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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 withdoi:10.1016/j.mathsocsci.2008.09.002 fatcat:kr2dxqhxdrc2zjf2b3oocph23m