.com/blog/wp-content/uploads/2026/06/composed_trust_polvi-e873e0d24bfb4397559e322760556ee6-768x560.png 768w, https://www.allendowney.com/blog/wp-content/uploads/2026/06/composed_trust_polvi-e873e0d24bfb4397559e322760556ee6-370x270.png 370w\" sizes=\"auto, (max-width: 1133px) 100vw, 1133px\" /><figcaption class=\"wp-element-caption\">Standardized period trend for generalized trust by political views (fixed within-group cohort weights)</figcaption></figure>\n\n\n\n<p class=\"wp-block-paragraph\">For conservatives and moderates, the period effect is generally downward, although small. For liberals, it’s the other way around, generally increasing since about 2000.</p>\n\n\n\n<p class=\"wp-block-paragraph\">The cohort-period decomposition provides some hints about what’s going on:</p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Among conservatives and moderates, the cohort and period effects are both downward, so they contributed to a steeper decline over time.</li>\n\n\n\n<li>Among liberals, the cohort effect is also downward, but the period effect is upward, so the period effect mitigates the cohort effect.</li>\n</ul>\n\n\n\n<p class=\"wp-block-paragraph\">To explain the cohort effect, I think Ryan’s suggestions are plausible. People born after 1995 have grown up during a discouraging time to be a liberal. Recent developments contrary to the liberal worldview include</p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>The rise of populist and nationalist movements in several countries, along with democratic backsliding or erosion of liberal norms.</li>\n\n\n\n<li>Slow progress or reversal on climate change.</li>\n\n\n\n<li>Increasing distrust of experts, journalists, scientists, and public institutions.</li>\n\n\n\n<li>Declining confidence in institutions such as Congress, the media, and organized religion.</li>\n\n\n\n<li>A series of conservative Supreme Court decisions, most notably the overturning of long-established abortion rights protections in 2022.</li>\n</ul>\n\n\n\n<p class=\"wp-block-paragraph\">Negativity bias in the media — especially social media — is probably a contributing factor. And going to school during the pandemic probably didn’t help.</p>\n\n\n\n<p class=\"wp-block-paragraph\">But what about that period effect — can we think of reasons liberals would be more trusting, starting around 2005? If the recent cohort effect among young liberals is driven by the Trump era (at least in part), maybe the period effect was driven by events and trends of the Obama era that were aligned with the liberal worldview:</p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Perception that the country was becoming more socially inclusive and diverse.</li>\n\n\n\n<li>Greater visibility and acceptance of LGBTQ people, and growing support for same-sex marriage, culminating in nationwide legalization in 2015.</li>\n\n\n\n<li>Expansion of health insurance coverage through the Patient Protection and Affordable Care Act.</li>\n</ul>\n\n\n\n<p class=\"wp-block-paragraph\">And falling crime rates from the 1990s through the 2010s might have contributed more directly to increasing interpersonal trust.</p>\n\n\n\n<p class=\"wp-block-paragraph\">Of course these explanations are speculative, so let’s get back to what’s supported by the data:</p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Since the 1970s, interpersonal trust has declined consistently in all three groups (liberal, conservative, and moderate).</li>\n\n\n\n<li>Before 2005, liberals and conservatives were about equally trusting; since then, the decline among liberals has slowed, so they are now the most trusting group.</li>\n\n\n\n<li>Among conservatives and moderates, the cohort and period effects are both downward, so they contribute to steeper decline.</li>\n\n\n\n<li>Among liberals, the cohort effect is steeply downward in the most recent cohorts, but the decline is mitigated by a positive period effect.</li>\n</ul>\n\n\n\n<p class=\"wp-block-paragraph\">For now, liberals are the most trusting group, but if the cohort effect persists, they might not be for long.</p>\n\n\n\n<p class=\"wp-block-paragraph\"></p>\n<p>The post <a href=\"https://www.allendowney.com/blog/2026/06/12/who-is-more-trusting-liberals-or-conservatives/\">Who Is More Trusting: Liberals or Conservatives?</a> appeared first on <a href=\"https://www.allendowney.com/blog\">Probably Overthinking It</a>.</p>",
"image": null,
"media": [],
"authors": [
{
"name": "AllenDowney",
"email": null,
"url": null
}
],
"categories": [
{
"label": "Uncategorized",
"term": "Uncategorized",
"url": null
},
{
"label": "age period cohort analysis",
"term": "age period cohort analysis",
"url": null
},
{
"label": "bayesian statistics",
"term": "bayesian statistics",
"url": null
},
{
"label": "general social survey",
"term": "general social survey",
"url": null
},
{
"label": "political alignment",
"term": "political alignment",
"url": null
}
]
},
{
"id": "https://www.allendowney.com/blog/?p=1828",
"title": "The Frog Puzzle",
"description": "<p>Here’s a probability puzzle from a TED-Ed video called Can you solve the frog riddle? by Derek Abbott. It came up recently in this Reddit thread: You’re stranded in a rainforest after accidentally eating a poisonous mushroom. To survive the poison, you need to lick a certain species of frog. Only female frogs produce the antidote. Male and female frogs occur in equal numbers and look identical, but male frogs have a distinctive croak. You see one frog alone on...</p>\n<p class=\"read-more\"><a class=\"btn btn-default\" href=\"https://www.allendowney.com/blog/2026/06/04/the-frog-puzzle/\"> Read More<span class=\"screen-reader-text\"> Read More</span></a></p>\n<p>The post <a href=\"https://www.allendowney.com/blog/2026/06/04/the-frog-puzzle/\">The Frog Puzzle</a> appeared first on <a href=\"https://www.allendowney.com/blog\">Probably Overthinking It</a>.</p>",
"url": "https://www.allendowney.com/blog/2026/06/04/the-frog-puzzle/",
"published": "2026-06-04T19:13:19.000Z",
"updated": "2026-06-04T19:13:19.000Z",
"content": "<p class=\"wp-block-paragraph\">Here’s a probability puzzle from a TED-Ed video called <a href=\"https://www.youtube.com/watch?v=cpwSGsb-rTs\">Can you solve the frog riddle?</a> by Derek Abbott. It came up recently in this <a href=\"https://www.reddit.com/r/probabilitytheory/comments/1ttzcjt/frog_riddle_again/\">Reddit thread</a>:</p>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\">\n<p class=\"wp-block-paragraph\">You’re stranded in a rainforest after accidentally eating a poisonous mushroom. To survive the poison, you need to lick a certain species of frog. Only female frogs produce the antidote. Male and female frogs occur in equal numbers and look identical, but male frogs have a distinctive croak.</p>\n\n\n\n<p class=\"wp-block-paragraph\">You see one frog alone on a tree stump. In another direction, you hear the croak of a male frog coming from a clearing with two frogs. You can’t tell which one made the sound.</p>\n\n\n\n<p class=\"wp-block-paragraph\">You only have time to go to one place. What are your chances of survival if you go to the clearing and lick both frogs? What if you go to the lone frog?</p>\n</blockquote>\n\n\n\n<p class=\"wp-block-paragraph\">The second question is relatively easy: if we assume that you are equally likely to see a male or female frog, the probability is 50% that the lone frog is female.</p>\n\n\n\n<p class=\"wp-block-paragraph\">The first question depends on how we interpret the puzzle. In particular, it hinges on the word “distinctive” – does that mean:</p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Only male frogs croak, and the sound is distinguishable from background noises, or</li>\n\n\n\n<li>Both male and female frogs croak, but the male croak is distinguishable from the female croak.</li>\n</ul>\n\n\n\n<p class=\"wp-block-paragraph\">Based on the answer presented in the video, the first meaning is intended. So we’ll start by solving that version.</p>\n\n\n\n<p class=\"wp-block-paragraph\">But the second meaning makes the problem a little harder, so we’ll solve that one, too.</p>\n\n\n\n<h2 class=\"wp-block-heading\">Only Male Frogs Croak</h2>\n\n\n\n<p class=\"wp-block-paragraph\">To solve the intended version of the puzzle, we’ll assume</p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Only male frogs croak, and</li>\n\n\n\n<li>When two frogs appear together, their sexes are independent.</li>\n</ul>\n\n\n\n<p class=\"wp-block-paragraph\">So we’ll start with a prior where all two-frog combinations are equally likely.</p>\n\n\n\n<pre class=\"wp-block-preformatted\">from sympy import Rational\n\nhypo = ['FF', 'FM', 'MF', 'MM']\nprior = Rational(1)\n</pre>\n\n\n\n<p class=\"wp-block-paragraph\">Now let’s think about the likelihood of the data under each scenario. In the video, the solution is based on these assumptions:</p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>If both frogs are female, the probability of hearing the male croak is 0.</li>\n\n\n\n<li>If either frog is male, the probability that one of them croaks is 1.</li>\n</ul>\n\n\n\n<pre class=\"wp-block-preformatted\">likelihood = [0, 1, 1, 1]\n</pre>\n\n\n\n<p class=\"wp-block-paragraph\">I’ll use a <code>BayesTable</code> to compute the posterior probability for each scenario.</p>\n\n\n\n<pre class=\"wp-block-preformatted\">import pandas as pd\nimport numpy as np\n\nclass BayesTable(pd.DataFrame):\n def __init__(self, hypo, prior=1, **options):\n columns = ['prior', 'likelihood', 'unnorm', 'posterior']\n super().__init__(index=hypo, columns=columns, **options)\n self.prior = prior\n \n def update(self, likelihood):\n self.likelihood = likelihood\n self.unnorm = self.prior * self.likelihood\n nc = self.unnorm.sum()\n self.posterior = self.unnorm / nc\n</pre>\n\n\n\n<pre class=\"wp-block-preformatted\">table = BayesTable(hypo, prior)\ntable.update(likelihood)\ntable\n</pre>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><thead><tr><th></th><th>prior</th><th>likelihood</th><th>unnorm</th><th>posterior</th></tr></thead><tbody><tr><th>FF</th><td>1</td><td>0</td><td>0</td><td>0</td></tr><tr><th>FM</th><td>1</td><td>1</td><td>1</td><td>1/3</td></tr><tr><th>MF</th><td>1</td><td>1</td><td>1</td><td>1/3</td></tr><tr><th>MM</th><td>1</td><td>1</td><td>1</td><td>1/3</td></tr></tbody></table></figure>\n\n\n\n<p class=\"wp-block-paragraph\">From the table, we can extract the posterior probability that both frogs are male.</p>\n\n\n\n<pre class=\"wp-block-preformatted\">from sympy import init_printing\ninit_printing(use_latex=False)\n</pre>\n\n\n\n<pre class=\"wp-block-preformatted\">table.posterior['MM']\n</pre>\n\n\n\n<pre class=\"wp-block-preformatted\">1/3\n</pre>\n\n\n\n<p class=\"wp-block-paragraph\">With these assumptions, the probability 1/3 that both frogs are male (and you die), so the probability is 2/3 that at least one is female (and you live).</p>\n\n\n\n<p class=\"wp-block-paragraph\">And that’s the answer in the video.</p>\n\n\n\n<h2 class=\"wp-block-heading\">Poisson (not Poison) Frogs</h2>\n\n\n\n<p class=\"wp-block-paragraph\">But is that the right likelihood? Suppose frogs are equally likely to croak at any instant in time, so their croaks follow a Poisson process. If we assume that these croaking processes are independent, two frogs would be more likely to croak, during a given interval, than one.</p>\n\n\n\n<p class=\"wp-block-paragraph\">If the interval is much longer than the average time between croaks, the probability that either frog croaks approaches 1, which is consistent with the previous solution.</p>\n\n\n\n<p class=\"wp-block-paragraph\">But if the interval is short – as it might be if you were deciding whether to approach the first frog – the probability of hearing a croak would be double if there are two male frogs rather than one.</p>\n\n\n\n<p class=\"wp-block-paragraph\">In that case, the likelihood of the data would be:</p>\n\n\n\n<pre class=\"wp-block-preformatted\">half = Rational(1, 2)\nlikelihood = [0, half, half, 1]\n</pre>\n\n\n\n<p class=\"wp-block-paragraph\">And here are the posterior probabilities:</p>\n\n\n\n<pre class=\"wp-block-preformatted\">table = BayesTable(hypo, prior)\ntable.update(likelihood)\ntable\n</pre>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><thead><tr><th></th><th>prior</th><th>likelihood</th><th>unnorm</th><th>posterior</th></tr></thead><tbody><tr><th>FF</th><td>1</td><td>0</td><td>0</td><td>0</td></tr><tr><th>FM</th><td>1</td><td>1/2</td><td>1/2</td><td>1/4</td></tr><tr><th>MF</th><td>1</td><td>1/2</td><td>1/2</td><td>1/4</td></tr><tr><th>MM</th><td>1</td><td>1</td><td>1</td><td>1/2</td></tr></tbody></table></figure>\n\n\n\n<p class=\"wp-block-paragraph\">With Poisson frogs and a short interval, the probability of two male frogs is 1/2, so it doesn’t matter whether you approach the lone frog or the pair of frogs.</p>\n\n\n\n<h2 class=\"wp-block-heading\">Female Frogs Croak, Too</h2>\n\n\n\n<p class=\"wp-block-paragraph\">Now let’s think about the other interpretation of the puzzle: suppose both male and female frogs croak, but we can distinguish one from the other. And suppose male and female frogs croak at different rates, but they are still independent.</p>\n\n\n\n<p class=\"wp-block-paragraph\">Assume that male frogs croak at a rate of 1 per time unit, and female frogs at a rate of <code>r</code> per time unit. In that case, if we start listening at a random time, the probability that we hear a male frog first is <code>1 / (r+1)</code> if there’s only one male frog, and <code>1</code> if there are two male frogs.</p>\n\n\n\n<p class=\"wp-block-paragraph\">So the likelihood in this case is:</p>\n\n\n\n<pre class=\"wp-block-preformatted\">from sympy import symbols\n\nr = symbols('r')\nlikelihood = [0, 1 / (r+1), 1 / (r+1), 1]\n</pre>\n\n\n\n<p class=\"wp-block-paragraph\">And here are the posteriors</p>\n\n\n\n<pre class=\"wp-block-preformatted\">table = BayesTable(hypo, prior)\ntable.update(likelihood)\ntable\n</pre>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><thead><tr><th></th><th>prior</th><th>likelihood</th><th>unnorm</th><th>posterior</th></tr></thead><tbody><tr><th>FF</th><td>1</td><td>0</td><td>0</td><td>0</td></tr><tr><th>FM</th><td>1</td><td>1/(r + 1)</td><td>1/(r + 1)</td><td>1/((1 + 2/(r + 1))*(r + 1))</td></tr><tr><th>MF</th><td>1</td><td>1/(r + 1)</td><td>1/(r + 1)</td><td>1/((1 + 2/(r + 1))*(r + 1))</td></tr><tr><th>MM</th><td>1</td><td>1</td><td>1</td><td>1/(1 + 2/(r + 1))</td></tr></tbody></table></figure>\n\n\n\n<p class=\"wp-block-paragraph\">In this scenario, here’s the probability you die.</p>\n\n\n\n<pre class=\"wp-block-preformatted\">prob_die = table.posterior['MM']\nprob_die.simplify()\n</pre>\n\n\n\n<pre class=\"wp-block-preformatted\">r + 1\n─────\nr + 3\n</pre>\n\n\n\n<p class=\"wp-block-paragraph\">If female frogs don’t croak, we get the same answer as in the first scenario.</p>\n\n\n\n<pre class=\"wp-block-preformatted\">prob_die.subs({r: 0})\n</pre>\n\n\n\n<pre class=\"wp-block-preformatted\">1/3\n</pre>\n\n\n\n<p class=\"wp-block-paragraph\">If male and female frogs croak at the same rate, the probability that both frogs are male is 1/2.</p>\n\n\n\n<pre class=\"wp-block-preformatted\">prob_die.subs({r: 1})\n</pre>\n\n\n\n<pre class=\"wp-block-preformatted\">1/2\n</pre>\n\n\n\n<p class=\"wp-block-paragraph\">But if female frogs croak much more often, the fact that a male croaked first is strong evidence that both are male, so the posterior probability is close to 1.</p>\n\n\n\n<pre class=\"wp-block-preformatted\">prob_die.subs({r: 1000}).evalf()\n</pre>\n\n\n\n<pre class=\"wp-block-preformatted\">0.998005982053839\n</pre>\n\n\n\n<h2 class=\"wp-block-heading\">Assortative Mating</h2>\n\n\n\n<p class=\"wp-block-paragraph\">Now suppose that when we see two frogs together, their sexes are not independent; specifically, let’s assume that the probability of a same-sex pair is <code>p</code>, so the probability of a mixed-sex pair is <code>1-p</code>. In this scenario, the priors (before we hear the croak) are not equal.</p>\n\n\n\n<pre class=\"wp-block-preformatted\">p = symbols('p')\nprior = [p, 1-p, 1-p, p]\n</pre>\n\n\n\n<p class=\"wp-block-paragraph\">Here are the posterior probabilities, assuming again that both male and female frogs, possibly at different rates.</p>\n\n\n\n<pre class=\"wp-block-preformatted\">likelihood = [0, 1 / (r+1), 1 / (r+1), 1]\ntable = BayesTable(hypo, prior)\ntable.update(likelihood)\ntable\n</pre>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><thead><tr><th></th><th>prior</th><th>likelihood</th><th>unnorm</th><th>posterior</th></tr></thead><tbody><tr><th>FF</th><td>p</td><td>0</td><td>0</td><td>0</td></tr><tr><th>FM</th><td>1 – p</td><td>1/(r + 1)</td><td>(1 – p)/(r + 1)</td><td>(1 – p)/((p + 2*(1 – p)/(r + 1))*(r + 1))</td></tr><tr><th>MF</th><td>1 – p</td><td>1/(r + 1)</td><td>(1 – p)/(r + 1)</td><td>(1 – p)/((p + 2*(1 – p)/(r + 1))*(r + 1))</td></tr><tr><th>MM</th><td>p</td><td>1</td><td>p</td><td>p/(p + 2*(1 – p)/(r + 1))</td></tr></tbody></table></figure>\n\n\n\n<pre class=\"wp-block-preformatted\">table.posterior['MM'].simplify()\n</pre>\n\n\n\n<pre class=\"wp-block-preformatted\"> p⋅(r + 1) \n───────────\np⋅r - p + 2\n</pre>\n\n\n\n<p class=\"wp-block-paragraph\">If <code>p=1/2</code>, this simplifies to the previous scenario.</p>\n\n\n\n<pre class=\"wp-block-preformatted\">table.posterior['MM'].subs({p: half}).simplify()\n</pre>\n\n\n\n<pre class=\"wp-block-preformatted\">r + 1\n─────\nr + 3\n</pre>\n\n\n\n<p class=\"wp-block-paragraph\">And if <code>r=0</code> (female frogs don’t croak), we get the answer presented in the video.</p>\n\n\n\n<pre class=\"wp-block-preformatted\">table.posterior['MM'].subs({p: half, r: 0}).simplify()\n</pre>\n\n\n\n<pre class=\"wp-block-preformatted\">1/3\n</pre>\n\n\n\n<p class=\"wp-block-paragraph\">But depending on the assumptions, the probability can be as low as <code>0</code></p>\n\n\n\n<pre class=\"wp-block-preformatted\">table.posterior['MM'].subs({p: 0, r: 1}).simplify()\n</pre>\n\n\n\n<pre class=\"wp-block-preformatted\">0\n</pre>\n\n\n\n<p class=\"wp-block-paragraph\">Or as high as <code>1</code>.</p>\n\n\n\n<pre class=\"wp-block-preformatted\">table.posterior['MM'].subs({p: 1, r: 0}).simplify()\n</pre>\n\n\n\n<pre class=\"wp-block-preformatted\">1\n</pre>\n\n\n\n<p class=\"wp-block-paragraph\">Or anything in between. As is often the case with problems like these, the answer depends on a precise specification of the data-generating process.</p>\n\n\n\n<h2 class=\"wp-block-heading\">Discussion</h2>\n\n\n\n<p class=\"wp-block-paragraph\">If all of this seems like more trouble than it’s worth, let me suggest a metacognitive shortcut for solving puzzles like this.</p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>Notice that in all probability puzzles, the answer is either 1/2 or 1/3.</li>\n\n\n\n<li>Also, the answer is always counterintuitive; otherwise it wouldn’t be a puzzle.</li>\n\n\n\n<li>Therefore, if your intuition says the answer is 1/2, it’s actually 1/3, and vice versa.</li>\n</ol>\n\n\n\n<p class=\"wp-block-paragraph\">That might save you some time.</p>\n\n\n\n<p class=\"wp-block-paragraph\">This notebook uses methods and materials from <em>Think Bayes</em>, second edition. If you like this sort of thing, you can read the whole book, and more examples, at <a href=\"https://allendowney.github.io/ThinkBayes2/\">allendowney.github.io/ThinkBayes2/</a>.</p>\n\n\n\n<p class=\"wp-block-paragraph\"><br><br></p>\n\n\n\n<p class=\"wp-block-paragraph\"></p>\n<p>The post <a href=\"https://www.allendowney.com/blog/2026/06/04/the-frog-puzzle/\">The Frog Puzzle</a> appeared first on <a href=\"https://www.allendowney.com/blog\">Probably Overthinking It</a>.</p>",
"image": null,
"media": [],
"authors": [
{
"name": "AllenDowney",
"email": null,
"url": null
}
],
"categories": [
{
"label": "Uncategorized",
"term": "Uncategorized",
"url": null
},
{
"label": "Bayes's Theorem",
"term": "Bayes's Theorem",
"url": null
},
{
"label": "Frog Puzzle",
"term": "Frog Puzzle",
"url": null
},
{
"label": "probability",
"term": "probability",
"url": null
}
]
},
{
"id": "https://www.allendowney.com/blog/?p=1818",
"title": "Sexual morality",
"description": "<p>This article is one of a series looking at changes in public opinion over the last 50 years, with a focus on culture war topics. In this installment, we’ll look at responses to four questions in the General Social Survey (GSS) related to sexual activity: As we’ll see, answers to these questions have diverged in the last 50 years. A large majority answer that extramarital and teen sex are wrong, and that has barely changed (although opposition). At the same...</p>\n<p class=\"read-more\"><a class=\"btn btn-default\" href=\"https://www.allendowney.com/blog/2026/05/28/sexual-morality/\"> Read More<span class=\"screen-reader-text\"> Read More</span></a></p>\n<p>The post <a href=\"https://www.allendowney.com/blog/2026/05/28/sexual-morality/\">Sexual morality</a> appeared first on <a href=\"https://www.allendowney.com/blog\">Probably Overthinking It</a>.</p>",
"url": "https://www.allendowney.com/blog/2026/05/28/sexual-morality/",
"published": "2026-05-28T18:21:52.000Z",
"updated": "2026-05-28T18:21:52.000Z",
"content": "<p class=\"wp-block-paragraph\">This article is one of a series looking at changes in public opinion over the last 50 years, with a focus on culture war topics. In this installment, we’ll look at responses to four questions in the General Social Survey (GSS) related to sexual activity:</p>\n\n\n\n<ol start=\"1\" class=\"wp-block-list\">\n<li><strong>Premarital sex</strong> (<code>premarsx</code>): <em>There’s been a lot of discussion about the way morals and attitudes about sex are changing in this country. If a man and woman have sex relations before marriage, do you think it is always wrong, almost always wrong, wrong only sometimes, or not wrong at all?</em></li>\n\n\n\n<li><strong>Teen premarital sex</strong> (<code>teensex</code>): <em>What if they are in their early teens, say 14 to 16 years old? In that case, do you think sex relations before marriage are always wrong, almost always wrong, wrong only sometimes, or not wrong at all?</em></li>\n\n\n\n<li><strong>Extramarital sex</strong> (<code>xmarsex</code>): <em>What is your opinion about a married person having sexual relations with someone other than the marriage partner—is it always wrong, almost always wrong, wrong only sometimes, or not wrong at all?</em></li>\n\n\n\n<li><strong>Same-sex relations</strong> (<code>homosex</code>): <em>What about sexual relations between two adults of the same sex—do you think it is always wrong, almost always wrong, wrong only sometimes, or not wrong at all?</em></li>\n</ol>\n\n\n\n<p class=\"wp-block-paragraph\">As we’ll see, answers to these questions have diverged in the last 50 years. A large majority answer that extramarital and teen sex are wrong, and that has barely changed (although opposition). At the same time, opposition to premarital sex and same-sex relations has declined substantially.</p>\n\n\n\n<p class=\"wp-block-paragraph\">In this article, we’ll look at these trends and decompose them into cohort and period effects. In the next article, we’ll look at the relationship between these responses and religion, both affiliation and attendance.</p>\n\n\n\n<p class=\"wp-block-paragraph\">We’ll start with the first question, on premarital sex.</p>\n\n\n\n<h2 class=\"wp-block-heading\">Premarital sex</h2>\n\n\n\n<p class=\"wp-block-paragraph\">The following figure shows the percentage of respondents saying premarital sex is always or almost always wrong, from 1972 to 2024. The shaded area shows the results from a Bayesian model that estimates the latent trend — that is, a slowly varying underlying level of opposition to premarital sex.</p>\n\n\n\n<figure class=\"wp-block-image\" id=\"premarsx-time-model\"><img loading=\"lazy\" decoding=\"async\" width=\"1145\" height=\"826\" src=\"https://www.allendowney.com/blog/wp-content/uploads/2026/05/time_model_premarsx_-92782a5d81ed3c322ce3a3b74a1a1525.png\" alt=\"Time series national trend: percent saying premarital sex is always or almost always wrong (premarsx).\" class=\"wp-image-1820\" srcset=\"https://www.allendowney.com/blog/wp-content/uploads/2026/05/time_model_premarsx_-92782a5d81ed3c322ce3a3b74a1a1525.png 1145w, https://www.allendowney.com/blog/wp-content/uploads/2026/05/time_model_premarsx_-92782a5d81ed3c322ce3a3b74a1a1525-300x216.png 300w, https://www.allendowney.com/blog/wp-content/uploads/2026/05/time_model_premarsx_-92782a5d81ed3c322ce3a3b74a1a1525-1024x739.png 1024w, https://www.allendowney.com/blog/wp-content/uploads/2026/05/time_model_premarsx_-92782a5d81ed3c322ce3a3b74a1a1525-768x554.png 768w, https://www.allendowney.com/blog/wp-content/uploads/2026/05/time_model_premarsx_-92782a5d81ed3c322ce3a3b74a1a1525-374x270.png 374w\" sizes=\"auto, (max-width: 1145px) 100vw, 1145px\" /></figure>\n\n\n\n<p class=\"wp-block-paragraph\">Opposition to premarital sex has declined since 1972, from about 47% to about 20%.</p>\n\n\n\n<p class=\"wp-block-paragraph\">As always, when we see this kind of change over time, it might be caused by cohort or period effects, or a combination of the two. Using a Bayesian model, I estimate a cohort effect for each birth year and a period effect for each survey year. The following figure shows the resulting trajectory for each cohort over time.</p>\n\n\n\n<figure class=\"wp-block-image\" id=\"premarsx-cohort-trajectories\"><img loading=\"lazy\" decoding=\"async\" width=\"1330\" height=\"773\" src=\"https://www.allendowney.com/blog/wp-content/uploads/2026/05/cohort_trajectory_pr-795031a5150bdfce6ad7635df8bae9d3.png\" alt=\"Cohort trajectories: percent always or almost always wrong (premarsx), one line per birth year.\" class=\"wp-image-1826\" srcset=\"https://www.allendowney.com/blog/wp-content/uploads/2026/05/cohort_trajectory_pr-795031a5150bdfce6ad7635df8bae9d3.png 1330w, https://www.allendowney.com/blog/wp-content/uploads/2026/05/cohort_trajectory_pr-795031a5150bdfce6ad7635df8bae9d3-300x174.png 300w, https://www.allendowney.com/blog/wp-content/uploads/2026/05/cohort_trajectory_pr-795031a5150bdfce6ad7635df8bae9d3-1024x595.png 1024w, https://www.allendowney.com/blog/wp-content/uploads/2026/05/cohort_trajectory_pr-795031a5150bdfce6ad7635df8bae9d3-768x446.png 768w, https://www.allendowney.com/blog/wp-content/uploads/2026/05/cohort_trajectory_pr-795031a5150bdfce6ad7635df8bae9d3-465x270.png 465w\" sizes=\"auto, (max-width: 1330px) 100vw, 1330px\" /></figure>\n\n\n\n<p class=\"wp-block-paragraph\">Each line represents a single birth year. For example, the yellow line at the top shows the fitted trajectory for people born in 1900, who were 72 when the survey started in 1972 and 90 when they aged out in 1990. The blue line in the bottom right shows responses of people born in 2000, who became eligible to participate in the survey when they turned 18 in 2018.</p>\n\n\n\n<p class=\"wp-block-paragraph\">One pattern is clear: each cohort is less likely than the previous cohort to say that premarital sex is wrong. Among people born in 1900, it was more than 70%. Among people born in the 2000s, it is close to 10%. So that’s a big difference.</p>\n\n\n\n<p class=\"wp-block-paragraph\">From these results, we can estimate the cohort and period effects separately. The following figure shows the cohort effect, standardized to control for the period effect by simulating responses as if every cohort was interviewed during every iteration of the survey.</p>\n\n\n\n<figure class=\"wp-block-image\" id=\"premarsx-cohort-standardized\"><img loading=\"lazy\" decoding=\"async\" width=\"1145\" height=\"826\" src=\"https://www.allendowney.com/blog/wp-content/uploads/2026/05/cohort_standardized_-2ddcc0ce51962fa548b8944732f56f2c.png\" alt=\"Standardized cohort component with uniform weights on observed survey years (premarsx).\" class=\"wp-image-1821\" srcset=\"https://www.allendowney.com/blog/wp-content/uploads/2026/05/cohort_standardized_-2ddcc0ce51962fa548b8944732f56f2c.png 1145w, https://www.allendowney.com/blog/wp-content/uploads/2026/05/cohort_standardized_-2ddcc0ce51962fa548b8944732f56f2c-300x216.png 300w, https://www.allendowney.com/blog/wp-content/uploads/2026/05/cohort_standardized_-2ddcc0ce51962fa548b8944732f56f2c-1024x739.png 1024w, https://www.allendowney.com/blog/wp-content/uploads/2026/05/cohort_standardized_-2ddcc0ce51962fa548b8944732f56f2c-768x554.png 768w, https://www.allendowney.com/blog/wp-content/uploads/2026/05/cohort_standardized_-2ddcc0ce51962fa548b8944732f56f2c-374x270.png 374w\" sizes=\"auto, (max-width: 1145px) 100vw, 1145px\" /></figure>\n\n\n\n<p class=\"wp-block-paragraph\">The decline was steepest between the cohorts born in 1900 and 1950. After that, it leveled off, then declined again among the cohorts born in the 1980s.</p>\n\n\n\n<p class=\"wp-block-paragraph\">Now we can estimate the period effect, standardized to control for the cohort effect, shown in the following figure.</p>\n\n\n\n<figure class=\"wp-block-image\" id=\"premarsx-period-standardized\"><img loading=\"lazy\" decoding=\"async\" width=\"1145\" height=\"826\" src=\"https://www.allendowney.com/blog/wp-content/uploads/2026/05/time_standardized_pr-3ad2679bfedff58845cbd5c8219ec152.png\" alt=\"Standardized period component with fixed cohort mix (premarsx).\" class=\"wp-image-1822\" srcset=\"https://www.allendowney.com/blog/wp-content/uploads/2026/05/time_standardized_pr-3ad2679bfedff58845cbd5c8219ec152.png 1145w, https://www.allendowney.com/blog/wp-content/uploads/2026/05/time_standardized_pr-3ad2679bfedff58845cbd5c8219ec152-300x216.png 300w, https://www.allendowney.com/blog/wp-content/uploads/2026/05/time_standardized_pr-3ad2679bfedff58845cbd5c8219ec152-1024x739.png 1024w, https://www.allendowney.com/blog/wp-content/uploads/2026/05/time_standardized_pr-3ad2679bfedff58845cbd5c8219ec152-768x554.png 768w, https://www.allendowney.com/blog/wp-content/uploads/2026/05/time_standardized_pr-3ad2679bfedff58845cbd5c8219ec152-374x270.png 374w\" sizes=\"auto, (max-width: 1145px) 100vw, 1145px\" /></figure>\n\n\n\n<p class=\"wp-block-paragraph\">The period effect is smaller than the cohort effect — about 8 percentage points from peak to trough — and less consistent. Opposition to premarital sex increased between 1980 and 2000, which coincides with increasing awareness of AIDS and public messaging about sexual risk, as well as the rise of the Religious Right and “family values” politics.</p>\n\n\n\n<p class=\"wp-block-paragraph\">But before I speculate about the causes of these patterns, it will be useful to look at the responses to the other questions.</p>\n\n\n\n<h2 class=\"wp-block-heading\">When is sex wrong?</h2>\n\n\n\n<p class=\"wp-block-paragraph\">The following figure shows the estimated percentage who think sex is wrong (always or almost always) in each of the four scenarios: premarital, teen, extramarital, and same-sex.</p>\n\n\n\n<figure class=\"wp-block-image\" id=\"sex-wrongness-composite-time-model\"><img loading=\"lazy\" decoding=\"async\" width=\"1145\" height=\"766\" src=\"https://www.allendowney.com/blog/wp-content/uploads/2026/05/section1a_sex_wrongn-80473854b8315d2c65a20e45ee21992c.png\" alt=\"Composite overlay: sexual-behavior wrongness scale — national time-series model (four items).\" class=\"wp-image-1824\" srcset=\"https://www.allendowney.com/blog/wp-content/uploads/2026/05/section1a_sex_wrongn-80473854b8315d2c65a20e45ee21992c.png 1145w, https://www.allendowney.com/blog/wp-content/uploads/2026/05/section1a_sex_wrongn-80473854b8315d2c65a20e45ee21992c-300x201.png 300w, https://www.allendowney.com/blog/wp-content/uploads/2026/05/section1a_sex_wrongn-80473854b8315d2c65a20e45ee21992c-1024x685.png 1024w, https://www.allendowney.com/blog/wp-content/uploads/2026/05/section1a_sex_wrongn-80473854b8315d2c65a20e45ee21992c-768x514.png 768w, https://www.allendowney.com/blog/wp-content/uploads/2026/05/section1a_sex_wrongn-80473854b8315d2c65a20e45ee21992c-404x270.png 404w\" sizes=\"auto, (max-width: 1145px) 100vw, 1145px\" /></figure>\n\n\n\n<p class=\"wp-block-paragraph\">Reading from top to bottom:</p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Nearly everyone thinks “a married person having sexual relations with someone other than the marriage partner” is wrong, and the percentage has barely changed in more than 50 years.</li>\n\n\n\n<li>Opposition to teen sex (the question specifies ages 14-16) is nearly as high, although it has declined since 2005 by about 15 percentage points.</li>\n\n\n\n<li>Opposition to same-sex relations was high and mostly unchanged between 1972 and 1990. Since then it has decreased by almost 50 percentage points in 30 years, which is an astonishing speed for this kind of social change. Since 2020, opposition has increased a little.</li>\n\n\n\n<li>Finally, as we’ve already seen, opposition to premarital sex declined substantially since the beginning of the survey.</li>\n</ul>\n\n\n\n<p class=\"wp-block-paragraph\">For all four scenarios, we can estimate the cohort effect, controlling for the period effect, shown in the following figure.</p>\n\n\n\n<figure class=\"wp-block-image\" id=\"sex-wrongness-composite-cohort\"><img loading=\"lazy\" decoding=\"async\" width=\"1145\" height=\"766\" src=\"https://www.allendowney.com/blog/wp-content/uploads/2026/05/section1a_sex_wrongn-f61ab0124fa6ad280ce97c7fe9addcba.png\" alt=\"Composite overlay: standardized cohort component with uniform weights on observed years (four items).\" class=\"wp-image-1825\" srcset=\"https://www.allendowney.com/blog/wp-content/uploads/2026/05/section1a_sex_wrongn-f61ab0124fa6ad280ce97c7fe9addcba.png 1145w, https://www.allendowney.com/blog/wp-content/uploads/2026/05/section1a_sex_wrongn-f61ab0124fa6ad280ce97c7fe9addcba-300x201.png 300w, https://www.allendowney.com/blog/wp-content/uploads/2026/05/section1a_sex_wrongn-f61ab0124fa6ad280ce97c7fe9addcba-1024x685.png 1024w, https://www.allendowney.com/blog/wp-content/uploads/2026/05/section1a_sex_wrongn-f61ab0124fa6ad280ce97c7fe9addcba-768x514.png 768w, https://www.allendowney.com/blog/wp-content/uploads/2026/05/section1a_sex_wrongn-f61ab0124fa6ad280ce97c7fe9addcba-404x270.png 404w\" sizes=\"auto, (max-width: 1145px) 100vw, 1145px\" /></figure>\n\n\n\n<p class=\"wp-block-paragraph\">For all four scenarios, there is a consistent downward trend in the cohort effect, modest for extramarital and teen sex, much steeper for premarital and same-sex relations.</p>\n\n\n\n<p class=\"wp-block-paragraph\">The following figure shows the period effects.</p>\n\n\n\n<figure class=\"wp-block-image\" id=\"sex-wrongness-composite-period\"><img loading=\"lazy\" decoding=\"async\" width=\"1145\" height=\"766\" src=\"https://www.allendowney.com/blog/wp-content/uploads/2026/05/section1a_sex_wrongn-f67ed5b82acbc806401f00d555e7c43e.png\" alt=\"Composite overlay: standardized period component with fixed cohort mix (four items).\" class=\"wp-image-1823\" srcset=\"https://www.allendowney.com/blog/wp-content/uploads/2026/05/section1a_sex_wrongn-f67ed5b82acbc806401f00d555e7c43e.png 1145w, https://www.allendowney.com/blog/wp-content/uploads/2026/05/section1a_sex_wrongn-f67ed5b82acbc806401f00d555e7c43e-300x201.png 300w, https://www.allendowney.com/blog/wp-content/uploads/2026/05/section1a_sex_wrongn-f67ed5b82acbc806401f00d555e7c43e-1024x685.png 1024w, https://www.allendowney.com/blog/wp-content/uploads/2026/05/section1a_sex_wrongn-f67ed5b82acbc806401f00d555e7c43e-768x514.png 768w, https://www.allendowney.com/blog/wp-content/uploads/2026/05/section1a_sex_wrongn-f67ed5b82acbc806401f00d555e7c43e-404x270.png 404w\" sizes=\"auto, (max-width: 1145px) 100vw, 1145px\" /></figure>\n\n\n\n<p class=\"wp-block-paragraph\">After controlling for the cohort effects, the remaining period effects are more modest.</p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Opposition to teen sex is mostly unchanged, with some decline since 2010.</li>\n\n\n\n<li>Opposition to extramarital sex increased between 1972 and 2010, and decreased since then.</li>\n\n\n\n<li>Opposition to same-sex relations shows by far the largest period effect, increasing between 1972 and 1990, and decreasing since then — although increasing again since 2020.</li>\n\n\n\n<li>Opposition to premarital sex has increased and decreased modestly.</li>\n</ul>\n\n\n\n<p class=\"wp-block-paragraph\">In most scenarios, the cohort effect accounts for more of the observed change — but for same-sex relations, the period effect also makes a substantial contribution.</p>\n\n\n\n<h2 class=\"wp-block-heading\">Dogma, morality, and health</h2>\n\n\n\n<p class=\"wp-block-paragraph\">To make sense of these patterns, let’s think about what people might mean when they say that sex is wrong.</p>\n\n\n\n<p class=\"wp-block-paragraph\">Taking premarital sex as an example, some people consider sex outside marriage to be contrary to spiritual values or religious teachings. Others might be concerned with sexually-transmitted disease or the social consequences of children born outside of stable families.</p>\n\n\n\n<p class=\"wp-block-paragraph\">And for teens specifically, some object because they see adolescence as a period of innocence that should be protected, believe sexual activity compromises purity or chastity, or think sexual restraint reflects virtues like self-discipline and respect for social norms. Also, some might think teenagers don’t have the knowledge, experience, and impulse control to avoid health consequences of sex, especially pregnancy, or the maturity to handle emotional challenges.</p>\n\n\n\n<p class=\"wp-block-paragraph\">Similarly, some people object to same-sex relations because they see them as contrary to religious teachings, inconsistent with traditional ideas about gender and family, or incompatible with social norms about sexuality.</p>\n\n\n\n<p class=\"wp-block-paragraph\">And people might object to extramarital sex because of the emotional harm it causes, because it breaks a vow, because it threatens families and social stability, or because it violates holy matrimony.</p>\n\n\n\n<p class=\"wp-block-paragraph\">In each scenario, objections arise from different concerns: practical risks and harms, social concerns about norms and stability, and moral or religious beliefs. Looking only at multiple-choice responses, we don’t know what respondents had in mind.</p>\n\n\n\n<p class=\"wp-block-paragraph\">But the differences we see — between teen and extramarital sex on one hand, and premarital sex and same-sex relations on the other — suggest a conjecture: objections rooted in immediate harms and concrete consequences might be more stable over time; objections rooted in social norms, morality, and religion might be more historically contingent.</p>\n\n\n\n<p class=\"wp-block-paragraph\">In the next article, we’ll test this conjecture by looking at relationships between religion and attitudes about sex — and how both have changed over time.</p>\n\n\n\n<p class=\"wp-block-paragraph\"><a href=\"https://allendowney.github.io/CultureWar//blog8-confidence\"></a><a href=\"https://allendowney.github.io/CultureWar//blog8-confidence\"></a></p>\n\n\n\n<p class=\"wp-block-paragraph\"></p>\n<p>The post <a href=\"https://www.allendowney.com/blog/2026/05/28/sexual-morality/\">Sexual morality</a> appeared first on <a href=\"https://www.allendowney.com/blog\">Probably Overthinking It</a>.</p>",
"image": null,
"media": [],
"authors": [
{
"name": "AllenDowney",
"email": null,
"url": null
}
],
"categories": [
{
"label": "Uncategorized",
"term": "Uncategorized",
"url": null
},
{
"label": "age period cohort analysis",
"term": "age period cohort analysis",
"url": null
},
{
"label": "bayesian statistics",
"term": "bayesian statistics",
"url": null
},
{
"label": "general social survey",
"term": "general social survey",
"url": null
}
]
},
{
"id": "https://www.allendowney.com/blog/?p=1803",
"title": "Confidence in Institutions",
"description": "<p>This article is one of a series exploring responses to core questions in the General Social Survey (GSS), estimating period and cohort effects, and looking for historical events that might explain the trends we see. Confidence in American institutions In this installment, we’ll look at 13 questions related to confidence in institutions. We’ll start with a detailed look at confidence in “the people running Congress”, and then summarize results from the other questions. The complete survey question is: I am...</p>\n<p class=\"read-more\"><a class=\"btn btn-default\" href=\"https://www.allendowney.com/blog/2026/05/19/confidence-in-institutions/\"> Read More<span class=\"screen-reader-text\"> Read More</span></a></p>\n<p>The post <a href=\"https://www.allendowney.com/blog/2026/05/19/confidence-in-institutions/\">Confidence in Institutions</a> appeared first on <a href=\"https://www.allendowney.com/blog\">Probably Overthinking It</a>.</p>",
"url": "https://www.allendowney.com/blog/2026/05/19/confidence-in-institutions/",
"published": "2026-05-19T15:04:04.000Z",
"updated": "2026-05-19T15:04:04.000Z",
"content": "<p class=\"wp-block-paragraph\">This article is one of a series exploring responses to core questions in the General Social Survey (GSS), estimating period and cohort effects, and looking for historical events that might explain the trends we see.<a href=\"https://github.com/AllenDowney/CultureWar\" target=\"_blank\" rel=\"noreferrer noopener\"></a><a href=\"https://github.com/AllenDowney/CultureWar/edit/main/jb/blog8_confidence.md\" target=\"_blank\" rel=\"noreferrer noopener\"></a></p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"confidence-in-american-institutions\">Confidence in American institutions</h2>\n\n\n\n<p class=\"wp-block-paragraph\">In this installment, we’ll look at 13 questions related to confidence in institutions. We’ll start with a detailed look at confidence in “the people running Congress”, and then summarize results from the other questions. The <a href=\"https://gssdataexplorer.norc.org/variables/459/vshow\" target=\"_blank\" rel=\"noreferrer noopener\">complete survey question</a> is:</p>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\">\n<p class=\"wp-block-paragraph\">I am going to name some institutions in this country. As far as the people running these institutions are concerned, would you say you have a great deal of confidence, only some confidence, or hardly any confidence at all in […] Congress.</p>\n</blockquote>\n\n\n\n<p class=\"wp-block-paragraph\">The following figure shows the fraction of people who answered “a great deal of confidence” or “only some confidence,” and a smooth line fitted to the raw percentages.</p>\n\n\n\n<figure class=\"wp-block-image\" id=\"conlegis-time-model\"><img loading=\"lazy\" decoding=\"async\" width=\"1145\" height=\"790\" src=\"https://www.allendowney.com/blog/wp-content/uploads/2026/05/time_model_conlegis_-e47a9b867ea68609944d3abe98446e29.png\" alt=\"Time-only model, confidence in the people running Congress.\" class=\"wp-image-1808\" srcset=\"https://www.allendowney.com/blog/wp-content/uploads/2026/05/time_model_conlegis_-e47a9b867ea68609944d3abe98446e29.png 1145w, https://www.allendowney.com/blog/wp-content/uploads/2026/05/time_model_conlegis_-e47a9b867ea68609944d3abe98446e29-300x207.png 300w, https://www.allendowney.com/blog/wp-content/uploads/2026/05/time_model_conlegis_-e47a9b867ea68609944d3abe98446e29-1024x707.png 1024w, https://www.allendowney.com/blog/wp-content/uploads/2026/05/time_model_conlegis_-e47a9b867ea68609944d3abe98446e29-768x530.png 768w, https://www.allendowney.com/blog/wp-content/uploads/2026/05/time_model_conlegis_-e47a9b867ea68609944d3abe98446e29-391x270.png 391w\" sizes=\"auto, (max-width: 1145px) 100vw, 1145px\" /></figure>\n\n\n\n<p class=\"wp-block-paragraph\">The long-term trend is downward, from about 80% during the first iteration of the survey to below 50% in the most recent iterations. But there are ups and downs.</p>\n\n\n\n<p class=\"wp-block-paragraph\">It looks like confidence was increasing during the 1980s before collapsing in the early 1990s. Possible causes of the decline include:</p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>The <a href=\"https://en.wikipedia.org/wiki/House_banking_scandal\" target=\"_blank\" rel=\"noreferrer noopener\">House banking scandal</a>, also known as Rubbergate, and the <a href=\"https://en.wikipedia.org/wiki/Congressional_Post_Office_scandal\" target=\"_blank\" rel=\"noreferrer noopener\">Congressional Post Office scandal</a>.</li>\n\n\n\n<li>Increased polarization and perception of dysfunction during the period when <a href=\"https://en.wikipedia.org/wiki/Newt_Gingrich#Speaker_of_the_House\" target=\"_blank\" rel=\"noreferrer noopener\">Newt Gingrich</a> was minority whip (1989-1995).</li>\n\n\n\n<li>An <a href=\"https://en.wikipedia.org/wiki/Early_1990s_recession_in_the_United_States\" target=\"_blank\" rel=\"noreferrer noopener\">economic recession</a> from 1990 into 1991.</li>\n</ul>\n\n\n\n<p class=\"wp-block-paragraph\">Confidence in Congress recovered between 1995 and 2005, and declined again between 2005 and 2015. A likely contributor is the <a href=\"https://en.wikipedia.org/wiki/Great_Recession\" target=\"_blank\" rel=\"noreferrer noopener\">Great Recession</a> from late 2007 to mid-2009.</p>\n\n\n\n<p class=\"wp-block-paragraph\">This period also saw the rise of anti-establishment politics, including the <a href=\"https://en.wikipedia.org/wiki/Tea_Party_movement\" target=\"_blank\" rel=\"noreferrer noopener\">Tea Party movement</a> and <a href=\"https://en.wikipedia.org/wiki/Ron_Paul\" target=\"_blank\" rel=\"noreferrer noopener\">Ron Paul’s</a> presidential campaign.</p>\n\n\n\n<p class=\"wp-block-paragraph\">Now we’ll decompose these changes into period and cohort effects.</p>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"period-and-cohort-effects\">Period and cohort effects</h3>\n\n\n\n<p class=\"wp-block-paragraph\">Using the <a href=\"https://allendowney.github.io/CultureWar/tech-report/\" target=\"_blank\" rel=\"noreferrer noopener\">Bayesian model described here</a> we can estimate a latent “confidence in Congress” factor for each birth cohort over time. The following figure shows these estimates; each line represents a single birth year.</p>\n\n\n\n<figure class=\"wp-block-image\" id=\"conlegis-cohort-trajectories\"><img loading=\"lazy\" decoding=\"async\" width=\"1330\" height=\"778\" src=\"https://www.allendowney.com/blog/wp-content/uploads/2026/05/cohort_trajectory_co-d5cd0d30431d1f3f08bcc503ebb4d786.png\" alt=\"Cohort trajectories, percent with a great deal or only some confidence in the people running Congress.\" class=\"wp-image-1814\" srcset=\"https://www.allendowney.com/blog/wp-content/uploads/2026/05/cohort_trajectory_co-d5cd0d30431d1f3f08bcc503ebb4d786.png 1330w, https://www.allendowney.com/blog/wp-content/uploads/2026/05/cohort_trajectory_co-d5cd0d30431d1f3f08bcc503ebb4d786-300x175.png 300w, https://www.allendowney.com/blog/wp-content/uploads/2026/05/cohort_trajectory_co-d5cd0d30431d1f3f08bcc503ebb4d786-1024x599.png 1024w, https://www.allendowney.com/blog/wp-content/uploads/2026/05/cohort_trajectory_co-d5cd0d30431d1f3f08bcc503ebb4d786-768x449.png 768w, https://www.allendowney.com/blog/wp-content/uploads/2026/05/cohort_trajectory_co-d5cd0d30431d1f3f08bcc503ebb4d786-462x270.png 462w\" sizes=\"auto, (max-width: 1330px) 100vw, 1330px\" /></figure>\n\n\n\n<p class=\"wp-block-paragraph\">Those results are easier to interpret if we factor out the cohort effect (keeping the mixture of survey years constant) and the period effect (keeping the mixture of cohorts constant). The following figure shows the standardized cohort effect.</p>\n\n\n\n<figure class=\"wp-block-image\" id=\"conlegis-cohort-standardized\"><img loading=\"lazy\" decoding=\"async\" width=\"1145\" height=\"790\" src=\"https://www.allendowney.com/blog/wp-content/uploads/2026/05/cohort_standardized_-aca7608b25112981c03dc33fffe90a93.png\" alt=\"Standardized cohort effect with fixed time mix, confidence in Congress.\" class=\"wp-image-1812\" srcset=\"https://www.allendowney.com/blog/wp-content/uploads/2026/05/cohort_standardized_-aca7608b25112981c03dc33fffe90a93.png 1145w, https://www.allendowney.com/blog/wp-content/uploads/2026/05/cohort_standardized_-aca7608b25112981c03dc33fffe90a93-300x207.png 300w, https://www.allendowney.com/blog/wp-content/uploads/2026/05/cohort_standardized_-aca7608b25112981c03dc33fffe90a93-1024x707.png 1024w, https://www.allendowney.com/blog/wp-content/uploads/2026/05/cohort_standardized_-aca7608b25112981c03dc33fffe90a93-768x530.png 768w, https://www.allendowney.com/blog/wp-content/uploads/2026/05/cohort_standardized_-aca7608b25112981c03dc33fffe90a93-391x270.png 391w\" sizes=\"auto, (max-width: 1145px) 100vw, 1145px\" /></figure>\n\n\n\n<p class=\"wp-block-paragraph\">Among people born between 1900 and 1950, there is almost no change. Then starting with people born in the 1960s, confidence in Congress has increased consistently and substantially.</p>\n\n\n\n<p class=\"wp-block-paragraph\">To interpret this result, it is helpful to go back to the previous figure. Starting in the upper left:</p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Among people born in the 1960s and 1970s, about 80% reported confidence in Congress when they were surveyed as young adults.</li>\n\n\n\n<li>Among people born in the 1980s and 1990s, it was closer to 70%.</li>\n\n\n\n<li>And among people born in the 2000s it’s below 70%.</li>\n</ul>\n\n\n\n<p class=\"wp-block-paragraph\">The entry point of each cohort is below the entry point of previous cohorts, but because these entry points are above the declining trend of previous generations, this <em>relative</em> optimism is interpreted as an increasing cohort effect.</p>\n\n\n\n<p class=\"wp-block-paragraph\">So we should not conclude that younger generations are more confident in Congress, only that when they are first surveyed, they start out above the trajectory of previous cohorts.</p>\n\n\n\n<p class=\"wp-block-paragraph\">As a simplification, we might imagine an 18-year-old entering adulthood with a relatively idealized understanding of American government — shaped by civics classes and maybe a school trip to Washington D.C. — before later political experiences erode some of that confidence.</p>\n\n\n\n<p class=\"wp-block-paragraph\">Another possibility is that younger generations have grown up with lower expectations of government, so when they say they have “some confidence”, they might be evaluating Congress against a lower standard.</p>\n\n\n\n<p class=\"wp-block-paragraph\">The following figure shows the estimated period effect, with the mix of cohorts held constant.</p>\n\n\n\n<figure class=\"wp-block-image\" id=\"conlegis-period-standardized\"><img loading=\"lazy\" decoding=\"async\" width=\"1145\" height=\"790\" src=\"https://www.allendowney.com/blog/wp-content/uploads/2026/05/time_standardized_co-d65cdea9156d375abd801cc2826c9844.png\" alt=\"Standardized period effect with fixed cohort mix, Congress.\" class=\"wp-image-1807\" srcset=\"https://www.allendowney.com/blog/wp-content/uploads/2026/05/time_standardized_co-d65cdea9156d375abd801cc2826c9844.png 1145w, https://www.allendowney.com/blog/wp-content/uploads/2026/05/time_standardized_co-d65cdea9156d375abd801cc2826c9844-300x207.png 300w, https://www.allendowney.com/blog/wp-content/uploads/2026/05/time_standardized_co-d65cdea9156d375abd801cc2826c9844-1024x707.png 1024w, https://www.allendowney.com/blog/wp-content/uploads/2026/05/time_standardized_co-d65cdea9156d375abd801cc2826c9844-768x530.png 768w, https://www.allendowney.com/blog/wp-content/uploads/2026/05/time_standardized_co-d65cdea9156d375abd801cc2826c9844-391x270.png 391w\" sizes=\"auto, (max-width: 1145px) 100vw, 1145px\" /></figure>\n\n\n\n<p class=\"wp-block-paragraph\">This decline is steeper than what we saw in the time-only model, because we have factored out the mitigating effect of relative optimism in recent generations.</p>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"government-institutions\">Government Institutions</h3>\n\n\n\n<p class=\"wp-block-paragraph\">Now we’ll apply the same analysis to questions about the executive branch of the federal government, the Supreme Court, and the military (technically part of the executive branch).</p>\n\n\n\n<p class=\"wp-block-paragraph\">The following figure shows the estimated cohort effects for each of these institutions.</p>\n\n\n\n<figure class=\"wp-block-image\" id=\"cluster-gov-cohort\"><img loading=\"lazy\" decoding=\"async\" width=\"1145\" height=\"764\" src=\"https://www.allendowney.com/blog/wp-content/uploads/2026/05/con_cluster_1_govern-7c461121f9363f4e9a2440f4a41ce384.png\" alt=\"Government and security institutions, standardized cohort component (uniform survey years).\" class=\"wp-image-1811\" srcset=\"https://www.allendowney.com/blog/wp-content/uploads/2026/05/con_cluster_1_govern-7c461121f9363f4e9a2440f4a41ce384.png 1145w, https://www.allendowney.com/blog/wp-content/uploads/2026/05/con_cluster_1_govern-7c461121f9363f4e9a2440f4a41ce384-300x200.png 300w, https://www.allendowney.com/blog/wp-content/uploads/2026/05/con_cluster_1_govern-7c461121f9363f4e9a2440f4a41ce384-1024x683.png 1024w, https://www.allendowney.com/blog/wp-content/uploads/2026/05/con_cluster_1_govern-7c461121f9363f4e9a2440f4a41ce384-768x512.png 768w, https://www.allendowney.com/blog/wp-content/uploads/2026/05/con_cluster_1_govern-7c461121f9363f4e9a2440f4a41ce384-405x270.png 405w\" sizes=\"auto, (max-width: 1145px) 100vw, 1145px\" /></figure>\n\n\n\n<p class=\"wp-block-paragraph\">And the following figure shows the period effect, after factoring out the cohort effect.</p>\n\n\n\n<figure class=\"wp-block-image\" id=\"cluster-gov-standardized-period\"><img loading=\"lazy\" decoding=\"async\" width=\"1145\" height=\"764\" src=\"https://www.allendowney.com/blog/wp-content/uploads/2026/05/con_cluster_1_govern-b24ed098d4d8b3b779b1face8e1cd0be.png\" alt=\"Government and security institutions, standardized period component (fixed cohort mix).\" class=\"wp-image-1813\" srcset=\"https://www.allendowney.com/blog/wp-content/uploads/2026/05/con_cluster_1_govern-b24ed098d4d8b3b779b1face8e1cd0be.png 1145w, https://www.allendowney.com/blog/wp-content/uploads/2026/05/con_cluster_1_govern-b24ed098d4d8b3b779b1face8e1cd0be-300x200.png 300w, https://www.allendowney.com/blog/wp-content/uploads/2026/05/con_cluster_1_govern-b24ed098d4d8b3b779b1face8e1cd0be-1024x683.png 1024w, https://www.allendowney.com/blog/wp-content/uploads/2026/05/con_cluster_1_govern-b24ed098d4d8b3b779b1face8e1cd0be-768x512.png 768w, https://www.allendowney.com/blog/wp-content/uploads/2026/05/con_cluster_1_govern-b24ed098d4d8b3b779b1face8e1cd0be-405x270.png 405w\" sizes=\"auto, (max-width: 1145px) 100vw, 1145px\" /></figure>\n\n\n\n<p class=\"wp-block-paragraph\">The results for the executive branch are similar to the results for Congress.</p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>The cohort effect is flat between people born in the 1900s and 1950s, and increasing after that.</li>\n\n\n\n<li>The period effect declines substantially and consistently — without the ups and downs of confidence in Congress.</li>\n</ul>\n\n\n\n<p class=\"wp-block-paragraph\">When respondents are asked about the “executive branch”, it’s not clear whether they think primarily about the president, federal agencies, or the federal government in general.</p>\n\n\n\n<p class=\"wp-block-paragraph\">The patterns for the military and Supreme Court are different.</p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Confidence in the military is generally high. The cohort effect declined gradually, and possibly more steeply among people born after 1980. The period effect gradually increased.</li>\n\n\n\n<li>Confidence in the Supreme Court is higher than confidence in other branches, although the period effect has dropped steeply since 2015. The cohort effect increased among people born between 1900 and 1960; among more recent generations it is gradually declining.</li>\n</ul>\n\n\n\n<p class=\"wp-block-paragraph\">Historically, the Court cultivated an image of being above politics; that perception weakened substantially in the 2010s. In March 2016, Merrick Garland was nominated to the Supreme Court after the death of Antonin Scalia. The Republican majority in the Senate refused to hold a hearing or vote on his nomination. The seat remained empty until Donald Trump nominated, and the Senate confirmed, Neil Gorsuch, who is considered to be more conservative. To many liberals, the Senate’s 293-day blockade undermined the legitimacy of the Court.</p>\n\n\n\n<p class=\"wp-block-paragraph\">Then when Ruth Bader Ginsburg died in September 2020, Donald Trump nominated Amy Coney Barrett and the Senate confirmed her 8 days before the 2020 presidential election, in a process criticized by Democratic leaders as illegitimate.</p>\n\n\n\n<p class=\"wp-block-paragraph\">These appointments, along with the confirmation of Brett Kavanaugh in 2018, shifted the composition of the Court toward conservatives, forming what is now described as a 6-3 supermajority of conservative justices.</p>\n\n\n\n<p class=\"wp-block-paragraph\">Since then, the Supreme Court has issued several decisions contrary to majority public opinion, most notably the 2022 decision overturning <em>Roe v. Wade</em>. Other unpopular decisions weakened gun control and limited federal regulatory authority, especially over environmental policy. Many of these decisions have been perceived, especially on the left, to be motivated by politics rather than constitutional principles and precedent.</p>\n\n\n\n<p class=\"wp-block-paragraph\">The slope of the cohort effect might reflect a generational change in associations with the Supreme Court. Older cohorts may associate the Supreme Court with landmark decisions like Brown v. Board of Education and the expansion of civil rights. Younger cohorts may instead associate it with partisan conflict, blocked reforms, and ideological polarization. Older generations might also have been more deferential toward the institution itself. Younger generations, exposed to more adversarial and partisan media coverage, might be less inclined to deference.</p>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"economic-institutions\">Economic institutions</h3>\n\n\n\n<p class=\"wp-block-paragraph\">The following figures show the cohort and period effects for confidence in economic institutions: banks, major companies, and organized labor.</p>\n\n\n\n<figure class=\"wp-block-image\" id=\"cluster-econ-cohort\"><img loading=\"lazy\" decoding=\"async\" width=\"1145\" height=\"764\" src=\"https://www.allendowney.com/blog/wp-content/uploads/2026/05/con_cluster_2_econom-b4cf1eea3eb5290377d151bac981fdaf.png\" alt=\"Economic institutions, standardized cohort component.\" class=\"wp-image-1809\" srcset=\"https://www.allendowney.com/blog/wp-content/uploads/2026/05/con_cluster_2_econom-b4cf1eea3eb5290377d151bac981fdaf.png 1145w, https://www.allendowney.com/blog/wp-content/uploads/2026/05/con_cluster_2_econom-b4cf1eea3eb5290377d151bac981fdaf-300x200.png 300w, https://www.allendowney.com/blog/wp-content/uploads/2026/05/con_cluster_2_econom-b4cf1eea3eb5290377d151bac981fdaf-1024x683.png 1024w, https://www.allendowney.com/blog/wp-content/uploads/2026/05/con_cluster_2_econom-b4cf1eea3eb5290377d151bac981fdaf-768x512.png 768w, https://www.allendowney.com/blog/wp-content/uploads/2026/05/con_cluster_2_econom-b4cf1eea3eb5290377d151bac981fdaf-405x270.png 405w\" sizes=\"auto, (max-width: 1145px) 100vw, 1145px\" /></figure>\n\n\n\n<p class=\"wp-block-paragraph\"></p>\n\n\n\n<figure class=\"wp-block-image\" id=\"cluster-econ-standardized-period\"><img loading=\"lazy\" decoding=\"async\" width=\"1145\" height=\"764\" src=\"https://www.allendowney.com/blog/wp-content/uploads/2026/05/con_cluster_2_econom-76a4be0f163f28d139a677ac90cfd0e5.png\" alt=\"Economic institutions, standardized period component.\" class=\"wp-image-1806\" srcset=\"https://www.allendowney.com/blog/wp-content/uploads/2026/05/con_cluster_2_econom-76a4be0f163f28d139a677ac90cfd0e5.png 1145w, https://www.allendowney.com/blog/wp-content/uploads/2026/05/con_cluster_2_econom-76a4be0f163f28d139a677ac90cfd0e5-300x200.png 300w, https://www.allendowney.com/blog/wp-content/uploads/2026/05/con_cluster_2_econom-76a4be0f163f28d139a677ac90cfd0e5-1024x683.png 1024w, https://www.allendowney.com/blog/wp-content/uploads/2026/05/con_cluster_2_econom-76a4be0f163f28d139a677ac90cfd0e5-768x512.png 768w, https://www.allendowney.com/blog/wp-content/uploads/2026/05/con_cluster_2_econom-76a4be0f163f28d139a677ac90cfd0e5-405x270.png 405w\" sizes=\"auto, (max-width: 1145px) 100vw, 1145px\" /></figure>\n\n\n\n<p class=\"wp-block-paragraph\">Confidence in these institutions is generally high. Looking at the cohort effects, the most salient feature is increased confidence in organized labor among people born after 1940.</p>\n\n\n\n<p class=\"wp-block-paragraph\">A possible explanation is that younger cohorts have less exposure to organized labor. Older generations were more likely to be affected by strikes and related economic disruption, and more likely to be aware of corruption in labor unions. As union membership has declined and the gig economy has expanded, younger cohorts are less aware of the negative aspects of organized labor, including dues, and more likely to perceive their lack of negotiating power in the labor market. Also, anti-labor ideology has declined since the end of the Cold War, as the framing has shifted from “labor versus management” to “workers versus corporations”.</p>\n\n\n\n<p class=\"wp-block-paragraph\">By comparison with the cohort effects, the period effects are modest:</p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>The period effect on organized labor is almost unchanged since the 1980s — the change we see over time is almost entirely due to generational replacement.</li>\n\n\n\n<li>The period effect on confidence in major companies has declined somewhat.</li>\n\n\n\n<li>The trend for banks and financial institutions is more complicated — arguably driven by shorter-term period effects like scandals and financial crises. The first notable downturn, in the 1980s, coincides with the <a href=\"https://en.wikipedia.org/wiki/Savings_and_loan_crisis\" target=\"_blank\" rel=\"noreferrer noopener\">savings and loan crisis</a>, when hundreds of financial institutions failed and taxpayers absorbed large bailout costs, followed by an <a href=\"https://en.wikipedia.org/wiki/Early_1990s_recession_in_the_United_States\" target=\"_blank\" rel=\"noreferrer noopener\">economic recession</a> from 1990 into 1991. The larger downturn around 2008 coincides with the <a href=\"https://en.wikipedia.org/wiki/2008_financial_crisis\" target=\"_blank\" rel=\"noreferrer noopener\">2008 global financial crisis</a>, when taxpayers were hit with even larger bailout costs, and public anger at “private gains, public losses” came to a focus in the <a href=\"https://en.wikipedia.org/wiki/Occupy_Wall_Street\" target=\"_blank\" rel=\"noreferrer noopener\">Occupy Wall Street protests</a>.</li>\n</ul>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"professions-knowledge-and-religion\">Professions, knowledge, and religion</h3>\n\n\n\n<p class=\"wp-block-paragraph\">The following figures show estimated cohort and period effects for confidence in education, medicine, the scientific community, and organized religion.</p>\n\n\n\n<figure class=\"wp-block-image\" id=\"cluster-prof-cohort\"><img loading=\"lazy\" decoding=\"async\" width=\"1145\" height=\"764\" src=\"https://www.allendowney.com/blog/wp-content/uploads/2026/05/con_cluster_3_profes-14bdbff63efcff6380045908aa3157ab.png\" alt=\"Professions and knowledge institutions, standardized cohort component.\" class=\"wp-image-1816\" srcset=\"https://www.allendowney.com/blog/wp-content/uploads/2026/05/con_cluster_3_profes-14bdbff63efcff6380045908aa3157ab.png 1145w, https://www.allendowney.com/blog/wp-content/uploads/2026/05/con_cluster_3_profes-14bdbff63efcff6380045908aa3157ab-300x200.png 300w, https://www.allendowney.com/blog/wp-content/uploads/2026/05/con_cluster_3_profes-14bdbff63efcff6380045908aa3157ab-1024x683.png 1024w, https://www.allendowney.com/blog/wp-content/uploads/2026/05/con_cluster_3_profes-14bdbff63efcff6380045908aa3157ab-768x512.png 768w, https://www.allendowney.com/blog/wp-content/uploads/2026/05/con_cluster_3_profes-14bdbff63efcff6380045908aa3157ab-405x270.png 405w\" sizes=\"auto, (max-width: 1145px) 100vw, 1145px\" /></figure>\n\n\n\n<p class=\"wp-block-paragraph\"></p>\n\n\n\n<figure class=\"wp-block-image\" id=\"cluster-prof-standardized-period\"><img loading=\"lazy\" decoding=\"async\" width=\"1145\" height=\"764\" src=\"https://www.allendowney.com/blog/wp-content/uploads/2026/05/con_cluster_3_profes-f5418c000cfe9c18849ed481e1182500.png\" alt=\"Professions and knowledge institutions, standardized period component.\" class=\"wp-image-1805\" srcset=\"https://www.allendowney.com/blog/wp-content/uploads/2026/05/con_cluster_3_profes-f5418c000cfe9c18849ed481e1182500.png 1145w, https://www.allendowney.com/blog/wp-content/uploads/2026/05/con_cluster_3_profes-f5418c000cfe9c18849ed481e1182500-300x200.png 300w, https://www.allendowney.com/blog/wp-content/uploads/2026/05/con_cluster_3_profes-f5418c000cfe9c18849ed481e1182500-1024x683.png 1024w, https://www.allendowney.com/blog/wp-content/uploads/2026/05/con_cluster_3_profes-f5418c000cfe9c18849ed481e1182500-768x512.png 768w, https://www.allendowney.com/blog/wp-content/uploads/2026/05/con_cluster_3_profes-f5418c000cfe9c18849ed481e1182500-405x270.png 405w\" sizes=\"auto, (max-width: 1145px) 100vw, 1145px\" /></figure>\n\n\n\n<p class=\"wp-block-paragraph\">Confidence in these institutions is highest for science and medicine, lower for education and religion.</p>\n\n\n\n<p class=\"wp-block-paragraph\">Looking at the period effects, they are all in decline. Confidence in education declined most steeply; confidence in the scientific community is relatively stable, although it declines after 2020.</p>\n\n\n\n<p class=\"wp-block-paragraph\">Thinking about confidence in education, it might be useful to separate colleges and universities from K-12 schools.</p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>In higher education, the decline might be due to increasing tuition and student debt, credential inflation, and increasing uncertainty about the economic return on a college degree, especially among majors in the arts and humanities. More recently, confidence in universities has decreased steeply, especially among conservatives, due to the perception of ideological bias.</li>\n\n\n\n<li>In K-12 education, declining confidence might be related to anxiety about standardized testing, international competition, and especially around the <a href=\"https://en.wikipedia.org/wiki/No_Child_Left_Behind_Act\" target=\"_blank\" rel=\"noreferrer noopener\">No Child Left Behind Act</a> in 2001, the framing of public schools as underperforming institutions requiring accountability reforms and federal intervention. Also, public schools have increasingly become focal points for political conflicts about curriculum, race, gender, religion, and parental authority.</li>\n</ul>\n\n\n\n<p class=\"wp-block-paragraph\">Most of the cohort effects have increased modestly; in particular confidence in education is higher among people born after 1980, compared to previous generations observed at the same time. But for these institutions, the interaction of the period and cohort effect is similar to what we saw for Congress — it’s not that recent generations have <em>more</em> confidence, it’s just that when they are surveyed as young adults, they come in at entry points above the declining trend of previous generations.</p>\n\n\n\n<p class=\"wp-block-paragraph\">Confidence in organized religion is the exception — the period and cohort effects both trend downward, so the decline is additive. A likely contributor to the period effect is growing public awareness of <a href=\"https://en.wikipedia.org/wiki/Catholic_Church_sex_abuse_cases_in_the_United_States\" target=\"_blank\" rel=\"noreferrer noopener\">sexual abuse and institutional coverups in the Catholic Church</a>, which received national attention beginning in the 1980s, escalated after the <a href=\"https://en.wikipedia.org/wiki/Sexual_abuse_scandal_in_the_Archdiocese_of_Boston\" target=\"_blank\" rel=\"noreferrer noopener\">Boston Globe investigations</a> published in 2002, and continues to the present with additional revelations in the United States and other countries. But the decline is not limited to the Catholic Church, and it began before these scandals were widely known.</p>\n\n\n\n<p class=\"wp-block-paragraph\">The cohort effect likely reflects broader secularization trends, including declining religious affiliation, lower church attendance, and weakening institutional authority among younger generations.</p>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"media\">Media</h3>\n\n\n\n<p class=\"wp-block-paragraph\">Finally, the following figures show estimated cohort and period effects for confidence in television and the press.</p>\n\n\n\n<figure class=\"wp-block-image\" id=\"cluster-media-cohort\"><img loading=\"lazy\" decoding=\"async\" width=\"1145\" height=\"764\" src=\"https://www.allendowney.com/blog/wp-content/uploads/2026/05/con_cluster_4_media_-8bf3f75d17ac4f1f8991025f1051ce52.png\" alt=\"Media, standardized cohort component.\" class=\"wp-image-1815\" srcset=\"https://www.allendowney.com/blog/wp-content/uploads/2026/05/con_cluster_4_media_-8bf3f75d17ac4f1f8991025f1051ce52.png 1145w, https://www.allendowney.com/blog/wp-content/uploads/2026/05/con_cluster_4_media_-8bf3f75d17ac4f1f8991025f1051ce52-300x200.png 300w, https://www.allendowney.com/blog/wp-content/uploads/2026/05/con_cluster_4_media_-8bf3f75d17ac4f1f8991025f1051ce52-1024x683.png 1024w, https://www.allendowney.com/blog/wp-content/uploads/2026/05/con_cluster_4_media_-8bf3f75d17ac4f1f8991025f1051ce52-768x512.png 768w, https://www.allendowney.com/blog/wp-content/uploads/2026/05/con_cluster_4_media_-8bf3f75d17ac4f1f8991025f1051ce52-405x270.png 405w\" sizes=\"auto, (max-width: 1145px) 100vw, 1145px\" /></figure>\n\n\n\n<p class=\"wp-block-paragraph\"></p>\n\n\n\n<figure class=\"wp-block-image\" id=\"cluster-media-standardized-period\"><img loading=\"lazy\" decoding=\"async\" width=\"1145\" height=\"764\" src=\"https://www.allendowney.com/blog/wp-content/uploads/2026/05/con_cluster_4_media_-db77e283c289a556c23c800a199f1ce9.png\" alt=\"Media, standardized period component.\" class=\"wp-image-1810\" srcset=\"https://www.allendowney.com/blog/wp-content/uploads/2026/05/con_cluster_4_media_-db77e283c289a556c23c800a199f1ce9.png 1145w, https://www.allendowney.com/blog/wp-content/uploads/2026/05/con_cluster_4_media_-db77e283c289a556c23c800a199f1ce9-300x200.png 300w, https://www.allendowney.com/blog/wp-content/uploads/2026/05/con_cluster_4_media_-db77e283c289a556c23c800a199f1ce9-1024x683.png 1024w, https://www.allendowney.com/blog/wp-content/uploads/2026/05/con_cluster_4_media_-db77e283c289a556c23c800a199f1ce9-768x512.png 768w, https://www.allendowney.com/blog/wp-content/uploads/2026/05/con_cluster_4_media_-db77e283c289a556c23c800a199f1ce9-405x270.png 405w\" sizes=\"auto, (max-width: 1145px) 100vw, 1145px\" /></figure>\n\n\n\n<p class=\"wp-block-paragraph\">There is almost no cohort effect, although the most recent cohorts might have a little more confidence in television.</p>\n\n\n\n<p class=\"wp-block-paragraph\">The headline here is the period effect, which is consistently downward, and steeper for the press than television. The steepest part of the decline for both media started around 1990, shortly after the 1987 abolition of the <a href=\"https://en.wikipedia.org/wiki/Fairness_doctrine\" target=\"_blank\" rel=\"noreferrer noopener\">fairness doctrine</a>, which required broadcast coverage of controversial topics to be “fair in the sense that it provides an opportunity for the presentation of contrasting points of view,” as described in the <a href=\"https://www.fcc.gov/document/editorializing-broadcast-licensees\" target=\"_blank\" rel=\"noreferrer noopener\">1949 FCC report</a> that established the doctrine.</p>\n\n\n\n<p class=\"wp-block-paragraph\">The end of the fairness doctrine coincided with the rise of talk radio programs with explicit political viewpoints, including <a href=\"https://en.wikipedia.org/wiki/The_Rush_Limbaugh_Show\" target=\"_blank\" rel=\"noreferrer noopener\">The Rush Limbaugh Show</a>, which was nationally syndicated in 1988.</p>\n\n\n\n<p class=\"wp-block-paragraph\">Cable television news followed, including <a href=\"https://en.wikipedia.org/wiki/Fox_News\" target=\"_blank\" rel=\"noreferrer noopener\">Fox News Channel</a> in 1996, with an explicit conservative orientation, and <a href=\"https://en.wikipedia.org/wiki/MSNBC\" target=\"_blank\" rel=\"noreferrer noopener\">MSNBC</a>, which developed a more liberal identity in the 2000s.</p>\n\n\n\n<p class=\"wp-block-paragraph\">During this period, more generally, media audiences became more fragmented. Prior to 1980, most Americans were exposed to a small number of shared news sources, notably the three major television networks. Talk radio and cable television offered more options and less common experience.</p>\n\n\n\n<p class=\"wp-block-paragraph\">And then the internet happened, starting in the 1990s with online news and political blogs, including the <a href=\"https://en.wikipedia.org/wiki/Drudge_Report\" target=\"_blank\" rel=\"noreferrer noopener\">Drudge Report</a> which started as a weekly email newsletter in 1995, and rose to national prominence when it broke the <a href=\"https://en.wikipedia.org/wiki/Clinton%E2%80%93Lewinsky_scandal\" target=\"_blank\" rel=\"noreferrer noopener\">Clinton-Lewinsky scandal</a> in 1998.</p>\n\n\n\n<p class=\"wp-block-paragraph\">Social media followed. YouTube was founded in 2005; Facebook and Twitter launched in 2006. While these platforms have become important sources of news for many Americans, engagement-driven algorithms often promote emotionally provocative and polarizing content over careful reporting. The rise of the internet contributed to the decline of local newspapers, and eventually national newspapers as well.</p>\n\n\n\n<p class=\"wp-block-paragraph\">Ownership of television stations became increasingly consolidated following the <a href=\"https://en.wikipedia.org/wiki/Telecommunications_Act_of_1996\" target=\"_blank\" rel=\"noreferrer noopener\">1996 Telecommunications Act</a>, allowing a small number of national media companies to control larger shares of local news programming. The effect of this consolidation is explained in <a href=\"https://www.vox.com/policy-and-politics/2018/4/2/17189302/sinclair-broadcast-fake-news-biased-trump-viral-video\" target=\"_blank\" rel=\"noreferrer noopener\">this Vox article</a> and memorably demonstrated in <a href=\"https://www.youtube.com/watch?v=hWLjYJ4BzvI\" target=\"_blank\" rel=\"noreferrer noopener\">this Deadspin compilation</a> showing dozens of TV news anchors reading nearly identical scripts provided by the <a href=\"https://en.wikipedia.org/wiki/Sinclair_Broadcast_Group\" target=\"_blank\" rel=\"noreferrer noopener\">Sinclair Broadcast Group</a>, which requires the channels it owns to air segments called <a href=\"https://www.nytimes.com/2017/05/12/business/media/sinclair-broadcast-komo-conservative-media.html\" target=\"_blank\" rel=\"noreferrer noopener\">“must-runs”</a> — many of them presenting conservative talking points.</p>\n\n\n\n<p class=\"wp-block-paragraph\">Finally, since the beginning of his presidential campaign in 2015, Donald Trump has repeatedly denigrated television and print media, frequently describing unfavorable coverage as “fake news” and labeling journalists “enemies of the people.” These attacks likely contribute to declining confidence in the press, especially among Republicans.</p>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"negativity-bias\">Negativity Bias</h3>\n\n\n\n<p class=\"wp-block-paragraph\">In the previous examples, you might notice that I offer explanations for the downturns, but no explanation for the upturns. That’s because bad things, like scandals and economic crises, often happen quickly and they get a lot of coverage; good things often happen slowly and continue without comment.</p>\n\n\n\n<p class=\"wp-block-paragraph\">For many institutions, no news is good news. When they do their jobs, they don’t get much attention, and public confidence drifts higher, even without specific positive events or coverage.</p>\n\n\n\n<p class=\"wp-block-paragraph\">So I want to end this article by highlighting some of the positive results we see in this data:</p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Confidence in education, science, and medicine is high and although the period effects are negative, the cohort effects are positive, which bodes well for the future.</li>\n\n\n\n<li>Confidence in financial institutions and organized labor is high.</li>\n\n\n\n<li>Confidence in government is lower and declining, but as each generation of young adults starts out more optimistic than their elders, there is hope for a turnaround.</li>\n</ul>\n\n\n\n<p class=\"wp-block-paragraph\">But the recent steep decline of confidence in the Supreme Court is a concern, as is the loss of confidence in the media. It’s hard to find a positive take on those trends.</p>\n\n\n\n<p class=\"wp-block-paragraph\"><a href=\"https://allendowney.github.io/CultureWar//blog7-hapgen\"></a><a href=\"https://allendowney.github.io/CultureWar//blog7-hapgen\"></a></p>\n\n\n\n<p class=\"wp-block-paragraph\"></p>\n<p>The post <a href=\"https://www.allendowney.com/blog/2026/05/19/confidence-in-institutions/\">Confidence in Institutions</a> appeared first on <a href=\"https://www.allendowney.com/blog\">Probably Overthinking It</a>.</p>",
"image": null,
"media": [],
"authors": [
{
"name": "AllenDowney",
"email": null,
"url": null
}
],
"categories": [
{
"label": "Uncategorized",
"term": "Uncategorized",
"url": null
},
{
"label": "age period cohort analysis",
"term": "age period cohort analysis",
"url": null
},
{
"label": "bayesian statistics",
"term": "bayesian statistics",
"url": null
},
{
"label": "general social survey",
"term": "general social survey",
"url": null
}
]
},
{
"id": "https://www.allendowney.com/blog/?p=1794",
"title": "Planning for your midlife crisis",
"description": "<p>Yesterday I presented a talk at ODSC East 2026, called “Counterfactual Analysis with Bayesian Models: What Drives the Life Expectancy Gap?” Here’s the abstract Across nearly every country in the world, women live longer than men—but the size of this gap varies from about two years in some countries to more than twelve in others. What explains these differences, and how much of the gap can be closed? In this talk, I present a practical approach to counterfactual analysis using...</p>\n<p class=\"read-more\"><a class=\"btn btn-default\" href=\"https://www.allendowney.com/blog/2026/05/01/planning-for-your-midlife-crisis/\"> Read More<span class=\"screen-reader-text\"> Read More</span></a></p>\n<p>The post <a href=\"https://www.allendowney.com/blog/2026/05/01/planning-for-your-midlife-crisis/\">Planning for your midlife crisis</a> appeared first on <a href=\"https://www.allendowney.com/blog\">Probably Overthinking It</a>.</p>",
"url": "https://www.allendowney.com/blog/2026/05/01/planning-for-your-midlife-crisis/",
"published": "2026-05-01T19:34:53.000Z",
"updated": "2026-05-01T19:34:53.000Z",
"content": "<p class=\"wp-block-paragraph\">Yesterday I presented a talk at ODSC East 2026, called “Counterfactual Analysis with Bayesian Models: What Drives the Life Expectancy Gap?” Here’s the abstract</p>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\">\n<p class=\"wp-block-paragraph\">Across nearly every country in the world, women live longer than men—but the size of this gap varies from about two years in some countries to more than twelve in others. What explains these differences, and how much of the gap can be closed?</p>\n\n\n\n<p class=\"wp-block-paragraph\">In this talk, I present a practical approach to counterfactual analysis using Bayesian regression models. Using publicly available mortality data, we build a model that relates the life expectancy gap between men and women to differences in cause-specific death rates, including homicide, drug overdoses, traffic fatalities, smoking-related disease, and chronic illness.</p>\n\n\n\n<p class=\"wp-block-paragraph\">The model generates posterior simulations that answer “what-if” questions. For example: How much smaller would the U.S. life expectancy gap be if homicide rates matched those in Western Europe?</p>\n\n\n\n<p class=\"wp-block-paragraph\">The talk presents the workflow—from assembling global datasets to fitting interpretable Bayesian models with PyMC and generating counterfactual simulations. Attendees will learn how Bayesian models can support explainable modeling and analysis under uncertainty.</p>\n</blockquote>\n\n\n\n<p class=\"wp-block-paragraph\">I think the talk went well, and we got some good questions at the end. There’s no recording, unfortunately, <a href=\"https://docs.google.com/presentation/d/e/2PACX-1vSiwjA6Mi95poqGQJiXw7Mdy0BgPa-aEmVhJHXwP35QRjt2dduEEN53yZi4fnpAReVaS-EDWS3CwMt1/pub?start=false&loop=false&delayms=3000\">but my slides are here</a>. And if you want to know more, I have a series of blog posts on Substack</p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><a href=\"https://allendowney.substack.com/p/the-gender-gap-in-life-expectancy\">The Gender Gap in Life Expectancy</a></li>\n\n\n\n<li><a href=\"https://allendowney.substack.com/p/what-drives-the-life-expectancy-gender\">What Drives the Life Expectancy Gender Gap?</a></li>\n\n\n\n<li><a href=\"https://allendowney.substack.com/p/how-much-of-the-life-expectancy-gap\">How Much of the Life Expectancy Gap Could We Close?</a></li>\n\n\n\n<li><a href=\"https://allendowney.substack.com/p/international-patterns-in-the-life\">International Patterns in the Life Expectancy Gap</a></li>\n</ul>\n\n\n\n<p class=\"wp-block-paragraph\">The fifth and final post is on the way. In the meantime, here’s a quick post on a related topic.</p>\n\n\n\n<h2 class=\"wp-block-heading\">Are you middle-aged?</h2>\n\n\n\n<p class=\"wp-block-paragraph\">Here’s a question from Reddit’s <a href=\"https://www.reddit.com/r/stupidquestions/comments/1sxesux/what_age_is_actually_considered_middle_age/\">Stupid Questions forum</a>:</p>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\">\n<p class=\"wp-block-paragraph\">I always thought middle age was in your 40s but since life expectancy is around 75 or so, wouldn’t it be about 35?</p>\n</blockquote>\n\n\n\n<p class=\"wp-block-paragraph\">If life expectancy is 75, you might think the midpoint is half that, which is 37.5. But if 75 is life expectancy <em>at birth</em> and you survive to age 37.5, your life expectancy <em>at that age</em> is higher than 75. So 37.5 is not halfway!</p>\n\n\n\n<p class=\"wp-block-paragraph\">If we really want to find the midpoint – and it wouldn’t be <em>Probably Overthinking It</em> if we didn’t – we have to find the age where your expected remaining lifetime equals your current age.</p>\n\n\n\n<p class=\"wp-block-paragraph\">Let’s do it.</p>\n\n\n\n<h2 class=\"wp-block-heading\">Data</h2>\n\n\n\n<p class=\"wp-block-paragraph\">From the <a href=\"https://www.mortality.org/Country/Country?cntr=USA\">Human Mortality Database</a> I downloaded life tables for the United States, combined and broken down for men and women. The following function reads and cleans a table.</p>\n\n\n\n<pre id=\"codecell1\" class=\"wp-block-preformatted\">def read_life_table(filename):\n lt = pd.read_fwf(filename, skiprows=2, infer_nrows=200)\n lt['Age'] = lt['Age'].str.replace('+', '', regex=False).astype(int)\n return lt\n</pre>\n\n\n\n<p class=\"wp-block-paragraph\">Here are the first few rows of the combined table (see notes below for details).</p>\n\n\n\n<pre id=\"codecell2\" class=\"wp-block-preformatted\">blt = read_life_table('../data/bltper_1x1.txt')\nblt.head()\n</pre>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><thead><tr><th></th><th>Year</th><th>Age</th><th>mx</th><th>qx</th><th>ax</th><th>lx</th><th>dx</th><th>Lx</th><th>Tx</th><th>ex</th></tr></thead><tbody><tr><th>0</th><td>1933</td><td>0</td><td>0.06129</td><td>0.05861</td><td>0.25</td><td>100000</td><td>5861</td><td>95624</td><td>6089609</td><td>60.90</td></tr><tr><th>1</th><td>1933</td><td>1</td><td>0.00946</td><td>0.00941</td><td>0.50</td><td>94139</td><td>886</td><td>93696</td><td>5993985</td><td>63.67</td></tr><tr><th>2</th><td>1933</td><td>2</td><td>0.00435</td><td>0.00434</td><td>0.50</td><td>93253</td><td>405</td><td>93050</td><td>5900289</td><td>63.27</td></tr><tr><th>3</th><td>1933</td><td>3</td><td>0.00310</td><td>0.00310</td><td>0.50</td><td>92848</td><td>288</td><td>92704</td><td>5807239</td><td>62.55</td></tr><tr><th>4</th><td>1933</td><td>4</td><td>0.00239</td><td>0.00238</td><td>0.50</td><td>92560</td><td>221</td><td>92450</td><td>5714535</td><td>61.74</td></tr></tbody></table></figure>\n\n\n\n<p class=\"wp-block-paragraph\">We’ll also read the female and male tables.</p>\n\n\n\n<pre id=\"codecell3\" class=\"wp-block-preformatted\">flt = read_life_table('../data/fltper_1x1.txt')\n</pre>\n\n\n\n<pre id=\"codecell4\" class=\"wp-block-preformatted\">mlt = read_life_table('../data/mltper_1x1.txt')\n</pre>\n\n\n\n<p class=\"wp-block-paragraph\">The tables include data from 1933 to 2024, so we’ll select the most recent data.</p>\n\n\n\n<pre id=\"codecell5\" class=\"wp-block-preformatted\">year = blt['Year'].unique()[-1]\ntable = blt.query('Year == @year').set_index('Age')\n</pre>\n\n\n\n<p class=\"wp-block-paragraph\">The column we’ll use is <code>ex</code>, which is life expectancy as a function of age.</p>\n\n\n\n<pre id=\"codecell6\" class=\"wp-block-preformatted\">age = table.index.to_series()\nex = table['ex']\n</pre>\n\n\n\n<p class=\"wp-block-paragraph\">Life expectancy at birth is 79 years, so the naive midpoint is 39.5.</p>\n\n\n\n<pre id=\"codecell7\" class=\"wp-block-preformatted\">ex[0], ex[0] / 2\n</pre>\n\n\n\n<pre id=\"codecell8\" class=\"wp-block-preformatted\">(79.08, 39.54)\n</pre>\n\n\n\n<p class=\"wp-block-paragraph\">But at age 40, expected remaining lifetime is 41.1, so 39.5 is not the midpoint.</p>\n\n\n\n<pre id=\"codecell9\" class=\"wp-block-preformatted\">ex[39], ex[40]\n</pre>\n\n\n\n<pre id=\"codecell10\" class=\"wp-block-preformatted\">(42.04, 41.12)\n</pre>\n\n\n\n<p class=\"wp-block-paragraph\">This plot shows life expectancy at each age, compared to age.</p>\n\n\n\n<pre id=\"codecell11\" class=\"wp-block-preformatted\">ex.plot(label='Remaining life expectancy')\nage.plot(label='Age')\ndecorate(ylabel='Years',\n title='Remaining life expectancy vs age, United States 2024')\n</pre>\n\n\n\n<figure class=\"wp-block-image\"><img loading=\"lazy\" decoding=\"async\" width=\"438\" height=\"250\" src=\"https://www.allendowney.com/blog/wp-content/uploads/2026/05/a55e9cbde25b36d9c42e2ede2a78a827460d537f230b5cc4e7dfcb519a44bbc6.png\" alt=\"_images/a55e9cbde25b36d9c42e2ede2a78a827460d537f230b5cc4e7dfcb519a44bbc6.png\" class=\"wp-image-1797\" srcset=\"https://www.allendowney.com/blog/wp-content/uploads/2026/05/a55e9cbde25b36d9c42e2ede2a78a827460d537f230b5cc4e7dfcb519a44bbc6.png 438w, https://www.allendowney.com/blog/wp-content/uploads/2026/05/a55e9cbde25b36d9c42e2ede2a78a827460d537f230b5cc4e7dfcb519a44bbc6-300x171.png 300w\" sizes=\"auto, (max-width: 438px) 100vw, 438px\" /></figure>\n\n\n\n<p class=\"wp-block-paragraph\">“Middle age” is where the lines cross, which we can compute by linear interpolation.</p>\n\n\n\n<pre id=\"codecell12\" class=\"wp-block-preformatted\">from scipy.interpolate import interp1d\n\ninverse = interp1d(ex - age, age)\ninverse(0)\n</pre>\n\n\n\n<pre id=\"codecell13\" class=\"wp-block-preformatted\">array(40.58638743)\n</pre>\n\n\n\n<p class=\"wp-block-paragraph\">So the overall midpoint is 40.6 years. But as you might expect, it’s different for men and women. Let’s put the analysis we did in a function.</p>\n\n\n\n<pre id=\"codecell14\" class=\"wp-block-preformatted\">def get_midpoint(filename):\n lt = read_life_table(filename)\n year = lt['Year'].unique()[-1]\n table = lt.query('Year == @year').set_index('Age')\n\n age = pd.Series(table.index)\n ex = table['ex']\n\n inverse = interp1d(ex - age, age)\n return inverse(0)\n</pre>\n\n\n\n<p class=\"wp-block-paragraph\">And run it for men.</p>\n\n\n\n<pre id=\"codecell15\" class=\"wp-block-preformatted\">get_midpoint('../data/mltper_1x1.txt')\n</pre>\n\n\n\n<pre id=\"codecell16\" class=\"wp-block-preformatted\">array(39.57142857)\n</pre>\n\n\n\n<p class=\"wp-block-paragraph\">And women.</p>\n\n\n\n<pre id=\"codecell17\" class=\"wp-block-preformatted\">get_midpoint('../data/fltper_1x1.txt')\n</pre>\n\n\n\n<pre id=\"codecell18\" class=\"wp-block-preformatted\">array(41.56185567)\n</pre>\n\n\n\n<p class=\"wp-block-paragraph\">Men hit middle age at 39.6, women at 41.6.</p>\n\n\n\n<h2 class=\"wp-block-heading\">The Gender Gap and Age</h2>\n\n\n\n<p class=\"wp-block-paragraph\">Finally, let’s see how the gender gap in life expectancy changes as a function of age.</p>\n\n\n\n<pre id=\"codecell19\" class=\"wp-block-preformatted\">ex_male = mlt.query('Year == @year').set_index('Age')['ex']\nex_female = flt.query('Year == @year').set_index('Age')['ex']\ngap = ex_female - ex_male\n</pre>\n\n\n\n<pre id=\"codecell20\" class=\"wp-block-preformatted\">gap.plot(label='')\ndecorate(ylabel='Years',\n title='Life expectancy gender gap vs age')\n</pre>\n\n\n\n<figure class=\"wp-block-image\"><img loading=\"lazy\" decoding=\"async\" width=\"438\" height=\"250\" src=\"https://www.allendowney.com/blog/wp-content/uploads/2026/05/2cf48be5acc971ad8f6973506c224767a25ef2e38bcf53c5b12b0f895c26ed11.png\" alt=\"_images/2cf48be5acc971ad8f6973506c224767a25ef2e38bcf53c5b12b0f895c26ed11.png\" class=\"wp-image-1796\" srcset=\"https://www.allendowney.com/blog/wp-content/uploads/2026/05/2cf48be5acc971ad8f6973506c224767a25ef2e38bcf53c5b12b0f895c26ed11.png 438w, https://www.allendowney.com/blog/wp-content/uploads/2026/05/2cf48be5acc971ad8f6973506c224767a25ef2e38bcf53c5b12b0f895c26ed11-300x171.png 300w\" sizes=\"auto, (max-width: 438px) 100vw, 438px\" /></figure>\n\n\n\n<p class=\"wp-block-paragraph\">At birth the life expectancy gap is close to five years. At age 100, it is close to zero.</p>\n\n\n\n<p class=\"wp-block-paragraph\">But just looking at the gap might be misleading. For a more complete picture let’s also look at the ratio.</p>\n\n\n\n<pre id=\"codecell21\" class=\"wp-block-preformatted\">ratio = ex_female / ex_male\nratio.plot(label='')\n\ndecorate(ylabel='Ratio',\n title='Life expectancy gender ratio (female / male)')\n</pre>\n\n\n\n<figure class=\"wp-block-image\"><img loading=\"lazy\" decoding=\"async\" width=\"446\" height=\"250\" src=\"https://www.allendowney.com/blog/wp-content/uploads/2026/05/1a514d22895c3e18a767184700d6edf467975abb4b302afe044fd42c002ae21c.png\" alt=\"_images/1a514d22895c3e18a767184700d6edf467975abb4b302afe044fd42c002ae21c.png\" class=\"wp-image-1798\" srcset=\"https://www.allendowney.com/blog/wp-content/uploads/2026/05/1a514d22895c3e18a767184700d6edf467975abb4b302afe044fd42c002ae21c.png 446w, https://www.allendowney.com/blog/wp-content/uploads/2026/05/1a514d22895c3e18a767184700d6edf467975abb4b302afe044fd42c002ae21c-300x168.png 300w\" sizes=\"auto, (max-width: 446px) 100vw, 446px\" /></figure>\n\n\n\n<p class=\"wp-block-paragraph\">The life expectancy ratio tells a more complicated story.</p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>At birth, the ratio is 1.06, which means female babies live 6% longer, on average.</li>\n\n\n\n<li>Around age 80, the ratio peaks at nearly 1.14 – so between female and male octogenarians, we expect the women to live 14% longer.</li>\n\n\n\n<li>At advanced ages, the ratio declines steeply and actually crosses over after age 100 – although the crossover is minimal and might not be statistically valid.</li>\n</ul>\n\n\n\n<p class=\"wp-block-paragraph\">To interpret these results, we can think about the causes of death that contribute to age-specific death rates at different stages of life.</p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>In young adulthood, the causes of death that contribute most to gender gaps include road traffic, homicide, accidental injury, drug use disorders.</li>\n\n\n\n<li>In advanced adulthood, they include cancer, cardiovascular disease, respiratory disease, liver disease, diabetes, and suicide.</li>\n</ul>\n\n\n\n<p class=\"wp-block-paragraph\">The causes that affect younger people have large gender gaps, but relatively low death rates. As people get older, these low-rate causes contribute less to age-specific death rates, and the higher-rate causes contribute more.</p>\n\n\n\n<p class=\"wp-block-paragraph\">I think that’s a plausible explanation for the increasing ratio from age 0 to 80. For the decline that follows, I can only speculate that there is a selection effect: people who get to these advanced ages are likely to have better-than-average lifestyle histories (less smoking and drinking, better diet, more exercise) – and among people with better lifestyles, the gender gap is small.</p>\n\n\n\n<h2 class=\"wp-block-heading\">Notes</h2>\n\n\n\n<p class=\"wp-block-paragraph\">Data credit: HMD. Human Mortality Database. Max Planck Institute for Demographic Research (Germany), University of California, Berkeley (USA), and French Institute for Demographic Studies (France). Available at [<a href=\"http://www.mortality.org\">www.mortality.org</a>].</p>\n\n\n\n<p class=\"wp-block-paragraph\">Here are the columns of the 1×1 Period Life Tables:</p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Year</strong>: Calendar year to which the period life table refers.</li>\n\n\n\n<li><strong>Age</strong>: Exact age (x), in years, at the beginning of the interval ([x, x+1)).</li>\n\n\n\n<li><strong>mx</strong>: Central death rate at age (x):</li>\n</ul>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>qx</strong>: Probability of dying between ages (x) and (x+1):</li>\n</ul>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>ax</strong>: Average fraction of the interval lived by those who die in ([x, x+1)). Typically around 0.5 for most ages, lower for infants (reflecting higher early mortality within the year).</li>\n\n\n\n<li><strong>lx</strong>: Number of survivors at exact age (x), out of a radix (usually 100,000 births).</li>\n\n\n\n<li><strong>dx</strong>: Number of deaths between ages (x) and (x+1):</li>\n</ul>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Lx</strong>: Person-years lived between ages (x) and (x+1), approximately</li>\n</ul>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Tx</strong>: Total person-years remaining above age (x):</li>\n</ul>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>ex</strong>: Life expectancy at age (x):</li>\n</ul>\n\n\n\n<p class=\"wp-block-paragraph\">The details are in<a href=\"https://github.com/AllenDowney/ProbablyOverthinkingIt/blob/book/examples/midlife.ipynb\"> this Jupyter notebook</a>.</p>\n<p>The post <a href=\"https://www.allendowney.com/blog/2026/05/01/planning-for-your-midlife-crisis/\">Planning for your midlife crisis</a> appeared first on <a href=\"https://www.allendowney.com/blog\">Probably Overthinking It</a>.</p>",
"image": null,
"media": [],
"authors": [
{
"name": "AllenDowney",
"email": null,
"url": null
}
],
"categories": [
{
"label": "Uncategorized",
"term": "Uncategorized",
"url": null
},
{
"label": "life expectancy",
"term": "life expectancy",
"url": null
},
{
"label": "mortality",
"term": "mortality",
"url": null
},
{
"label": "ODSC",
"term": "ODSC",
"url": null
}
]
},
{
"id": "https://www.allendowney.com/blog/?p=1782",
"title": "Changing Opinions on Assisted Suicide",
"description": "<p>In Graphs About Religion, Ryan Burge recently wrote about changing opinions about assisted suicide and how they relate to religion. As always, when I see survey responses changing over time, I wonder whether it is driven primarily by period or cohort effects. And if you’ve read my last few posts, you know I’ve been working on a Bayesian model to answer that question. Ryan’s analysis is based on four questions from the General Social Survey (GSS): In addition, we’ll look...</p>\n<p class=\"read-more\"><a class=\"btn btn-default\" href=\"https://www.allendowney.com/blog/2026/04/16/changing-opinions-on-assisted-suicide/\"> Read More<span class=\"screen-reader-text\"> Read More</span></a></p>\n<p>The post <a href=\"https://www.allendowney.com/blog/2026/04/16/changing-opinions-on-assisted-suicide/\">Changing Opinions on Assisted Suicide</a> appeared first on <a href=\"https://www.allendowney.com/blog\">Probably Overthinking It</a>.</p>",
"url": "https://www.allendowney.com/blog/2026/04/16/changing-opinions-on-assisted-suicide/",
"published": "2026-04-16T20:01:37.000Z",
"updated": "2026-04-16T20:01:37.000Z",
"content": "<p class=\"wp-block-paragraph\">In <a href=\"https://www.graphsaboutreligion.com/p/god-death-and-the-right-to-choose\" target=\"_blank\" rel=\"noreferrer noopener\">Graphs About Religion</a>, Ryan Burge recently wrote about changing opinions about assisted suicide and how they relate to religion.</p>\n\n\n\n<p class=\"wp-block-paragraph\">As always, when I see survey responses changing over time, I wonder whether it is driven primarily by period or cohort effects. And if you’ve read my last few posts, you know I’ve been working on a Bayesian model to answer that question.</p>\n\n\n\n<p class=\"wp-block-paragraph\">Ryan’s analysis is based on four questions from the General Social Survey (GSS):</p>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\">\n<p class=\"wp-block-paragraph\">Do you think a person has the right to end his or her own life if this person:</p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Has an incurable disease? (<code>suicide1</code>)</li>\n\n\n\n<li>Has gone bankrupt? (<code>suicide2</code>)</li>\n\n\n\n<li>Has dishonored his or her family? (<code>suicide3</code>)</li>\n\n\n\n<li>Is tired of living and ready to die? (<code>suicide4</code>)</li>\n</ul>\n</blockquote>\n\n\n\n<p class=\"wp-block-paragraph\">In addition, we’ll look at results from a related question (<code>letdie1</code>):</p>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\">\n<p class=\"wp-block-paragraph\">When a person has a disease that cannot be cured, do you think doctors should be allowed by law to end the patient’s life by some painless means if the patient and his family request it?</p>\n</blockquote>\n\n\n\n<p class=\"wp-block-paragraph\">The framing of the questions is different: the first four are about the right to end one’s life and the last is about the legality of doctor-assisted suicide.</p>\n\n\n\n<p class=\"wp-block-paragraph\">Before we look at the breakdown of period and cohort effects, here are the results from a model that estimates latent opposition to each proposition as a smooth function over time.</p>\n\n\n\n<figure class=\"wp-block-image\" id=\"letdie-single-time\"><img loading=\"lazy\" decoding=\"async\" width=\"1108\" height=\"704\" src=\"https://www.allendowney.com/blog/wp-content/uploads/2026/04/letdie_compare_time_-340f828df36b2086971ded6f63293cf6.png\" alt=\"Time-only trends.\" class=\"wp-image-1784\" srcset=\"https://www.allendowney.com/blog/wp-content/uploads/2026/04/letdie_compare_time_-340f828df36b2086971ded6f63293cf6.png 1108w, https://www.allendowney.com/blog/wp-content/uploads/2026/04/letdie_compare_time_-340f828df36b2086971ded6f63293cf6-300x191.png 300w, https://www.allendowney.com/blog/wp-content/uploads/2026/04/letdie_compare_time_-340f828df36b2086971ded6f63293cf6-1024x651.png 1024w, https://www.allendowney.com/blog/wp-content/uploads/2026/04/letdie_compare_time_-340f828df36b2086971ded6f63293cf6-768x488.png 768w, https://www.allendowney.com/blog/wp-content/uploads/2026/04/letdie_compare_time_-340f828df36b2086971ded6f63293cf6-425x270.png 425w\" sizes=\"auto, (max-width: 1108px) 100vw, 1108px\" /></figure>\n\n\n\n<p class=\"wp-block-paragraph\">Opposition to suicide is high in three of the scenarios — bankrupt, dishonored family, and tired of living — and lower in the incurable disease scenarios.</p>\n\n\n\n<p class=\"wp-block-paragraph\">In all five questions, opposition has declined over time, although for the incurable disease scenarios, it might have leveled off after 1990.</p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"doctor-assisted-death\">Doctor-assisted death</h2>\n\n\n\n<p class=\"wp-block-paragraph\">Now let’s see if we can decompose these changes into period and cohort effects. We’ll start with the question about doctor-assisted death when the patient has an incurable disease.</p>\n\n\n\n<p class=\"wp-block-paragraph\">As in the previous posts, I used a Bayesian model to estimate a trajectory over time for each birth cohort, shown in the following figure.</p>\n\n\n\n<figure class=\"wp-block-image\" id=\"letdie1-cohort-trajectories\"><img loading=\"lazy\" decoding=\"async\" width=\"1330\" height=\"778\" src=\"https://www.allendowney.com/blog/wp-content/uploads/2026/04/cohort_trajectory_le-28df4a8cc3e21cad9b463f53ddf9a3ef.png\" alt=\"Cohort trajectories: letdie1.\" class=\"wp-image-1785\" srcset=\"https://www.allendowney.com/blog/wp-content/uploads/2026/04/cohort_trajectory_le-28df4a8cc3e21cad9b463f53ddf9a3ef.png 1330w, https://www.allendowney.com/blog/wp-content/uploads/2026/04/cohort_trajectory_le-28df4a8cc3e21cad9b463f53ddf9a3ef-300x175.png 300w, https://www.allendowney.com/blog/wp-content/uploads/2026/04/cohort_trajectory_le-28df4a8cc3e21cad9b463f53ddf9a3ef-1024x599.png 1024w, https://www.allendowney.com/blog/wp-content/uploads/2026/04/cohort_trajectory_le-28df4a8cc3e21cad9b463f53ddf9a3ef-768x449.png 768w, https://www.allendowney.com/blog/wp-content/uploads/2026/04/cohort_trajectory_le-28df4a8cc3e21cad9b463f53ddf9a3ef-462x270.png 462w\" sizes=\"auto, (max-width: 1330px) 100vw, 1330px\" /></figure>\n\n\n\n<p class=\"wp-block-paragraph\">Reading from top to bottom, we can see that opposition has declined from one cohort to the next, and reading from left to right, we can see that opposition has varied over time within each cohort.</p>\n\n\n\n<p class=\"wp-block-paragraph\">The following figure shows the cohort component alone, standardized to factor out the period effect.</p>\n\n\n\n<figure class=\"wp-block-image\" id=\"letdie1-cohort-component\"><img loading=\"lazy\" decoding=\"async\" width=\"1166\" height=\"790\" src=\"https://www.allendowney.com/blog/wp-content/uploads/2026/04/cohort_standardized_-d780162e3521c3e8c568d864d1d04042.png\" alt=\"Cohort component (uniform years): letdie1.\" class=\"wp-image-1786\" srcset=\"https://www.allendowney.com/blog/wp-content/uploads/2026/04/cohort_standardized_-d780162e3521c3e8c568d864d1d04042.png 1166w, https://www.allendowney.com/blog/wp-content/uploads/2026/04/cohort_standardized_-d780162e3521c3e8c568d864d1d04042-300x203.png 300w, https://www.allendowney.com/blog/wp-content/uploads/2026/04/cohort_standardized_-d780162e3521c3e8c568d864d1d04042-1024x694.png 1024w, https://www.allendowney.com/blog/wp-content/uploads/2026/04/cohort_standardized_-d780162e3521c3e8c568d864d1d04042-768x520.png 768w, https://www.allendowney.com/blog/wp-content/uploads/2026/04/cohort_standardized_-d780162e3521c3e8c568d864d1d04042-399x270.png 399w\" sizes=\"auto, (max-width: 1166px) 100vw, 1166px\" /></figure>\n\n\n\n<p class=\"wp-block-paragraph\">Opposition to doctor-assisted suicide has declined from more than 40% in the earliest cohorts to 20% among people born in 2006.</p>\n\n\n\n<p class=\"wp-block-paragraph\">A possible explanation for the cohort pattern is that people anchor their moral judgments to the legal environment they encounter when they are young. During the “impressionable years” of late adolescence and early adulthood, existing laws can establish a moral baseline, so that what is illegal is inferred to be wrong, and therefore should remain illegal. As a result, gradual legalization can generate long-run attitudinal change through cohort replacement: people who grow up after a practice becomes legal are less likely to see it as morally problematic.</p>\n\n\n\n<p class=\"wp-block-paragraph\">The following figure shows the period effect alone, along with the results from the time model (which includes both period and cohort effects).</p>\n\n\n\n<figure class=\"wp-block-image\" id=\"letdie1-period-time\"><img loading=\"lazy\" decoding=\"async\" width=\"1166\" height=\"790\" src=\"https://www.allendowney.com/blog/wp-content/uploads/2026/04/time_standardized_le-c7580a12cc292dbce6e525849d0e6220.png\" alt=\"Standardized period component with time model: letdie1.\" class=\"wp-image-1788\" srcset=\"https://www.allendowney.com/blog/wp-content/uploads/2026/04/time_standardized_le-c7580a12cc292dbce6e525849d0e6220.png 1166w, https://www.allendowney.com/blog/wp-content/uploads/2026/04/time_standardized_le-c7580a12cc292dbce6e525849d0e6220-300x203.png 300w, https://www.allendowney.com/blog/wp-content/uploads/2026/04/time_standardized_le-c7580a12cc292dbce6e525849d0e6220-1024x694.png 1024w, https://www.allendowney.com/blog/wp-content/uploads/2026/04/time_standardized_le-c7580a12cc292dbce6e525849d0e6220-768x520.png 768w, https://www.allendowney.com/blog/wp-content/uploads/2026/04/time_standardized_le-c7580a12cc292dbce6e525849d0e6220-399x270.png 399w\" sizes=\"auto, (max-width: 1166px) 100vw, 1166px\" /></figure>\n\n\n\n<p class=\"wp-block-paragraph\">Comparing the two lines, we can conclude that the decline we see over time is entirely due to the cohort effect — when we control for generational replacement, the estimated period effect has generally <em>increased</em> since 1990.</p>\n\n\n\n<p class=\"wp-block-paragraph\">The increase between 1990 and 2005 might reflect increasing moral concern due to advances in life-sustaining medical technology, high-profile legal disputes like the <a href=\"https://en.wikipedia.org/wiki/Terri_Schiavo_case\" target=\"_blank\" rel=\"noreferrer noopener\">Terri Schiavo case</a>, and broader discussions of the sanctity of life.</p>\n\n\n\n<p class=\"wp-block-paragraph\">The decline between 2005 to 2015 might reflect normalization of assisted dying following legalization in several states (Oregon in 1997, Washington in 2008, and Montana in 2009, Vermont in 2013), along with a shift in public discourse toward autonomy, dignity, and patient choice, reinforced by high-profile cases like <a href=\"https://en.wikipedia.org/wiki/Brittany_Maynard\" target=\"_blank\" rel=\"noreferrer noopener\">Brittany Maynard</a>.</p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"other-scenarios\">Other Scenarios</h2>\n\n\n\n<p class=\"wp-block-paragraph\">The following figure shows the estimated cohort effects for all five questions.</p>\n\n\n\n<figure class=\"wp-block-image\" id=\"letdie-single-cohort\"><img loading=\"lazy\" decoding=\"async\" width=\"1108\" height=\"704\" src=\"https://www.allendowney.com/blog/wp-content/uploads/2026/04/letdie_compare_cohor-ca0769cc27ba5266de2e551bbf9f7ec3.png\" alt=\"Cohort margins, single panel.\" class=\"wp-image-1789\" srcset=\"https://www.allendowney.com/blog/wp-content/uploads/2026/04/letdie_compare_cohor-ca0769cc27ba5266de2e551bbf9f7ec3.png 1108w, https://www.allendowney.com/blog/wp-content/uploads/2026/04/letdie_compare_cohor-ca0769cc27ba5266de2e551bbf9f7ec3-300x191.png 300w, https://www.allendowney.com/blog/wp-content/uploads/2026/04/letdie_compare_cohor-ca0769cc27ba5266de2e551bbf9f7ec3-1024x651.png 1024w, https://www.allendowney.com/blog/wp-content/uploads/2026/04/letdie_compare_cohor-ca0769cc27ba5266de2e551bbf9f7ec3-768x488.png 768w, https://www.allendowney.com/blog/wp-content/uploads/2026/04/letdie_compare_cohor-ca0769cc27ba5266de2e551bbf9f7ec3-425x270.png 425w\" sizes=\"auto, (max-width: 1108px) 100vw, 1108px\" /></figure>\n\n\n\n<p class=\"wp-block-paragraph\">For the incurable disease scenario, opposition has declined from more than 60% in the earliest cohorts to less than 40% among cohorts born after 1950 — although it might have leveled off since then.</p>\n\n\n\n<p class=\"wp-block-paragraph\">In the other scenarios, opposition has also declined from one cohort to the next, but the size of the effect is smaller.</p>\n\n\n\n<p class=\"wp-block-paragraph\">The following figure shows the estimated period effects, controlling for generational replacement.</p>\n\n\n\n<figure class=\"wp-block-image\" id=\"letdie-single-period\"><img loading=\"lazy\" decoding=\"async\" width=\"1108\" height=\"704\" src=\"https://www.allendowney.com/blog/wp-content/uploads/2026/04/letdie_compare_perio-76fe4f16ad277fcdde3a47797ddbb13e.png\" alt=\"Period margins, single panel.\" class=\"wp-image-1787\" srcset=\"https://www.allendowney.com/blog/wp-content/uploads/2026/04/letdie_compare_perio-76fe4f16ad277fcdde3a47797ddbb13e.png 1108w, https://www.allendowney.com/blog/wp-content/uploads/2026/04/letdie_compare_perio-76fe4f16ad277fcdde3a47797ddbb13e-300x191.png 300w, https://www.allendowney.com/blog/wp-content/uploads/2026/04/letdie_compare_perio-76fe4f16ad277fcdde3a47797ddbb13e-1024x651.png 1024w, https://www.allendowney.com/blog/wp-content/uploads/2026/04/letdie_compare_perio-76fe4f16ad277fcdde3a47797ddbb13e-768x488.png 768w, https://www.allendowney.com/blog/wp-content/uploads/2026/04/letdie_compare_perio-76fe4f16ad277fcdde3a47797ddbb13e-425x270.png 425w\" sizes=\"auto, (max-width: 1108px) 100vw, 1108px\" /></figure>\n\n\n\n<p class=\"wp-block-paragraph\">Since 1990, most of the period effects are small. The only exception is the “tired of living” scenario, where there is some decline over time, independent of generational replacement.</p>\n\n\n\n<p class=\"wp-block-paragraph\">In the next post, we’ll do the same analysis with questions about abortion and the situations where it should be legal or not.</p>\n\n\n\n<p class=\"wp-block-paragraph\"></p>\n<p>The post <a href=\"https://www.allendowney.com/blog/2026/04/16/changing-opinions-on-assisted-suicide/\">Changing Opinions on Assisted Suicide</a> appeared first on <a href=\"https://www.allendowney.com/blog\">Probably Overthinking It</a>.</p>",
"image": null,
"media": [],
"authors": [
{
"name": "AllenDowney",
"email": null,
"url": null
}
],
"categories": [
{
"label": "Uncategorized",
"term": "Uncategorized",
"url": null
},
{
"label": "age period cohort analysis",
"term": "age period cohort analysis",
"url": null
},
{
"label": "bayesian statistics",
"term": "bayesian statistics",
"url": null
},
{
"label": "general social survey",
"term": "general social survey",
"url": null
}
]
},
{
"id": "https://www.allendowney.com/blog/?p=1766",
"title": "Trust and Well-Being",
"description": "<p>In a previous article, I claimed that Young adults are not very happy. Now the World Happiness Report 2026 has confirmed that young people in North America and Western Europe are less happy than they were fifteen years ago, and less happy than previous generations. In this article, we’ll look at results from three related questions in the General Social Survey (GSS): As we’ll see, young adults in the United States have a more negative outlook than previous generations: they...</p>\n<p class=\"read-more\"><a class=\"btn btn-default\" href=\"https://www.allendowney.com/blog/2026/04/03/trust-and-well-being/\"> Read More<span class=\"screen-reader-text\"> Read More</span></a></p>\n<p>The post <a href=\"https://www.allendowney.com/blog/2026/04/03/trust-and-well-being/\">Trust and Well-Being</a> appeared first on <a href=\"https://www.allendowney.com/blog\">Probably Overthinking It</a>.</p>",
"url": "https://www.allendowney.com/blog/2026/04/03/trust-and-well-being/",
"published": "2026-04-03T14:48:45.000Z",
"updated": "2026-04-03T14:48:45.000Z",
"content": "<p class=\"wp-block-paragraph\">In a previous article, I claimed that <a href=\"https://www.allendowney.com/blog/2026/03/19/young-adults-are-not-very-happy/\" target=\"_blank\" rel=\"noreferrer noopener\">Young adults are not very happy</a>. Now the <a href=\"https://worldhappiness.report/ed/2026/\" target=\"_blank\" rel=\"noreferrer noopener\">World Happiness Report 2026</a> has confirmed that young people in North America and Western Europe are less happy than they were fifteen years ago, and less happy than previous generations.</p>\n\n\n\n<p class=\"wp-block-paragraph\">In this article, we’ll look at results from three related questions in the General Social Survey (GSS):</p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Trust:</strong> “Generally speaking, would you say that most people can be trusted or that you can’t be too careful in dealing with people?”</li>\n\n\n\n<li><strong>Fair:</strong> “Do you think most people would try to take advantage of you if they got a chance, or would they try to be fair?”</li>\n\n\n\n<li><strong>Helpful:</strong> “Would you say that most of the time people try to be helpful, or that they are mostly just looking out for themselves?”</li>\n</ul>\n\n\n\n<p class=\"wp-block-paragraph\">As we’ll see, young adults in the United States have a more negative outlook than previous generations: they are less likely to say that people can be trusted, that they are fair, or that they are helpful. And we’ll consider connections between this bleak outlook and unhappiness.</p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"trust\">Trust</h2>\n\n\n\n<p class=\"wp-block-paragraph\">Using the same model from the previous articles, I estimated the percentage who say people can be trusted, following each birth year over time.</p>\n\n\n\n<figure class=\"wp-block-image\" id=\"cohort-trajectories-trust\"><img loading=\"lazy\" decoding=\"async\" width=\"1330\" height=\"778\" src=\"https://www.allendowney.com/blog/wp-content/uploads/2026/04/cohort_trajectory_tr-5809c4884f70b4b9b75cfe97047f2fe8.png\" alt=\"Cohort trajectories, percent saying most people can be trusted\" class=\"wp-image-1769\" srcset=\"https://www.allendowney.com/blog/wp-content/uploads/2026/04/cohort_trajectory_tr-5809c4884f70b4b9b75cfe97047f2fe8.png 1330w, https://www.allendowney.com/blog/wp-content/uploads/2026/04/cohort_trajectory_tr-5809c4884f70b4b9b75cfe97047f2fe8-300x175.png 300w, https://www.allendowney.com/blog/wp-content/uploads/2026/04/cohort_trajectory_tr-5809c4884f70b4b9b75cfe97047f2fe8-1024x599.png 1024w, https://www.allendowney.com/blog/wp-content/uploads/2026/04/cohort_trajectory_tr-5809c4884f70b4b9b75cfe97047f2fe8-768x449.png 768w, https://www.allendowney.com/blog/wp-content/uploads/2026/04/cohort_trajectory_tr-5809c4884f70b4b9b75cfe97047f2fe8-462x270.png 462w\" sizes=\"auto, (max-width: 1330px) 100vw, 1330px\" /></figure>\n\n\n\n<p class=\"wp-block-paragraph\"><em>Cohort trajectories, percent saying most people can be trusted</em></p>\n\n\n\n<p class=\"wp-block-paragraph\">With these trajectories, we can decompose the cohort and period effects. The following figure shows the cohort effect, standardized by holding the period effect constant.</p>\n\n\n\n<figure class=\"wp-block-image\" id=\"cohort-profile-trust\"><img loading=\"lazy\" decoding=\"async\" width=\"1133\" height=\"790\" src=\"https://www.allendowney.com/blog/wp-content/uploads/2026/04/cohort_standardized_-83920254db4863278c92f3cee792510c.png\" alt=\"Standardized cohort effect with fixed time mix, percent saying most people can be trusted\" class=\"wp-image-1772\" srcset=\"https://www.allendowney.com/blog/wp-content/uploads/2026/04/cohort_standardized_-83920254db4863278c92f3cee792510c.png 1133w, https://www.allendowney.com/blog/wp-content/uploads/2026/04/cohort_standardized_-83920254db4863278c92f3cee792510c-300x209.png 300w, https://www.allendowney.com/blog/wp-content/uploads/2026/04/cohort_standardized_-83920254db4863278c92f3cee792510c-1024x714.png 1024w, https://www.allendowney.com/blog/wp-content/uploads/2026/04/cohort_standardized_-83920254db4863278c92f3cee792510c-768x535.png 768w, https://www.allendowney.com/blog/wp-content/uploads/2026/04/cohort_standardized_-83920254db4863278c92f3cee792510c-387x270.png 387w\" sizes=\"auto, (max-width: 1133px) 100vw, 1133px\" /></figure>\n\n\n\n<p class=\"wp-block-paragraph\">Standardized cohort effect with fixed time mix, percent saying most people can be trusted</p>\n\n\n\n<p class=\"wp-block-paragraph\">The level of trust increased between the cohorts born in the 1900s through the 1940s, and then started a steep decline. This is a large cohort effect, dropping about 30 percentage points over 60 years.</p>\n\n\n\n<p class=\"wp-block-paragraph\">The following figure shows the period effect, standardized by holding the cohort mix constant.</p>\n\n\n\n<figure class=\"wp-block-image\" id=\"time-trend-trust\"><img loading=\"lazy\" decoding=\"async\" width=\"1133\" height=\"790\" src=\"https://www.allendowney.com/blog/wp-content/uploads/2026/04/time_standardized_tr-2f029b683d9ad86a39a536e4f95c8c0f.png\" alt=\"Standardized time trend with fixed cohort mix, percent saying most people can be trusted\" class=\"wp-image-1773\" srcset=\"https://www.allendowney.com/blog/wp-content/uploads/2026/04/time_standardized_tr-2f029b683d9ad86a39a536e4f95c8c0f.png 1133w, https://www.allendowney.com/blog/wp-content/uploads/2026/04/time_standardized_tr-2f029b683d9ad86a39a536e4f95c8c0f-300x209.png 300w, https://www.allendowney.com/blog/wp-content/uploads/2026/04/time_standardized_tr-2f029b683d9ad86a39a536e4f95c8c0f-1024x714.png 1024w, https://www.allendowney.com/blog/wp-content/uploads/2026/04/time_standardized_tr-2f029b683d9ad86a39a536e4f95c8c0f-768x535.png 768w, https://www.allendowney.com/blog/wp-content/uploads/2026/04/time_standardized_tr-2f029b683d9ad86a39a536e4f95c8c0f-387x270.png 387w\" sizes=\"auto, (max-width: 1133px) 100vw, 1133px\" /></figure>\n\n\n\n<p class=\"wp-block-paragraph\"><em>Standardized time trend with fixed cohort mix, percent saying most people can be trusted</em></p>\n\n\n\n<p class=\"wp-block-paragraph\">In contrast, there is almost no period effect.</p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"the-conjecture-part\">The conjecture part</h2>\n\n\n\n<p class=\"wp-block-paragraph\">About my previous article, one of my former colleagues said he appreciated my attempt to offer explanations, but reminded me that with this kind of data alone, it is hard to say what causes what with any confidence. That’s true, and it’s a good reminder — but we can get some clues:</p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>When we see a strong cohort effect and almost no period effect, that’s evidence that we’re seeing patterns set in childhood.</li>\n\n\n\n<li>When we see period effects, we should look for events that affected all cohorts at the same time.</li>\n</ul>\n\n\n\n<p class=\"wp-block-paragraph\">So let’s think about what was happening in the formative years of these cohorts, starting with the 1940 cohort, which was the high point in trust, before the decline:</p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Cohort 1940 (childhood: 1940–1960): dense local communities, strong civic and religious institutions, frequent face-to-face interaction, and shared media environment.</li>\n\n\n\n<li>Cohort 1950 (1950–1970): suburbanization expands, some weakening of community density, television becomes widespread but still shared.</li>\n\n\n\n<li>Cohort 1960 (1960–1980): civil rights conflict, Vietnam War, Watergate scandal, rising crime.</li>\n\n\n\n<li>Cohort 1970 (1970–1990): reduced civic participation, rising inequality, more cautious parenting, less unstructured social interaction.</li>\n\n\n\n<li>Cohort 1980 (1980–2000): increasing inequality, more segregation by class and education, early internet exposure, continued decline in shared institutions.</li>\n</ul>\n\n\n\n<p class=\"wp-block-paragraph\">At this point a multi-generational effect comes into play — the parents of Cohort 1980, born in the 1950s and 1960s, were less trusting than previous generations of parents.</p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Cohort 1990 (1990–2010): widespread internet use, early social media, more structured childhood, increasing awareness of global risks.</li>\n\n\n\n<li>Cohort 2000 (2000–2020): smartphones and social media throughout formative years, algorithmic content, reduced in-person interaction.</li>\n</ul>\n\n\n\n<p class=\"wp-block-paragraph\">If trust is largely set early in life, then differences between cohorts reflect the environments they experienced during their first two decades.</p>\n\n\n\n<p class=\"wp-block-paragraph\">In addition to this question about trust, the GSS includes related questions about fairness and mutual assistance.</p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"fair\">Fair</h2>\n\n\n\n<p class=\"wp-block-paragraph\">Do you think most people would try to take advantage of you if they got a chance, or would they try to be fair? The following figure shows the percentage who thought people would be fair.</p>\n\n\n\n<figure class=\"wp-block-image\" id=\"cohort-trajectories-fair\"><img loading=\"lazy\" decoding=\"async\" width=\"1330\" height=\"783\" src=\"https://www.allendowney.com/blog/wp-content/uploads/2026/04/cohort_trajectory_fa-941da70cb9e1fdb60ecd622a8e79f682.png\" alt=\"Cohort trajectories, percent saying people would try to be fair\" class=\"wp-image-1771\" srcset=\"https://www.allendowney.com/blog/wp-content/uploads/2026/04/cohort_trajectory_fa-941da70cb9e1fdb60ecd622a8e79f682.png 1330w, https://www.allendowney.com/blog/wp-content/uploads/2026/04/cohort_trajectory_fa-941da70cb9e1fdb60ecd622a8e79f682-300x177.png 300w, https://www.allendowney.com/blog/wp-content/uploads/2026/04/cohort_trajectory_fa-941da70cb9e1fdb60ecd622a8e79f682-1024x603.png 1024w, https://www.allendowney.com/blog/wp-content/uploads/2026/04/cohort_trajectory_fa-941da70cb9e1fdb60ecd622a8e79f682-768x452.png 768w, https://www.allendowney.com/blog/wp-content/uploads/2026/04/cohort_trajectory_fa-941da70cb9e1fdb60ecd622a8e79f682-459x270.png 459w\" sizes=\"auto, (max-width: 1330px) 100vw, 1330px\" /></figure>\n\n\n\n<p class=\"wp-block-paragraph\"><em>Cohort trajectories, percent saying people would try to be fair</em></p>\n\n\n\n<p class=\"wp-block-paragraph\">And here’s the cohort effect.</p>\n\n\n\n<figure class=\"wp-block-image\" id=\"cohort-profile-fair\"><img loading=\"lazy\" decoding=\"async\" width=\"1266\" height=\"764\" src=\"https://www.allendowney.com/blog/wp-content/uploads/2026/04/cohort_standardized_-e471d5b01144d15bbf17ba11755d7731.png\" alt=\"Standardized cohort effect with fixed time mix, percent saying people would try to be fair\" class=\"wp-image-1774\" srcset=\"https://www.allendowney.com/blog/wp-content/uploads/2026/04/cohort_standardized_-e471d5b01144d15bbf17ba11755d7731.png 1266w, https://www.allendowney.com/blog/wp-content/uploads/2026/04/cohort_standardized_-e471d5b01144d15bbf17ba11755d7731-300x181.png 300w, https://www.allendowney.com/blog/wp-content/uploads/2026/04/cohort_standardized_-e471d5b01144d15bbf17ba11755d7731-1024x618.png 1024w, https://www.allendowney.com/blog/wp-content/uploads/2026/04/cohort_standardized_-e471d5b01144d15bbf17ba11755d7731-768x463.png 768w, https://www.allendowney.com/blog/wp-content/uploads/2026/04/cohort_standardized_-e471d5b01144d15bbf17ba11755d7731-447x270.png 447w\" sizes=\"auto, (max-width: 1266px) 100vw, 1266px\" /></figure>\n\n\n\n<p class=\"wp-block-paragraph\"><em>Standardized cohort effect with fixed time mix, percent saying people would try to be fair</em></p>\n\n\n\n<p class=\"wp-block-paragraph\">And the period effect.</p>\n\n\n\n<figure class=\"wp-block-image\" id=\"time-trend-fair\"><img loading=\"lazy\" decoding=\"async\" width=\"1266\" height=\"764\" src=\"https://www.allendowney.com/blog/wp-content/uploads/2026/04/time_standardized_fa-c4e6dd0e53f81bd5148e3461a47a3664.png\" alt=\"Standardized time trend with fixed cohort mix, percent saying people would try to be fair\" class=\"wp-image-1775\" srcset=\"https://www.allendowney.com/blog/wp-content/uploads/2026/04/time_standardized_fa-c4e6dd0e53f81bd5148e3461a47a3664.png 1266w, https://www.allendowney.com/blog/wp-content/uploads/2026/04/time_standardized_fa-c4e6dd0e53f81bd5148e3461a47a3664-300x181.png 300w, https://www.allendowney.com/blog/wp-content/uploads/2026/04/time_standardized_fa-c4e6dd0e53f81bd5148e3461a47a3664-1024x618.png 1024w, https://www.allendowney.com/blog/wp-content/uploads/2026/04/time_standardized_fa-c4e6dd0e53f81bd5148e3461a47a3664-768x463.png 768w, https://www.allendowney.com/blog/wp-content/uploads/2026/04/time_standardized_fa-c4e6dd0e53f81bd5148e3461a47a3664-447x270.png 447w\" sizes=\"auto, (max-width: 1266px) 100vw, 1266px\" /></figure>\n\n\n\n<p class=\"wp-block-paragraph\"><em>Standardized time trend with fixed cohort mix, percent saying people would try to be fair</em></p>\n\n\n\n<p class=\"wp-block-paragraph\">The cohort pattern is similar to what we saw in trust: small changes between the 1900s and 1940s cohorts, and then a steep decline — almost 40 percentage points over 60 years.</p>\n\n\n\n<p class=\"wp-block-paragraph\">The period effect is relatively small, varying by only 10 percentage points from lowest to highest point, but it was generally positive until about 2015 (the onset of the Trump Era?).</p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"helpful\">Helpful</h2>\n\n\n\n<p class=\"wp-block-paragraph\">Would you say that most of the time people try to be helpful, or that they are mostly just looking out for themselves?</p>\n\n\n\n<p class=\"wp-block-paragraph\">Here is a period–cohort fingerprint of the responses, showing the percentage who thought people try to be helpful.</p>\n\n\n\n<figure class=\"wp-block-image\" id=\"cohort-trajectories-helpful\"><img loading=\"lazy\" decoding=\"async\" width=\"1330\" height=\"783\" src=\"https://www.allendowney.com/blog/wp-content/uploads/2026/04/cohort_trajectory_he-73b3c2f2b5af024ffd374acb439b3ec8.png\" alt=\"Cohort trajectories, percent saying people try to be helpful\" class=\"wp-image-1770\" srcset=\"https://www.allendowney.com/blog/wp-content/uploads/2026/04/cohort_trajectory_he-73b3c2f2b5af024ffd374acb439b3ec8.png 1330w, https://www.allendowney.com/blog/wp-content/uploads/2026/04/cohort_trajectory_he-73b3c2f2b5af024ffd374acb439b3ec8-300x177.png 300w, https://www.allendowney.com/blog/wp-content/uploads/2026/04/cohort_trajectory_he-73b3c2f2b5af024ffd374acb439b3ec8-1024x603.png 1024w, https://www.allendowney.com/blog/wp-content/uploads/2026/04/cohort_trajectory_he-73b3c2f2b5af024ffd374acb439b3ec8-768x452.png 768w, https://www.allendowney.com/blog/wp-content/uploads/2026/04/cohort_trajectory_he-73b3c2f2b5af024ffd374acb439b3ec8-459x270.png 459w\" sizes=\"auto, (max-width: 1330px) 100vw, 1330px\" /></figure>\n\n\n\n<p class=\"wp-block-paragraph\"><em>Cohort trajectories, percent saying people try to be helpful</em></p>\n\n\n\n<p class=\"wp-block-paragraph\">Here’s the cohort effect:</p>\n\n\n\n<figure class=\"wp-block-image\" id=\"cohort-profile-helpful\"><img loading=\"lazy\" decoding=\"async\" width=\"1337\" height=\"764\" src=\"https://www.allendowney.com/blog/wp-content/uploads/2026/04/cohort_standardized_-24a4cd718ef72385d57fbc3eb0dbc47d.png\" alt=\"Standardized cohort effect with fixed time mix, percent saying people try to be helpful\" class=\"wp-image-1777\" srcset=\"https://www.allendowney.com/blog/wp-content/uploads/2026/04/cohort_standardized_-24a4cd718ef72385d57fbc3eb0dbc47d.png 1337w, https://www.allendowney.com/blog/wp-content/uploads/2026/04/cohort_standardized_-24a4cd718ef72385d57fbc3eb0dbc47d-300x171.png 300w, https://www.allendowney.com/blog/wp-content/uploads/2026/04/cohort_standardized_-24a4cd718ef72385d57fbc3eb0dbc47d-1024x585.png 1024w, https://www.allendowney.com/blog/wp-content/uploads/2026/04/cohort_standardized_-24a4cd718ef72385d57fbc3eb0dbc47d-768x439.png 768w, https://www.allendowney.com/blog/wp-content/uploads/2026/04/cohort_standardized_-24a4cd718ef72385d57fbc3eb0dbc47d-473x270.png 473w\" sizes=\"auto, (max-width: 1337px) 100vw, 1337px\" /></figure>\n\n\n\n<p class=\"wp-block-paragraph\"><em>Standardized cohort effect with fixed time mix, percent saying people try to be helpful</em></p>\n\n\n\n<p class=\"wp-block-paragraph\">And the period effect.</p>\n\n\n\n<figure class=\"wp-block-image\" id=\"time-trend-helpful\"><img loading=\"lazy\" decoding=\"async\" width=\"1337\" height=\"764\" src=\"https://www.allendowney.com/blog/wp-content/uploads/2026/04/time_standardized_he-28e70c9d0a1b012cf525b854897416f2.png\" alt=\"Standardized time trend with fixed cohort mix, percent saying people try to be helpful\" class=\"wp-image-1776\" srcset=\"https://www.allendowney.com/blog/wp-content/uploads/2026/04/time_standardized_he-28e70c9d0a1b012cf525b854897416f2.png 1337w, https://www.allendowney.com/blog/wp-content/uploads/2026/04/time_standardized_he-28e70c9d0a1b012cf525b854897416f2-300x171.png 300w, https://www.allendowney.com/blog/wp-content/uploads/2026/04/time_standardized_he-28e70c9d0a1b012cf525b854897416f2-1024x585.png 1024w, https://www.allendowney.com/blog/wp-content/uploads/2026/04/time_standardized_he-28e70c9d0a1b012cf525b854897416f2-768x439.png 768w, https://www.allendowney.com/blog/wp-content/uploads/2026/04/time_standardized_he-28e70c9d0a1b012cf525b854897416f2-473x270.png 473w\" sizes=\"auto, (max-width: 1337px) 100vw, 1337px\" /></figure>\n\n\n\n<p class=\"wp-block-paragraph\"><em>Standardized time trend with fixed cohort mix, percent saying people try to be helpful</em></p>\n\n\n\n<p class=\"wp-block-paragraph\">Again we see the same pattern: little change between the cohorts born between 1900 and 1940, and then a decline of more than 30 percentage points over 60 years.</p>\n\n\n\n<p class=\"wp-block-paragraph\">And again, the period effect is comparatively small and generally increasing — but possibly declining in the most recent cycles of the survey.</p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"cause-and-effect\">Cause and Effect?</h2>\n\n\n\n<p class=\"wp-block-paragraph\">It is plausible that the decline in trust is a contributing factor to the decline in happiness. If you believe that people are out to get you, and 80% of your friends agree, that’s not a worldview conducive to a sense of well-being. And generational decline in trust precedes the decline in happiness, so it is at least a potential cause.</p>\n\n\n\n<p class=\"wp-block-paragraph\">The decline in trust-related beliefs also supports the interpretation that recent cohorts are <em>actually</em> unhappy, rather than interpreting the question differently, or being more willing than previous generations to say they are unhappy.</p>\n\n\n\n<p class=\"wp-block-paragraph\">I haven’t done full-on causal modeling to quantify these relationships, but I ran a few regression models to explore. To reduce the number of researcher degrees of freedom, I asked ChatGPT to interpret the results:</p>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\">\n<p class=\"wp-block-paragraph\">Differences in happiness across cohorts appear to be partly explained by differences in social outlook (trust, fairness, helpfulness), and these outlook variables behave like stable, cohort-structured traits rather than period-driven fluctuations.</p>\n</blockquote>\n\n\n\n<p class=\"wp-block-paragraph\">The AI-generated summary of the experiments follows.</p>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"model-1-cross-sectional-association-complete-cases\">Model 1: Cross-sectional association (complete cases)</h3>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Specification:</strong></p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Outcome: <code>very_happy</code> (binary)</li>\n\n\n\n<li>Predictors: <code>trust</code>, <code>fair</code>, <code>helpful</code> (all binary)</li>\n\n\n\n<li>Sample: complete cases with all variables observed</li>\n</ul>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Purpose:</strong></p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Estimate the <strong>cross-sectional relationship</strong> between social outlook and happiness.</li>\n\n\n\n<li>Provides baseline associations without accounting for cohort or period effects.</li>\n</ul>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Interpretation:</strong></p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Coefficients represent <strong>conditional associations</strong> among individuals at a point in time.</li>\n\n\n\n<li>Answers: <em>Are people with a more positive outlook more likely to be very happy?</em></li>\n</ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"/>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"model-2-outlook-cohort-period-restricted-sample\">Model 2: Outlook + cohort + period (restricted sample)</h3>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Specification:</strong></p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Outcome: <code>very_happy</code></li>\n\n\n\n<li>Predictors:\n<ul class=\"wp-block-list\">\n<li><code>trust</code>, <code>fair</code>, <code>helpful</code></li>\n\n\n\n<li><code>cohort_c</code> (mean-centered birth year)</li>\n\n\n\n<li><code>year_c</code> (mean-centered survey year)</li>\n</ul>\n</li>\n\n\n\n<li>Sample: respondents born ≥ 1940 with complete data</li>\n</ul>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Purpose:</strong></p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Assess whether the outlook–happiness relationship persists after accounting for:\n<ul class=\"wp-block-list\">\n<li><strong>Cohort effects</strong> (differences across birth cohorts)</li>\n\n\n\n<li><strong>Period effects</strong> (changes over survey years)</li>\n</ul>\n</li>\n</ul>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Interpretation:</strong></p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Coefficients for outlook variables reflect <strong>within-cohort, within-period associations</strong>.</li>\n\n\n\n<li>Cohort and year coefficients capture <strong>linear trends</strong> in happiness after controlling for outlook.</li>\n\n\n\n<li>Answers:\n<ul class=\"wp-block-list\">\n<li><em>Are outlook variables still associated with happiness after adjusting for historical context?</em></li>\n\n\n\n<li><em>Is there an independent cohort or period trend?</em></li>\n</ul>\n</li>\n</ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"/>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"model-3-cohort-period-only-no-outlook-variables\">Model 3: Cohort + period only (no outlook variables)</h3>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Specification:</strong></p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Outcome: <code>very_happy</code></li>\n\n\n\n<li>Predictors:\n<ul class=\"wp-block-list\">\n<li><code>cohort_c</code></li>\n\n\n\n<li><code>year_c</code></li>\n</ul>\n</li>\n\n\n\n<li>Sample: respondents born > 1940 (larger sample since outlook variables not required)</li>\n</ul>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Purpose:</strong></p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Estimate <strong>total cohort and period effects</strong> on happiness without controlling for outlook.</li>\n\n\n\n<li>Provides a baseline for comparison with Model 2.</li>\n</ul>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Interpretation:</strong></p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Cohort and year coefficients reflect <strong>combined (direct + indirect) effects</strong>.</li>\n\n\n\n<li>Comparing to Model 2 shows how much of these effects are <strong>accounted for by outlook variables</strong>.</li>\n\n\n\n<li>Answers:\n<ul class=\"wp-block-list\">\n<li><em>How does happiness vary across cohorts and over time in aggregate?</em></li>\n\n\n\n<li><em>How much do these patterns change when outlook is included?</em></li>\n</ul>\n</li>\n</ul>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"key-findings\">Key Findings</h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Positive social outlook is associated with higher happiness.</strong>\n<ul class=\"wp-block-list\">\n<li>Trust, fairness, and helpfulness all have positive and statistically significant associations with being “very happy.”</li>\n\n\n\n<li>Estimated odds ratios:\n<ul class=\"wp-block-list\">\n<li>Trust: ~1.25</li>\n\n\n\n<li>Fairness: ~1.36 (strongest)</li>\n\n\n\n<li>Helpfulness: ~1.29</li>\n</ul>\n</li>\n\n\n\n<li>These effects are modest in size and explain a small fraction of overall variation (Pseudo R² ≈ 0.016).</li>\n</ul>\n</li>\n\n\n\n<li><strong>These relationships are stable across cohorts and time.</strong>\n<ul class=\"wp-block-list\">\n<li>Adding cohort and survey year controls has little effect on the coefficients.</li>\n\n\n\n<li>This suggests the outlook–happiness relationship is primarily cross-sectional, not driven by historical shifts.</li>\n</ul>\n</li>\n</ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"/>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"cohort-and-period-effects\">Cohort and Period Effects</h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Without controlling for outlook:</strong>\n<ul class=\"wp-block-list\">\n<li>Later cohorts are less likely to report being very happy.</li>\n\n\n\n<li>There is also a negative period trend (declining happiness over time).</li>\n</ul>\n</li>\n\n\n\n<li><strong>With outlook variables included:</strong>\n<ul class=\"wp-block-list\">\n<li>The cohort effect becomes small and statistically insignificant.</li>\n\n\n\n<li>The period effect remains negative and significant.</li>\n</ul>\n</li>\n</ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"/>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"interpretation\">Interpretation</h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Outlook variables appear to mediate cohort differences in happiness.</strong>\n<ul class=\"wp-block-list\">\n<li>Later cohorts tend to report lower trust, fairness, and helpfulness.</li>\n\n\n\n<li>These differences account for much of the observed cohort decline in happiness.</li>\n</ul>\n</li>\n\n\n\n<li><strong>Period effects persist independently.</strong>\n<ul class=\"wp-block-list\">\n<li>There is a modest downward trend in happiness over time that is not explained by outlook variables.</li>\n</ul>\n</li>\n</ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"/>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"data-considerations\">Data Considerations</h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Approximately <strong>40% of observations are missing at least one outlook variable</strong>, reducing the complete-case sample.</li>\n\n\n\n<li>This raises the possibility of <strong>selection bias</strong> in the estimates.</li>\n</ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"/>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"bottom-line\">Bottom Line</h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>A more positive view of others (trust, fairness, helpfulness) is consistently associated with higher happiness.</li>\n\n\n\n<li>Differences in these outlook measures help explain why later cohorts report lower happiness.</li>\n\n\n\n<li>However, there is also an independent downward trend in happiness over time.</li>\n</ul>\n\n\n\n<p class=\"wp-block-paragraph\"><a href=\"https://allendowney.github.io/CultureWar//blog1-happy\"></a><a href=\"https://allendowney.github.io/CultureWar//blog1-happy\"></a></p>\n<p>The post <a href=\"https://www.allendowney.com/blog/2026/04/03/trust-and-well-being/\">Trust and Well-Being</a> appeared first on <a href=\"https://www.allendowney.com/blog\">Probably Overthinking It</a>.</p>",
"image": null,
"media": [],
"authors": [
{
"name": "AllenDowney",
"email": null,
"url": null
}
],
"categories": [
{
"label": "Uncategorized",
"term": "Uncategorized",
"url": null
},
{
"label": "age period cohort analysis",
"term": "age period cohort analysis",
"url": null
},
{
"label": "general social survey",
"term": "general social survey",
"url": null
},
{
"label": "happiness",
"term": "happiness",
"url": null
},
{
"label": "logistic regression",
"term": "logistic regression",
"url": null
}
]
},
{
"id": "https://www.allendowney.com/blog/?p=1756",
"title": "Have the Nones hit a ceiling?",
"description": "<p>Someone asked me recently why I stopped writing about religion, and I said there were two reasons: One is that the primary dataset I was following stopped updating; the other is that Ryan Burge is doing such a good job, I felt redundant. His most recent article presents evidence that the Nones have hit a ceiling — that is, that the percentage of people in the U.S. with no religious affiliation, which has consistently increased for several decades, has either...</p>\n<p class=\"read-more\"><a class=\"btn btn-default\" href=\"https://www.allendowney.com/blog/2026/03/30/have-the-nones-hit-a-ceiling/\"> Read More<span class=\"screen-reader-text\"> Read More</span></a></p>\n<p>The post <a href=\"https://www.allendowney.com/blog/2026/03/30/have-the-nones-hit-a-ceiling/\">Have the Nones hit a ceiling?</a> appeared first on <a href=\"https://www.allendowney.com/blog\">Probably Overthinking It</a>.</p>",
"url": "https://www.allendowney.com/blog/2026/03/30/have-the-nones-hit-a-ceiling/",
"published": "2026-03-30T15:51:55.000Z",
"updated": "2026-03-30T15:51:55.000Z",
"content": "<p class=\"wp-block-paragraph\">Someone asked me recently why I stopped writing about religion, and I said there were two reasons: One is that the <a href=\"https://heri.ucla.edu/publications-tfs/\" target=\"_blank\" rel=\"noreferrer noopener\">primary dataset I was following</a> stopped updating; the other is that <a href=\"https://en.wikipedia.org/wiki/Ryan_Burge_(political_scientist)\" target=\"_blank\" rel=\"noreferrer noopener\">Ryan Burge</a> is doing such a good job, I felt redundant.</p>\n\n\n\n<p class=\"wp-block-paragraph\">His <a href=\"https://substack.com/home/post/p-192339927\" target=\"_blank\" rel=\"noreferrer noopener\">most recent article</a> presents evidence that the Nones have hit a ceiling — that is, that the percentage of people in the U.S. with no religious affiliation, which has consistently increased for several decades, has either leveled off or started to reverse.</p>\n\n\n\n<p class=\"wp-block-paragraph\">He reports on new data from the Cooperative Election Study and the 2024 General Social Survey, including this figure based on the GSS.</p>\n\n\n\n<figure class=\"wp-block-image\" id=\"relig-burge-gss\"><img loading=\"lazy\" decoding=\"async\" width=\"2048\" height=\"1365\" src=\"https://www.allendowney.com/blog/wp-content/uploads/2026/03/gss_relig_raw_data_s-2320d07fdfaaf7f3e756fbec933e265b.png\" alt=\"The percentage of “Nones” from Ryan Burge’s Graphs About Religion.\" class=\"wp-image-1761\" srcset=\"https://www.allendowney.com/blog/wp-content/uploads/2026/03/gss_relig_raw_data_s-2320d07fdfaaf7f3e756fbec933e265b.png 2048w, https://www.allendowney.com/blog/wp-content/uploads/2026/03/gss_relig_raw_data_s-2320d07fdfaaf7f3e756fbec933e265b-300x200.png 300w, https://www.allendowney.com/blog/wp-content/uploads/2026/03/gss_relig_raw_data_s-2320d07fdfaaf7f3e756fbec933e265b-1024x683.png 1024w, https://www.allendowney.com/blog/wp-content/uploads/2026/03/gss_relig_raw_data_s-2320d07fdfaaf7f3e756fbec933e265b-768x512.png 768w, https://www.allendowney.com/blog/wp-content/uploads/2026/03/gss_relig_raw_data_s-2320d07fdfaaf7f3e756fbec933e265b-1536x1024.png 1536w, https://www.allendowney.com/blog/wp-content/uploads/2026/03/gss_relig_raw_data_s-2320d07fdfaaf7f3e756fbec933e265b-405x270.png 405w\" sizes=\"auto, (max-width: 2048px) 100vw, 2048px\" /></figure>\n\n\n\n<p class=\"wp-block-paragraph\">The percentage of “Nones” from Ryan Burge’s <a target=\"_blank\" rel=\"noreferrer noopener\" href=\"https://www.graphsaboutreligion.com/\">Graphs About Religion</a></p>\n\n\n\n<p class=\"wp-block-paragraph\">The observed percentage of Nones peaked in the 2021 survey and has dropped in the last two cycles. The CES data show a similar pattern, with a much larger sample size. So I’m not going to disagree with Ryan: it sure looks like the rise of the Nones has stalled or even reversed.</p>\n\n\n\n<p class=\"wp-block-paragraph\">However, since I am developing a model that decomposes trends like this into cohort and period effects, we can use it to check whether the turnaround is a cohort or a period effect. It turns out to be both.</p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"the-model\">The Model</h2>\n\n\n\n<p class=\"wp-block-paragraph\">The model assumes that each cohort in each year has an unobserved (latent) propensity to report a religious affiliation or none.</p>\n\n\n\n<p class=\"wp-block-paragraph\">The cohort and period effects are modeled as second-order Gaussian random walks, which means the model assumes these effects evolve smoothly over time, unless the data provide strong evidence otherwise. The amount of smoothing is estimated from the data.</p>\n\n\n\n<p class=\"wp-block-paragraph\">An additional random year effect captures variation from one survey to the next that is not explained by long-term trends, like current events and topics of discussion.</p>\n\n\n\n<p class=\"wp-block-paragraph\">The “time only” version of the model estimates a latent propensity for each cycle of the survey, so the result is a smooth curve through the raw proportions.</p>\n\n\n\n<p class=\"wp-block-paragraph\">The “time-cohort” version estimates a latent propensity for each cohort during each cycle, so the result is a trajectory over time for each birth year.</p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"results\">Results</h2>\n\n\n\n<p class=\"wp-block-paragraph\">Here are the results for the time-only model, showing the posterior mean and a 94% credible interval.</p>\n\n\n\n<figure class=\"wp-block-image\" id=\"time-model-relig\"><img loading=\"lazy\" decoding=\"async\" width=\"1133\" height=\"764\" src=\"https://www.allendowney.com/blog/wp-content/uploads/2026/03/time_model_relig_rw2-ab3b53dbf72feed6f35a356232032396.png\" alt=\"Time-only model, percent with no religious preference\" class=\"wp-image-1759\" srcset=\"https://www.allendowney.com/blog/wp-content/uploads/2026/03/time_model_relig_rw2-ab3b53dbf72feed6f35a356232032396.png 1133w, https://www.allendowney.com/blog/wp-content/uploads/2026/03/time_model_relig_rw2-ab3b53dbf72feed6f35a356232032396-300x202.png 300w, https://www.allendowney.com/blog/wp-content/uploads/2026/03/time_model_relig_rw2-ab3b53dbf72feed6f35a356232032396-1024x690.png 1024w, https://www.allendowney.com/blog/wp-content/uploads/2026/03/time_model_relig_rw2-ab3b53dbf72feed6f35a356232032396-768x518.png 768w, https://www.allendowney.com/blog/wp-content/uploads/2026/03/time_model_relig_rw2-ab3b53dbf72feed6f35a356232032396-400x270.png 400w\" sizes=\"auto, (max-width: 1133px) 100vw, 1133px\" /></figure>\n\n\n\n<p class=\"wp-block-paragraph\">The posterior mean indicates that the trend in the latent factor has probably slowed; the credible interval indicates that it might have leveled off or reversed.</p>\n\n\n\n<p class=\"wp-block-paragraph\">And here are the trajectories for each cohort:</p>\n\n\n\n<figure class=\"wp-block-image\" id=\"cohort-trajectories-relig\"><img loading=\"lazy\" decoding=\"async\" width=\"1330\" height=\"783\" src=\"https://www.allendowney.com/blog/wp-content/uploads/2026/03/cohort_trajectory_re-2dd48c8df781b26e84647025ea5891b6.png\" alt=\"Cohort trajectories, percent with no religious preference\" class=\"wp-image-1762\" srcset=\"https://www.allendowney.com/blog/wp-content/uploads/2026/03/cohort_trajectory_re-2dd48c8df781b26e84647025ea5891b6.png 1330w, https://www.allendowney.com/blog/wp-content/uploads/2026/03/cohort_trajectory_re-2dd48c8df781b26e84647025ea5891b6-300x177.png 300w, https://www.allendowney.com/blog/wp-content/uploads/2026/03/cohort_trajectory_re-2dd48c8df781b26e84647025ea5891b6-1024x603.png 1024w, https://www.allendowney.com/blog/wp-content/uploads/2026/03/cohort_trajectory_re-2dd48c8df781b26e84647025ea5891b6-768x452.png 768w, https://www.allendowney.com/blog/wp-content/uploads/2026/03/cohort_trajectory_re-2dd48c8df781b26e84647025ea5891b6-459x270.png 459w\" sizes=\"auto, (max-width: 1330px) 100vw, 1330px\" /></figure>\n\n\n\n<p class=\"wp-block-paragraph\">Starting at the bottom, we can see that cohorts born between 1900 and 1930 were not very different — fewer than 10% of them were Nones.</p>\n\n\n\n<p class=\"wp-block-paragraph\">People born in the 1940s were increasingly non-religious, but this first wave of secularization stalled in the cohorts born in the 1950s. The second wave got started with people born in the 1960s, and continued until the 2000s cohorts, where it seems to have stalled again.</p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"decomposition\">Decomposition</h2>\n\n\n\n<p class=\"wp-block-paragraph\">With these trajectories, we can decompose the cohort and period effects. The following figure shows the cohort effect, standardized by holding the period effect constant.</p>\n\n\n\n<figure class=\"wp-block-image\" id=\"cohort-profile-relig\"><img loading=\"lazy\" decoding=\"async\" width=\"1133\" height=\"764\" src=\"https://www.allendowney.com/blog/wp-content/uploads/2026/03/cohort_standardized_-8a992073e7d82ea3a375589a5651bb5d.png\" alt=\"Standardized cohort effect with fixed time mix, percent with no religious preference\" class=\"wp-image-1760\" srcset=\"https://www.allendowney.com/blog/wp-content/uploads/2026/03/cohort_standardized_-8a992073e7d82ea3a375589a5651bb5d.png 1133w, https://www.allendowney.com/blog/wp-content/uploads/2026/03/cohort_standardized_-8a992073e7d82ea3a375589a5651bb5d-300x202.png 300w, https://www.allendowney.com/blog/wp-content/uploads/2026/03/cohort_standardized_-8a992073e7d82ea3a375589a5651bb5d-1024x690.png 1024w, https://www.allendowney.com/blog/wp-content/uploads/2026/03/cohort_standardized_-8a992073e7d82ea3a375589a5651bb5d-768x518.png 768w, https://www.allendowney.com/blog/wp-content/uploads/2026/03/cohort_standardized_-8a992073e7d82ea3a375589a5651bb5d-400x270.png 400w\" sizes=\"auto, (max-width: 1133px) 100vw, 1133px\" /></figure>\n\n\n\n<p class=\"wp-block-paragraph\">As we saw in the previous figure, there was a period of relatively fast change in the 1940s cohorts that stalled among people born in the 1950s and then resumed among people born in the 1960s through the 1980s (primarily Gen X).</p>\n\n\n\n<p class=\"wp-block-paragraph\">Again, it looks like the most recent cohorts have leveled off, but with the width of the credible interval, it’s possible that the trend has continued or reversed.</p>\n\n\n\n<p class=\"wp-block-paragraph\">The following figure shows the period effect, standardized by holding the cohort mix constant.</p>\n\n\n\n<figure class=\"wp-block-image\" id=\"time-trend-relig\"><img loading=\"lazy\" decoding=\"async\" width=\"1133\" height=\"764\" src=\"https://www.allendowney.com/blog/wp-content/uploads/2026/03/time_standardized_re-748498d5f8212df060fbdbfffbe5f356.png\" alt=\"Standardized time trend with fixed cohort mix, percent with no religious preference\" class=\"wp-image-1757\" srcset=\"https://www.allendowney.com/blog/wp-content/uploads/2026/03/time_standardized_re-748498d5f8212df060fbdbfffbe5f356.png 1133w, https://www.allendowney.com/blog/wp-content/uploads/2026/03/time_standardized_re-748498d5f8212df060fbdbfffbe5f356-300x202.png 300w, https://www.allendowney.com/blog/wp-content/uploads/2026/03/time_standardized_re-748498d5f8212df060fbdbfffbe5f356-1024x690.png 1024w, https://www.allendowney.com/blog/wp-content/uploads/2026/03/time_standardized_re-748498d5f8212df060fbdbfffbe5f356-768x518.png 768w, https://www.allendowney.com/blog/wp-content/uploads/2026/03/time_standardized_re-748498d5f8212df060fbdbfffbe5f356-400x270.png 400w\" sizes=\"auto, (max-width: 1133px) 100vw, 1133px\" /></figure>\n\n\n\n<p class=\"wp-block-paragraph\">The period effect was generally increasing from 1990 to 2020, but seems to have leveled off or rolled over.</p>\n\n\n\n<p class=\"wp-block-paragraph\">So, if the rise of the Nones has stalled, at least temporarily, it seems to be a combination of a cohort effect among people born after 2000 and a period effect starting around 2020. This decomposition suggests we should look for at least two kinds of explanations:</p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Differences in the childhood of people born after 2000 that might make them more likely to have a religious affiliation as young adults, and</li>\n\n\n\n<li>Events since 2020 that have affected all cohorts in ways that might make them more religious.</li>\n</ul>\n\n\n\n<p class=\"wp-block-paragraph\">I’ll hold off on speculating.</p>\n\n\n\n<p class=\"wp-block-paragraph\">For purposes of comparison, here is the trend from the time-only model (blue) and the standardized time trend from the time-cohort model (purple).</p>\n\n\n\n<figure class=\"wp-block-image\" id=\"time-trend-relig-comparison\"><img loading=\"lazy\" decoding=\"async\" width=\"1133\" height=\"764\" src=\"https://www.allendowney.com/blog/wp-content/uploads/2026/03/time_standardized_re-251c2eac1b194a6d2418a92654e81829.png\" alt=\"Time-only trend (blue) and standardized time trend from the cohort–period model (purple), percent with no religious preference\" class=\"wp-image-1758\" srcset=\"https://www.allendowney.com/blog/wp-content/uploads/2026/03/time_standardized_re-251c2eac1b194a6d2418a92654e81829.png 1133w, https://www.allendowney.com/blog/wp-content/uploads/2026/03/time_standardized_re-251c2eac1b194a6d2418a92654e81829-300x202.png 300w, https://www.allendowney.com/blog/wp-content/uploads/2026/03/time_standardized_re-251c2eac1b194a6d2418a92654e81829-1024x690.png 1024w, https://www.allendowney.com/blog/wp-content/uploads/2026/03/time_standardized_re-251c2eac1b194a6d2418a92654e81829-768x518.png 768w, https://www.allendowney.com/blog/wp-content/uploads/2026/03/time_standardized_re-251c2eac1b194a6d2418a92654e81829-400x270.png 400w\" sizes=\"auto, (max-width: 1133px) 100vw, 1133px\" /></figure>\n\n\n\n<p class=\"wp-block-paragraph\">The difference between these lines is the part of the change due to the cohort effect. So we can see that most of the change over this interval is due to generational replacement rather than disaffiliation.</p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Methods</strong>: Details about the model are in the <a href=\"https://allendowney.github.io/CultureWar//tech-report\">Technical Report</a>.</p>\n\n\n\n<p class=\"wp-block-paragraph\"></p>\n<p>The post <a href=\"https://www.allendowney.com/blog/2026/03/30/have-the-nones-hit-a-ceiling/\">Have the Nones hit a ceiling?</a> appeared first on <a href=\"https://www.allendowney.com/blog\">Probably Overthinking It</a>.</p>",
"image": null,
"media": [],
"authors": [
{
"name": "AllenDowney",
"email": null,
"url": null
}
],
"categories": [
{
"label": "Uncategorized",
"term": "Uncategorized",
"url": null
},
{
"label": "bayesian statistics",
"term": "bayesian statistics",
"url": null
},
{
"label": "general social survey",
"term": "general social survey",
"url": null
},
{
"label": "religion",
"term": "religion",
"url": null
}
]
},
{
"id": "https://www.allendowney.com/blog/?p=1664",
"title": "Attention, Chinese Readers",
"description": "<p>The Chinese edition of Probably Overthinking It is available now (also here)! If you have the Chinese edition, there are two sections you won’t get to read — so I am including them here. Here is an excerpt from Chapter 3, including the deleted paragraph: In the Present The women surveyed in 1990 rejected the childbearing example of their mothers emphatically. On average, each woman had 2.3 fewer children than her mother. If that pattern had continued for another generation,...</p>\n<p class=\"read-more\"><a class=\"btn btn-default\" href=\"https://www.allendowney.com/blog/2026/03/29/attention-chinese-readers/\"> Read More<span class=\"screen-reader-text\"> Read More</span></a></p>\n<p>The post <a href=\"https://www.allendowney.com/blog/2026/03/29/attention-chinese-readers/\">Attention, Chinese Readers</a> appeared first on <a href=\"https://www.allendowney.com/blog\">Probably Overthinking It</a>.</p>",
"url": "https://www.allendowney.com/blog/2026/03/29/attention-chinese-readers/",
"published": "2026-03-29T00:31:52.000Z",
"updated": "2026-03-29T00:31:52.000Z",
"content": "<p class=\"wp-block-paragraph\">The Chinese edition of <em>Probably Overthinking It</em> is <a href=\"https://www.books.com.tw/products/CN17947121\">available now</a> (also <a href=\"https://product.dangdang.com/12469358967.html\">here</a>)!</p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"246\" height=\"346\" src=\"https://www.allendowney.com/blog/wp-content/uploads/2026/03/image-1.png\" alt=\"\" class=\"wp-image-1750\" srcset=\"https://www.allendowney.com/blog/wp-content/uploads/2026/03/image-1.png 246w, https://www.allendowney.com/blog/wp-content/uploads/2026/03/image-1-213x300.png 213w, https://www.allendowney.com/blog/wp-content/uploads/2026/03/image-1-192x270.png 192w\" sizes=\"auto, (max-width: 246px) 100vw, 246px\" /></figure>\n\n\n\n<p class=\"wp-block-paragraph\">If you have the Chinese edition, there are two sections you won’t get to read — so I am including them here.</p>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\">\n<p class=\"wp-block-paragraph\">Here is an excerpt from <a href=\"https://allendowney.github.io/ProbablyOverthinkingBook/preston.html#in-the-present\">Chapter 3</a>, including the deleted paragraph:</p>\n</blockquote>\n\n\n\n<h2 class=\"wp-block-heading\">In the Present</h2>\n\n\n\n<p class=\"wp-block-paragraph\">The women surveyed in 1990 rejected the childbearing example of their mothers emphatically. On average, each woman had 2.3 fewer children than her mother. If that pattern had continued for another generation, the average family size in 2018 would have been about 0.8. But it wasn’t.</p>\n\n\n\n<p class=\"wp-block-paragraph\">In fact, the average family size in 2018 was very close to 2, just as in 1990. So how did that happen?</p>\n\n\n\n<p class=\"wp-block-paragraph\">As it turns out, this is close to what we would expect if every woman had one child fewer than her mother. The following distribution shows the actual distribution in 2018, compared to the result if we start with the 1990 distribution and simulate the “one child fewer” scenario.</p>\n\n\n\n<figure class=\"wp-block-image\"><img loading=\"lazy\" decoding=\"async\" width=\"438\" height=\"250\" src=\"https://www.allendowney.com/blog/wp-content/uploads/2026/03/ddb1f82d657fad8171d5c400c9a539aead9ac1a4f85b7460f3a4ae7f7cb00237.png\" alt=\"_images/ddb1f82d657fad8171d5c400c9a539aead9ac1a4f85b7460f3a4ae7f7cb00237.png\" class=\"wp-image-1752\" srcset=\"https://www.allendowney.com/blog/wp-content/uploads/2026/03/ddb1f82d657fad8171d5c400c9a539aead9ac1a4f85b7460f3a4ae7f7cb00237.png 438w, https://www.allendowney.com/blog/wp-content/uploads/2026/03/ddb1f82d657fad8171d5c400c9a539aead9ac1a4f85b7460f3a4ae7f7cb00237-300x171.png 300w\" sizes=\"auto, (max-width: 438px) 100vw, 438px\" /></figure>\n\n\n\n<p class=\"wp-block-paragraph\">The means of the two distributions are almost the same, but the shapes are different. In reality, there were more zero- and two-child families in 1990 than the simulation predicts, and fewer one-child families. But at least on average, it seems like women in the U.S. have been following the “one child fewer” policy for the last 30 years.</p>\n\n\n\n<p class=\"wp-block-paragraph\">The scenario at the beginning of this chapter is meant to be light-hearted, but in reality governments in many places and times have enacted policies meant to control family sizes and population growth. <strong>Most famously, China implemented a one-child policy in 1980 that imposed severe penalties on families with more than one child. Of course, this policy is objectionable to anyone who considers reproductive freedom a fundamental human right. But even as a practical matter, the unintended consequences were profound.</strong></p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Rather than catalog them, I will mention one that is particularly ironic: while this policy was in effect, economic and social forces reduced the average <em>desired</em> family size so much that, when the policy was relaxed in 2015 and again in 2021, average lifetime fertility increased to only 1.3, far below the level needed to keep the population constant, near 2.1. Since then, China has implemented new policies intended to <em>increase</em> family sizes, but it is not clear whether they will have much effect. Demographers predict that by the time you read this, the population of China will probably be shrinking </strong>[UPDATE: It is.]<strong>. The consequences of the one-child policy are widespread and will affect China and the rest of the world for a long time.</strong></p>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\">\n<p class=\"wp-block-paragraph\">And here is an excerpt from <a href=\"https://allendowney.github.io/ProbablyOverthinkingBook/nbue.html#child-mortality\">Chapter 5</a>, including the deleted explanation.</p>\n</blockquote>\n\n\n\n<h2 class=\"wp-block-heading\">Child mortality</h2>\n\n\n\n<p class=\"wp-block-paragraph\">Fortunately, child mortality has decreased since 1900. The following figure shows the percentage of children who die before age 5 for four geographical regions, from 1900 to 2019. These data were combined from several sources by Gapminder, a foundation based in Sweden that “promotes sustainable global development […] by increased use and understanding of statistics.”</p>\n\n\n\n<figure class=\"wp-block-image\"><img loading=\"lazy\" decoding=\"async\" width=\"436\" height=\"250\" src=\"https://www.allendowney.com/blog/wp-content/uploads/2026/03/220c5c7e411ef012b610deab7f65ab6dbd0a010aa40d46318a9a14823f2a268e.png\" alt=\"_images/220c5c7e411ef012b610deab7f65ab6dbd0a010aa40d46318a9a14823f2a268e.png\" class=\"wp-image-1754\" srcset=\"https://www.allendowney.com/blog/wp-content/uploads/2026/03/220c5c7e411ef012b610deab7f65ab6dbd0a010aa40d46318a9a14823f2a268e.png 436w, https://www.allendowney.com/blog/wp-content/uploads/2026/03/220c5c7e411ef012b610deab7f65ab6dbd0a010aa40d46318a9a14823f2a268e-300x172.png 300w\" sizes=\"auto, (max-width: 436px) 100vw, 436px\" /></figure>\n\n\n\n<p class=\"wp-block-paragraph\">In every region, child mortality has decreased consistently and substantially. The only exceptions are indicated by the vertical lines: the 1918 influenza pandemic, which visibly affected Asia, the Americas, and Europe; World War II in Europe (1939-1945); <strong>and the Great Leap Forward in China (1958-1962)</strong>. In every case, these exceptions did not affect the long-term trend.</p>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\">\n<p class=\"wp-block-paragraph\">[COMMENT: I thought I was being diplomatic by referring generally to the <a href=\"https://en.wikipedia.org/wiki/Great_Leap_Forward\">Great Leap Forward</a> — rather than the <a href=\"https://en.wikipedia.org/wiki/Great_Chinese_Famine\">Great Chinese Famine</a> or “Three Years of Great Famine” (三年大饥荒) — but apparently that was not enough.]</p>\n</blockquote>\n\n\n\n<p class=\"wp-block-paragraph\">Although there is more work to do, especially in Africa, child mortality is substantially lower now, in every region of the world, than in 1900. As a result most people now are better new than used.</p>\n\n\n\n<p class=\"wp-block-paragraph\">To demonstrate this change, I collected recent mortality data from the Global Health Observatory of the World Health Organization (WHO). For people born in 2019, we don’t know what their future lifetimes will be, but we can estimate it if we assume that the mortality rate in each age group will not change over their lifetimes.</p>\n\n\n\n<p class=\"wp-block-paragraph\">Based on that simplification, the following figure shows average remaining lifetime as a function of age for Sweden and Nigeria in 2019, compared to Sweden in 1905.</p>\n\n\n\n<figure class=\"wp-block-image\"><img loading=\"lazy\" decoding=\"async\" width=\"438\" height=\"250\" src=\"https://www.allendowney.com/blog/wp-content/uploads/2026/03/6a45a65e6a7b3201af0f74c7b7df4d57ce5c5976972ce0e69538a1914fa5cc5b.png\" alt=\"_images/6a45a65e6a7b3201af0f74c7b7df4d57ce5c5976972ce0e69538a1914fa5cc5b.png\" class=\"wp-image-1753\" srcset=\"https://www.allendowney.com/blog/wp-content/uploads/2026/03/6a45a65e6a7b3201af0f74c7b7df4d57ce5c5976972ce0e69538a1914fa5cc5b.png 438w, https://www.allendowney.com/blog/wp-content/uploads/2026/03/6a45a65e6a7b3201af0f74c7b7df4d57ce5c5976972ce0e69538a1914fa5cc5b-300x171.png 300w\" sizes=\"auto, (max-width: 438px) 100vw, 438px\" /></figure>\n\n\n\n<p class=\"wp-block-paragraph\">Since 1905, Sweden has continued to make progress; life expectancy at every age is higher in 2019 than in 1905. And Swedes now have the new-better-than-used property. Their life expectancy at birth is about 82 years, and it declines consistently over their lives, just like a light bulb.</p>\n\n\n\n<p class=\"wp-block-paragraph\">Unfortunately, Nigeria has one of the highest rates of child mortality in the world: in 2019, almost 8% of babies died in their first year of life. After that, they are briefly better used than new: life expectancy at birth is about 62 years; however, a baby who survives the first year will live another 65 years, on average.</p>\n\n\n\n<p class=\"wp-block-paragraph\">Going forward, I hope we continue to reduce child mortality in every region; if we do, soon every person born will be better new than used. Or maybe we can do even better than that.</p>\n\n\n\n<p class=\"wp-block-paragraph\"></p>\n<p>The post <a href=\"https://www.allendowney.com/blog/2026/03/29/attention-chinese-readers/\">Attention, Chinese Readers</a> appeared first on <a href=\"https://www.allendowney.com/blog\">Probably Overthinking It</a>.</p>",
"image": null,
"media": [],
"authors": [
{
"name": "AllenDowney",
"email": null,
"url": null
}
],
"categories": [
{
"label": "Uncategorized",
"term": "Uncategorized",
"url": null
},
{
"label": "book",
"term": "book",
"url": null
},
{
"label": "censorship",
"term": "censorship",
"url": null
},
{
"label": "chinese",
"term": "chinese",
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},
{
"id": "https://www.allendowney.com/blog/?p=1736",
"title": "Young Adults Are Not Very Happy",
"description": "<p>Since 1972, the General Social Survey has asked respondents: “Taken all together, how would you say things are these days—would you say that you are very happy, pretty happy, or not too happy?” The following figure shows how the responses have changed over time and between birth cohorts. Each line represents one birth year. People born in 1900 were 72 years old when the survey started; at that point, about 37% said they were very happy. In 1990, the last...</p>\n<p class=\"read-more\"><a class=\"btn btn-default\" href=\"https://www.allendowney.com/blog/2026/03/19/young-adults-are-not-very-happy/\"> Read More<span class=\"screen-reader-text\"> Read More</span></a></p>\n<p>The post <a href=\"https://www.allendowney.com/blog/2026/03/19/young-adults-are-not-very-happy/\">Young Adults Are Not Very Happy</a> appeared first on <a href=\"https://www.allendowney.com/blog\">Probably Overthinking It</a>.</p>",
"url": "https://www.allendowney.com/blog/2026/03/19/young-adults-are-not-very-happy/",
"published": "2026-03-19T15:44:50.000Z",
"updated": "2026-03-19T15:44:50.000Z",
"content": "<p class=\"wp-block-paragraph\">Since 1972, the General Social Survey has asked respondents: “Taken all together, how would you say things are these days—would you say that you are very happy, pretty happy, or not too happy?”</p>\n\n\n\n<p class=\"wp-block-paragraph\">The following figure shows how the responses have changed over time and between birth cohorts. Each line represents one birth year.</p>\n\n\n\n<figure class=\"wp-block-image\" id=\"cohort-trajectories-happy\"><img loading=\"lazy\" decoding=\"async\" width=\"1330\" height=\"778\" src=\"https://www.allendowney.com/blog/wp-content/uploads/2026/03/cohort_trajectory_ha-ee8d3c24ba4d6e9d119c114dfd0b23c3.png\" alt=\"Cohort trajectories, percent who respond “very happy”\" class=\"wp-image-1739\" srcset=\"https://www.allendowney.com/blog/wp-content/uploads/2026/03/cohort_trajectory_ha-ee8d3c24ba4d6e9d119c114dfd0b23c3.png 1330w, https://www.allendowney.com/blog/wp-content/uploads/2026/03/cohort_trajectory_ha-ee8d3c24ba4d6e9d119c114dfd0b23c3-300x175.png 300w, https://www.allendowney.com/blog/wp-content/uploads/2026/03/cohort_trajectory_ha-ee8d3c24ba4d6e9d119c114dfd0b23c3-1024x599.png 1024w, https://www.allendowney.com/blog/wp-content/uploads/2026/03/cohort_trajectory_ha-ee8d3c24ba4d6e9d119c114dfd0b23c3-768x449.png 768w, https://www.allendowney.com/blog/wp-content/uploads/2026/03/cohort_trajectory_ha-ee8d3c24ba4d6e9d119c114dfd0b23c3-462x270.png 462w\" sizes=\"auto, (max-width: 1330px) 100vw, 1330px\" /></figure>\n\n\n\n<p class=\"wp-block-paragraph\">People born in 1900 were 72 years old when the survey started; at that point, about 37% said they were very happy. In 1990, the last year they were eligible to participate, a little more than 40% said they were very happy. So it seems like they aged well—or possibly the less happy died earlier.</p>\n\n\n\n<p class=\"wp-block-paragraph\">People born in 1910 were a little less happy when the survey started, but by the time they aged out, they also reached 40%. They were the last generation to reach that mark.</p>\n\n\n\n<p class=\"wp-block-paragraph\">Among people born between 1920 and 1950, each cohort was a little less happy than the one before (or maybe less likely to say they were happy). In these cohorts, we can see a general trend over time: increasing until about 2000, leveling off, and declining after 2010.</p>\n\n\n\n<p class=\"wp-block-paragraph\">The cohorts born in the 1960s and 1970s followed a similar trajectory, with only small differences from one birth year to the next.</p>\n\n\n\n<p class=\"wp-block-paragraph\">And then the bottom fell out. Starting with people born in the 1980s (the earliest Millennials), each successive cohort was substantially less happy than the one before.</p>\n\n\n\n<p class=\"wp-block-paragraph\">When people born in 1990 joined the survey in 2008 (at age 18), only 27% said they were very happy. In the most recent data, from 2024, the number had fallen to 22%.</p>\n\n\n\n<p class=\"wp-block-paragraph\">When people born in 2000 entered in 2018, they set a new record low at 21%, which has now fallen to 18%.</p>\n\n\n\n<p class=\"wp-block-paragraph\">And in the most recent cohort—born in 2006 and interviewed in 2024—only 16% said they were very happy.</p>\n\n\n\n<p class=\"wp-block-paragraph\">These percentages are based on a statistical model that estimates the proportion of “very happy” responses in each group at each point in time. The details of the model and its assumptions are below.</p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"the-time-trend\">The Time Trend</h2>\n\n\n\n<p class=\"wp-block-paragraph\">With an estimated proportion for each cohort and time step, we can compute separate contributions for changes over time and between cohorts.</p>\n\n\n\n<p class=\"wp-block-paragraph\">To characterize the contribution of time, we have to hold the cohort effect constant, which we can do by computing the distribution of birth years across the entire dataset and simulating a population where this distribution does not change over time. The following figure shows the result.</p>\n\n\n\n<figure class=\"wp-block-image\" id=\"time-trend-happy\"><img loading=\"lazy\" decoding=\"async\" width=\"1133\" height=\"790\" src=\"https://www.allendowney.com/blog/wp-content/uploads/2026/03/time_standardized_ha-26b65d5757264321ab30d96371b21ccf.png\" alt=\"Standardized time trend, percent who respond “very happy”\" class=\"wp-image-1738\" srcset=\"https://www.allendowney.com/blog/wp-content/uploads/2026/03/time_standardized_ha-26b65d5757264321ab30d96371b21ccf.png 1133w, https://www.allendowney.com/blog/wp-content/uploads/2026/03/time_standardized_ha-26b65d5757264321ab30d96371b21ccf-300x209.png 300w, https://www.allendowney.com/blog/wp-content/uploads/2026/03/time_standardized_ha-26b65d5757264321ab30d96371b21ccf-1024x714.png 1024w, https://www.allendowney.com/blog/wp-content/uploads/2026/03/time_standardized_ha-26b65d5757264321ab30d96371b21ccf-768x535.png 768w, https://www.allendowney.com/blog/wp-content/uploads/2026/03/time_standardized_ha-26b65d5757264321ab30d96371b21ccf-387x270.png 387w\" sizes=\"auto, (max-width: 1133px) 100vw, 1133px\" /></figure>\n\n\n\n<p class=\"wp-block-paragraph\">The overall level of happiness increased between 1972 and 2000, leveled off, and then declined after 2010.</p>\n\n\n\n<p class=\"wp-block-paragraph\">Of course it is speculation to say why that happened, but we can think about large-scale economic and social patterns and how they line up with these trends.</p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Economically, 1980 to 2000 was a period of growth and relative stability. That changed after the end of the Dot-com bubble in 2001 and, more importantly, the Global Financial Crisis in 2008, which had broad and persistent effects on employment, wealth, and economic security.</li>\n\n\n\n<li>Geopolitically, the 1970s through the 1990s were relatively quiet compared to what followed. The September 11 attacks in 2001, and the wars in Iraq (2003–2011) and Afghanistan (2001–2021) marked a shift toward a more uncertain and conflict-oriented global environment.</li>\n\n\n\n<li>Participation in civic organizations and religious institutions declined over the past several decades. These institutions traditionally provided social support, shared identity, and regular face-to-face interaction. Social isolation is strongly associated with lower well-being.</li>\n\n\n\n<li>At the same time, the media environment was transformed. The rise of 24-hour news increased exposure to negative and emotionally salient events, and after 2010 the spread of smartphones and social media made that exposure continuous and personalized.</li>\n\n\n\n<li>Finally, measures of trust in institutions and other people have generally declined over this period, while political polarization has increased. These trends may reduce people’s sense of stability and shared purpose.</li>\n</ul>\n\n\n\n<p class=\"wp-block-paragraph\">The COVID-19 pandemic likely contributed to the most recent decline, but the downward trend was already underway before 2020.</p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"the-cohort-effect\">The Cohort Effect</h2>\n\n\n\n<p class=\"wp-block-paragraph\">Just as we isolated the time trend by simulating a survey with a fixed distribution of cohorts, we can isolate the cohort effect by simulating a survey with a fixed distribution of times. The following figure shows the result.</p>\n\n\n\n<figure class=\"wp-block-image\" id=\"cohort-profile-happy\"><img loading=\"lazy\" decoding=\"async\" width=\"1133\" height=\"790\" src=\"https://www.allendowney.com/blog/wp-content/uploads/2026/03/cohort_standardized_-2dbe3fdd869f5be03f0b91d2cf3b980e.png\" alt=\"Standardized cohort effect, percent who respond “very happy”\" class=\"wp-image-1740\" srcset=\"https://www.allendowney.com/blog/wp-content/uploads/2026/03/cohort_standardized_-2dbe3fdd869f5be03f0b91d2cf3b980e.png 1133w, https://www.allendowney.com/blog/wp-content/uploads/2026/03/cohort_standardized_-2dbe3fdd869f5be03f0b91d2cf3b980e-300x209.png 300w, https://www.allendowney.com/blog/wp-content/uploads/2026/03/cohort_standardized_-2dbe3fdd869f5be03f0b91d2cf3b980e-1024x714.png 1024w, https://www.allendowney.com/blog/wp-content/uploads/2026/03/cohort_standardized_-2dbe3fdd869f5be03f0b91d2cf3b980e-768x535.png 768w, https://www.allendowney.com/blog/wp-content/uploads/2026/03/cohort_standardized_-2dbe3fdd869f5be03f0b91d2cf3b980e-387x270.png 387w\" sizes=\"auto, (max-width: 1133px) 100vw, 1133px\" /></figure>\n\n\n\n<p class=\"wp-block-paragraph\">The cohort effect is larger and more consistent than the time trend: the difference between the happiest and least happy cohorts is more than 20 percentage points.</p>\n\n\n\n<p class=\"wp-block-paragraph\">The decline was relatively slow for cohorts born between 1900 and 1950 and nearly zero for cohorts born in the 1950s, 1960s and 1970s (late Baby Boomers and Gen X). The steep decline begins with the Millennials and continues into Gen Z.</p>\n\n\n\n<p class=\"wp-block-paragraph\">Possible explanations for the recent decline include:</p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Transformation of childhood: <a href=\"https://jonathanhaidt.com/anxious-generation/\" target=\"_blank\" rel=\"noreferrer noopener\">Jonathan Haidt</a> has described childhood in recent cohorts as “overprotected in the real world and underprotected in the online world.” Increased parental monitoring, reduced independent play, and greater time spent online may affect the development of autonomy, risk tolerance, and social skills. If these early-life experiences shape long-term outlook, they could contribute to lower self-reported happiness.</li>\n\n\n\n<li>Greater and earlier exposure to media: Younger cohorts were exposed to a media landscape characterized by continuous, personalized, and often negative content. Social media platforms amplify social comparison and negative content, while displacing in-person interaction. Increased awareness of global risks—including climate change—may contribute to a more pessimistic worldview.</li>\n\n\n\n<li>Differential impact of economic conditions: Recent cohorts entered the labor market during periods of economic disruption, including the aftermath of the Global Financial Crisis and more recent pandemic-related shocks. These cohorts also face higher housing costs and greater student debt. Economic insecurity during the transition to adulthood may have lasting effects on well-being.</li>\n\n\n\n<li>Extension of “liminal” adulthood: Young adults are taking longer to complete education, establish careers, form long-term partnerships, and have children. This extended unsettled period may be associated with lower life satisfaction.</li>\n\n\n\n<li>Norms around self-reported well-being. Younger cohorts may also be less likely to say they are “very happy,” either because of changing norms around self-presentation or greater awareness of mental health.</li>\n</ul>\n\n\n\n<p class=\"wp-block-paragraph\">It’s hard to say how much of the recent decline we can attribute to these causes. But the decline is steep, and seems to be ongoing.</p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"how-the-model-works\">How the Model Works</h2>\n\n\n\n<p class=\"wp-block-paragraph\">One of the challenges with this kind of survey data is that the sample size is small for each birth year in each iteration of the survey. If we plot raw percentages over time, the result is noisy.</p>\n\n\n\n<p class=\"wp-block-paragraph\">In <a href=\"https://allendowney.github.io/ProbablyOverthinkingIt/simpson.html#old-optimists-young-pessimists\" target=\"_blank\" rel=\"noreferrer noopener\"><em>Probably Overthinking It</em></a>, I addressed this problem by grouping respondents into decade-of-birth cohorts and smoothing the resulting time series. That approach works, but it has drawbacks: aggregation removes detail, introduces edge effects for the earliest and latest cohorts, and requires an arbitrary choice about the level of smoothing.</p>\n\n\n\n<p class=\"wp-block-paragraph\">The new model takes a more principled approach. Instead of smoothing the observed data, it models an unobserved (latent) propensity to report being “very happy” for each cohort in each year.</p>\n\n\n\n<p class=\"wp-block-paragraph\">We assume that the number of “very happy” responses in each group follows a binomial distribution, where the probability of a “very happy” response depends on this latent propensity. The observed responses provide noisy information about the latent factor; the model combines information across cohorts and years to estimate it.</p>\n\n\n\n<p class=\"wp-block-paragraph\">The latent propensity is modeled as the sum of an intercept, representing the overall level of happiness, a smooth effect of birth cohort, a smooth effect of survey year, and a year-specific random effect that captures short-term fluctuations (overdispersion).</p>\n\n\n\n<p class=\"wp-block-paragraph\">The cohort and period effects are modeled as second-order Gaussian random walks (RW2), which means the model assumes these effects evolve smoothly over time, with a preference for gradual changes in slope rather than abrupt jumps, unless the data provide strong evidence otherwise. The amount of smoothing is not fixed in advance; it is estimated from the data.</p>\n\n\n\n<p class=\"wp-block-paragraph\">The random year effect captures variation from one survey to the next that is not explained by long-term trends, like current events and topics of discussion.</p>\n\n\n\n<p class=\"wp-block-paragraph\">Where we have a lot of data, the estimates track the observed proportions closely. Where data are sparse, the model borrows strength from neighboring cohorts and years, providing principled smoothing and interpolation without arbitrary grouping.</p>\n\n\n\n<p class=\"wp-block-paragraph\">For the details of the model, see the <a href=\"https://allendowney.github.io/CultureWar//tech-report\">Technical Report</a>.<a href=\"https://allendowney.github.io/CultureWar//\"></a><a href=\"https://allendowney.github.io/CultureWar//\"></a></p>\n\n\n\n<p class=\"wp-block-paragraph\"></p>\n<p>The post <a href=\"https://www.allendowney.com/blog/2026/03/19/young-adults-are-not-very-happy/\">Young Adults Are Not Very Happy</a> appeared first on <a href=\"https://www.allendowney.com/blog\">Probably Overthinking It</a>.</p>",
"image": null,
"media": [],
"authors": [
{
"name": "AllenDowney",
"email": null,
"url": null
}
],
"categories": [
{
"label": "Uncategorized",
"term": "Uncategorized",
"url": null
},
{
"label": "age period cohort analysis",
"term": "age period cohort analysis",
"url": null
},
{
"label": "bayesian statistics",
"term": "bayesian statistics",
"url": null
},
{
"label": "general social survey",
"term": "general social survey",
"url": null
}
]
}
]
}