or for $B)$ and then we consider what we call *sophisticated jurors*, who receive real number signals in the interval $[-1, +1]$.

Condorcet jurors
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We begin with a simple model with three jurors, who we call jurors $J_1$, $J_2$ and $J_3$ in terms of voting order and get *correct* binary signals $s\in\{A, B\}$ with probabilities $p_1$, $p_2$ and $p_3$, respectively. We also write $\{ p_1,p_2, p_3\} =\{p,q,r\}$ where $p\leq q\leq r$, and also call the jurors P, Q and R in terms of ability. So if the juror of highest ability votes first, then we have $J_1$ = R. We similarly label the signals received by the jurors as $\{s_{1},s_{2},s_{3}\}$ or $\{s_{p},s_{q},s_{r}\}$. For example, signal $s_{1}$ is correct with probability $p_1$. Given the three signals $\{s_{p},s_{q},s_{r}\}$, it is easy to calculate the most likely state of Nature, which we call the *Full Information Solution* (FIS). Clearly, such a state is either $s_{r}$ (dictator verdict) or $s_{p}=s_{q} \neq s_r$ (majority verdict). If $s_{r}=A$ and $s_{p}=s_{q}=B$, the posterior probability of $A$ is given by $$\frac{r( 1-p) ( 1-q) }{r( 1-p) (1-q) +( 1-r) pq}.$$ A simple calculation shows that the signal $A$ of juror R is more likely to be the 