vote with probability $p_{x}>1/2$ rather than with probability $1/2$. So it is better for the boffin to vote second than to vote first. However now it is better for the smarter boffin to vote first, so that $p_{x}$ in the previous argument is in fact $p_{b}$ rather than $p_{a}$. So with two yokels and a boffin, the optimal ordering is smarter yokel, then boffin, then dumber yokel, or $\left(
b,a,c\right)$.

We note that this is a very special case of our main result, Theorem \[thm:optimal-sequence\], which says that the ordering $\left(  b,a,c\right)  $ is always optimal. Neither that result or any other result requires Proposition \[pro:main\_special\], which is why we are content with the above fairly informal proof of Proposition \[pro:main\_special\].

Signals, abilities and voting thresholds {#sec:preliminaries}
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In both the Condorcet model and in our model, there are two equiprobable states of Nature, called $A$ and $B$. In the Condorcet model, private information of jurors is in the form of a binary signal $\{A, B\}$. The ability of a juror to guess the true state is given as a probability, called $p$, that the signal received corresponds to the actual state of Nature. This probability $p$ ranges between $1/2$ 