that the signal is above the threshold $\tau=-1$ says nothing about the signal (they are always at least $-1$) and indeed $p_{-1}=1/2$, the same as the *a priori* probability of $A$. Thus in our model, the ability level $a$ is a proxy for Condorcet’s probability $p$, but in a more general context of continuous rather than binary signals. We now describe the signal distribution which gives these outcomes and . This continuous signal-ability model has been used before in the literature [e.g., @AlCh17b].

Signal distributions {#sec:signal-distributions}
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We assume two states of Nature $A$ and $B$, considered as negation of $A$, with *a priori* probability of $A$ given by $\Pr\left(A\right)  =\theta_{0}$. To simplify the analysis we will assume the equiprobable case $\theta_{0}=1/2$, although our results are robust for $\theta_{0}$ values around $1/2$. Individuals have private information about the state of Nature modeled as a signal $s$ in the *signal interval* $[-1,+1]$. Positive signals are indications of $A$; negative signals $B$. The signal $s=0$ is neutral. Higher positive signals indicate $A$ more strongly; similarly for negative signals and $B$. Thus a stronger signal is one with a higher absolute value.

Individual jurors have an ability $a$ in the *ability interval* $[0,1]$, 