Typo

Always more to fix

misc/LearningPreferences.html

@@ -416,7 +416,7 @@ <h2>Step 1: Noise: <em>Random Utility Model</em></h2>
 <li><span class="math inline">\(x^*=\arg\max_j\{u(x_j)+\zeta_j\}\)</span> induces <span class="math inline">\(P(x^*=x_j)\)</span> (Conditional) Choice probability (CCP)</li>
 <li>(Multinomial) Logit model, or <strong>Plackett-Luce</strong> (1959) choice model
 <ul>
-<li><span class="math inline">\(\zeta_j\overset{iid}{\sim}\text{Gumbel}\implies P(x^*=x_k)=\frac{exp(u(x_k))}{\sum_j exp(u(x_k))}\)</span></li>
+<li><span class="math inline">\(\zeta_j\overset{iid}{\sim}\text{Gumbel}\implies P(x^*=x_k)=\frac{exp(u(x_k))}{\sum_j exp(u(x_j))}\)</span></li>
 <li>Alternate derivations: maximum entropy among all multinomial distributions, Luce axioms directly over choice probabilities</li>
 <li>Special property: <em>Independence of irrelevant alternatives</em>
 <ul>

misc/LearningPreferences.qmd

@@ -68,7 +68,7 @@ scrollable: true
 - Replace $u(x_j)$ with $u(x_j)+\zeta_j$, $\zeta\sim P(\zeta)$
 - $x^*=\arg\max_j\{u(x_j)+\zeta_j\}$ induces $P(x^*=x_j)$ (Conditional) Choice probability (CCP)
 - (Multinomial) Logit model, or **Plackett-Luce** (1959) choice model
-    - $\zeta_j\overset{iid}{\sim}\text{Gumbel}\implies P(x^*=x_k)=\frac{exp(u(x_k))}{\sum_j exp(u(x_k))}$
+    - $\zeta_j\overset{iid}{\sim}\text{Gumbel}\implies P(x^*=x_k)=\frac{exp(u(x_k))}{\sum_j exp(u(x_j))}$
     - Alternate derivations: maximum entropy among all multinomial distributions, Luce axioms directly over choice probabilities
     - Special property: *Independence of irrelevant alternatives*
         - $Pr(a|\{a,b\})/Pr(b|\{a,b\})=Pr(a|\{a,b,c\})/Pr(b|\{a,b,c\})$