The epistemology of special majority voting

It is known that, in Condorcet's classical jury model, the proportion of jurors supporting a decision is not a significant indicator of that decision's reliability: the probability that a particular majority decision is correct given the majority size depends only on the absolute margin between the majority and the minority, and is invariant under changes of the proportion in the majority if the absolute margin is held fixed. Here I show that, if juror competence depends on the jury size, the proportion may become significant: there are then conditions in which the probability that a given majority decision is correct depends only on the proportion of jurors supporting that decision, and is invariant under changes of the jury size. The proportion is significant in this way if and only if juror competence is a particular decreasing function of the jury size. Yet the required condition on juror competence is not only highly special – thereby casting doubt on the significance of the proportion in realistic conditions – but it also undermines the Condorcet jury theorem. If the proportion is significant, then the jury theorem fails to hold; and if the jury theorem holds, then the proportion is not significant. I discuss the implications of these results for defining and justifying special majority voting from the perspective of an epistemic account of voting.