The Probability of Condorcet Cycles and Super Majority Rules

Majority voting aggregates individual preference profiles into a binary relation on the set of alternatives. Condorcet cycles are cycles of the aggregated binary relation. We show that the relative volume of the subset of the (n!−1)-simplex that represents profile distributions such that the aggregated preferences display Condorcet cycles is a decreasing function of the super majority levelτbounded by the expressionn!1−τ0.4714n!.This expression shows that Condorcet cycles become rare events for super majority rules larger than 53%.Journal of Economic LiteratureClassification Number: D71.