where individuals of higher ability are generally (but not always) able to make better guesses about the state of Nature. We will define our ability-signal model in such a way that the conditional probability of state $A$ given a positive signal $s>0$ is proportional to the juror’s ability $a$. In this way our definition of ability is analogous to Condorcet’s definition of $p$ as the probability that the binary signal $A$ corresponds to Nature being in state $A$. When Nature is in state $A$ (resp. $B$), jurors receive independent signals $s\in [-1,1]$ with probability density given by $f_{a}(s)$ (resp. $g_a(s)$) if they have ability $a$. We make the simplest nontrivial assumption on $f_{a}(s)$ and $g_a(s)$, namely that they are linear in $s$. The slope of the density functions $f_{a}(s)$ and $g_a(s)$ for a juror of ability $a$ is proportional to $a$. Given that $f_{a}$ and $g_a(s)$ are density functions on $[-1,+1]$, they take the following form: $$\begin{aligned}
f_{a}(s) &  =(1+as)/2,\ -1\leq s\leq+1,\text{ when Nature is }A;\\
g_{a}(s) &  =(1-as)/2,\ -1\leq s\leq+1,\text{ when Nature is }B.\end{aligned}$$ It is easily checked that $f_a(\cdot)$ and $g_a(\cdot)$ defined above are indeed density functions for any $a\in [0,1]$. The probability of a correct signal, that 