An invariance result for homogeneous juries with correlated votes

A joint probability distribution on the set of voting profiles is called second-order invariant if the probability of a jury collectively making the correct decision under simple majority rule (Condorcet’s probability) is independent of second-order correlations. This paper establishes the existence of such distributions for homogeneous juries of an arbitrary size. In a homogeneous jury each juror’s vote has an equal probability of being correct, and each pair of jurors’ votes correlates with the same correlation coefficient.