Regenerate explainer pages after the simpsons-paradox/CDP/subgroup-fairness content fixes

make build-explainers after the 3 preceding content-fix commits. Also
picks up first-commit datePublished/dateModified for all 4 explainers
added in #541 (git-log-derived; couldn't resolve until those files had
a real commit history, the same one-time chicken-and-egg noted in
check_generated_files_current.py's own docstring).

Author: yakew7

assets/og-light/conditional-demographic-parity.png

@@ -110,7 +110,9 @@
         "@type": "DefinedTermSet",
         "name": "Fair Code Explainers",
         "url": "https://www.thefaircode.xyz/index.html#explainers"
-      }
+      },
+      "datePublished": "2026-09-09",
+      "dateModified": "2026-09-09"
     },
     {
       "@type": "FAQPage",
@@ -204,17 +206,17 @@ <h3 id="how-it-works">How It Works</h3>
 <p>The aggregate rate is a weighted average of within-stratum rates, weighted by how group <code>g</code> is distributed across the strata of <code>L</code>. Subtracting the two groups&#x27; aggregate rates gives a gap with two sources: different within-stratum rates (<code>P(Y_hat = 1 | G = g, L = l)</code> differs by <code>g</code>), and different stratum weights (<code>P(L = l | G = g)</code> differs by <code>g</code>).</p>
 <p>Conditional demographic parity zeroes out the second source by construction: it only compares groups at the same value of <code>L</code>. What is left is the within-stratum gap. A sample-size-weighted average of the within-stratum gaps is the part of the aggregate gap that stratifying on <code>L</code> does <em>not</em> remove.</p>
 <p>The catch is entirely in the choice of <code>L</code>. If <code>L</code> is a genuine exogenous factor, the within-stratum gap is the disparity net of a real confounder. If <code>L</code> is a <a href="proxy-variables.html">proxy</a> for the protected attribute, conditioning on it absorbs the discrimination into the &quot;legitimate&quot; term and the within-stratum gap understates the real harm. CDP gives you a knob; it does not tell you where to set it.</p>
-<h3 id="concrete-example-benefits-denial-audit-04">Concrete Example: Benefits Denial - Audit 04</h3>
+<h3 id="concrete-example-benefits-denial-audit-05">Concrete Example: Benefits Denial - Audit 05</h3>
 <p><code>Benefits Denial/</code> audits the Adult Census Income dataset (<code>adult.csv</code>, 32,561 rows). The target is <code>income == &#x27;&gt;50K&#x27;</code> and <code>sex</code> is a declared protected attribute. Using the dataset&#x27;s own outcome rates (the base rate a label-level demographic parity check compares):</p>
 <p><strong>Unconditional:</strong></p>
-<div class="explainer-table-wrap"><table class="explainer-table"><thead><tr><th>Group</th><th>n</th><th>P(income &gt; 50K)</th></tr></thead><tbody><tr><td>Male</td><td>21,790</td><td>30.6%</td></tr><tr><td>Female</td><td>10,771</td><td>11.0%</td></tr><tr><td>Gap (M - F)</td><td></td><td><strong>+19.6 pp</strong></td></tr></tbody></table></div>
+<div class="explainer-table-wrap"><table class="explainer-table"><thead><tr><th>Group</th><th>n</th><th>P(income &gt; 50K)</th></tr></thead><tbody><tr><td>Male</td><td>21,790</td><td>30.6%</td></tr><tr><td>Female</td><td>10,771</td><td>10.9%</td></tr><tr><td>Gap (M - F)</td><td></td><td><strong>+19.6 pp</strong></td></tr></tbody></table></div>
 <p>Now apply CDP with two different choices of legitimate factor <code>L</code>.</p>
-<h4 id="l-education-level-education-num-15-levels">L = education level (<code>education.num</code>, 15 levels)</h4>
-<div class="explainer-table-wrap"><table class="explainer-table"><thead><tr><th>education.num</th><th>n</th><th>Gap (M - F)</th></tr></thead><tbody><tr><td>9 (HS grad)</td><td>10,501</td><td>+13.7 pp</td></tr><tr><td>10 (some college)</td><td>7,291</td><td>+19.5 pp</td></tr><tr><td>13 (Bachelors)</td><td>5,355</td><td>+29.4 pp</td></tr><tr><td>14 (Masters)</td><td>1,723</td><td>+32.3 pp</td></tr><tr><td>15 (Prof-school)</td><td>576</td><td>+33.1 pp</td></tr><tr><td>16 (Doctorate)</td><td>413</td><td>+20.2 pp</td></tr></tbody></table></div>
+<h4 id="l-education-level-education-num-16-levels">L = education level (<code>education.num</code>, 16 levels)</h4>
+<div class="explainer-table-wrap"><table class="explainer-table"><thead><tr><th>education.num</th><th>n</th><th>Gap (M - F)</th></tr></thead><tbody><tr><td>9 (HS grad)</td><td>10,501</td><td>+13.7 pp</td></tr><tr><td>10 (some college)</td><td>7,291</td><td>+19.5 pp</td></tr><tr><td>13 (Bachelors)</td><td>5,355</td><td>+29.4 pp</td></tr><tr><td>14 (Masters)</td><td>1,723</td><td>+32.3 pp</td></tr><tr><td>15 (Prof-school)</td><td>576</td><td>+33.1 pp</td></tr><tr><td>16 (Doctorate)</td><td>413</td><td>+20.1 pp</td></tr></tbody></table></div>
 <p>Sample-weighted within-stratum gap: <strong>+18.4 pp</strong>. Conditioning on education removes almost none of the aggregate gap - within every education level men are markedly more likely to be high earners, and at the top three levels the gap is <em>larger</em> than the unconditional +19.6. CDP conditioned on education says: the disparity is not an artifact of women being less educated in this dataset.</p>
 <h4 id="l-marital-status-marital-status">L = marital status (<code>marital.status</code>)</h4>
 <div class="explainer-table-wrap"><table class="explainer-table"><thead><tr><th>marital.status</th><th>n</th><th>Gap (M - F)</th></tr></thead><tbody><tr><td>Married-civ-spouse</td><td>14,976</td><td>-0.9 pp</td></tr><tr><td>Never-married</td><td>10,683</td><td>+2.0 pp</td></tr><tr><td>Divorced</td><td>4,443</td><td>+9.3 pp</td></tr><tr><td>Widowed</td><td>993</td><td>+17.6 pp</td></tr></tbody></table></div>
-<p>Sample-weighted within-stratum gap: roughly <strong>+3 pp</strong>, and inside the single largest stratum the sign reverses (women 0.9 points ahead). Conditioning on marital status makes most of the aggregate gap disappear.</p>
+<p>Sample-weighted within-stratum gap: roughly <strong>+2 pp</strong>, and inside the single largest stratum the sign reverses (women 0.9 points ahead). Conditioning on marital status makes most of the aggregate gap disappear.</p>
 <h4 id="the-two-answers-disagree-and-that-is-the-point">The two answers disagree, and that is the point</h4>
 <p>Same protected attribute, same dataset, same +19.6 pp aggregate. Condition on education and the gap stands. Condition on marital status and it nearly vanishes. CDP did not resolve the fairness question - it moved it to a new one: <em>is marital status a legitimate basis for a 20-point income difference between men and women, or is it a proxy for a sex-role division of unpaid labor that the outcome variable should not be conditioned on?</em> That is a normative and legal question, not a statistical one, and CDP&#x27;s output is only as defensible as the answer to it. (This is the same aggregate-vs-stratified divergence covered from the other direction in <a href="simpsons-paradox.html">Simpson&#x27;s Paradox</a>.)</p>
 <pre><code class="language-python">import pandas as pd
@@ -241,7 +243,7 @@ <h4 id="the-two-answers-disagree-and-that-is-the-point">The two answers disagree
     _, w = within_stratum_gap(df, col)
     print(f&quot;condition on {col:16s}: weighted within-stratum gap = {w:+.4f}&quot;)
 # condition on education.num   : weighted within-stratum gap = +0.1844
-# condition on marital.status  : weighted within-stratum gap = +0.0305</code></pre>
+# condition on marital.status  : weighted within-stratum gap = +0.0243</code></pre>
 <h3 id="detection-code">Detection Code</h3>
 <p>The following module computes the unconditional demographic parity gap, the conditional (within-stratum) gap for a chosen legitimate factor, and the fraction of the unconditional gap that conditioning explains away.</p>
 <pre><code class="language-python">import numpy as np
@@ -333,7 +335,7 @@ <h3 id="detection-code">Detection Code</h3>
 # print_cdp_report(conditional_demographic_parity(
 #     df, &quot;high_income&quot;, &quot;sex&quot;, &quot;Male&quot;, &quot;Female&quot;, [&quot;marital.status&quot;]),
 #     &quot;marital.status&quot;)</code></pre>
-<p>Against <code>Benefits Denial/adult.csv</code> this reports an <code>explained_fraction</code> near <code>0.06</code> for <code>education.num</code> (conditioning removes almost nothing) and near <code>0.84</code> for <code>marital.status</code> (conditioning removes most of the gap) - the same +19.6 pp aggregate, two incompatible readings.</p>
+<p>Against <code>Benefits Denial/adult.csv</code> this reports an <code>explained_fraction</code> near <code>0.06</code> for <code>education.num</code> (conditioning removes almost nothing) and near <code>0.88</code> for <code>marital.status</code> (conditioning removes most of the gap) - the same +19.6 pp aggregate, two incompatible readings.</p>
 <h3 id="limitations-and-trade-offs">Limitations and Trade-offs</h3>
 <h4 id="1-the-conditioning-set-is-a-value-judgment-not-a-statistical-choice">1. The conditioning set is a value judgment, not a statistical choice</h4>
 <p>Everything CDP reports is downstream of which factors you declared &quot;legitimate&quot;. There is no test that tells you whether marital status, or occupation, or prior loan history, is a fair thing to condition on. Pick a factor that is genuinely a proxy for the protected attribute and CDP will confidently report that the disparity is &quot;explained&quot;, which is exactly the <a href="proxy-variables.html">proxy-variable</a> trap.</p>

assets/og-light/differential-privacy.png

@@ -110,7 +110,9 @@
         "@type": "DefinedTermSet",
         "name": "Fair Code Explainers",
         "url": "https://www.thefaircode.xyz/index.html#explainers"
-      }
+      },
+      "datePublished": "2026-09-09",
+      "dateModified": "2026-09-09"
     },
     {
       "@type": "FAQPage",