Probabilities of Preferences and Cycles with Super Majority Rules
Abstract Balasko and Cres [2] introduce a probabilistic model of population preference profiles onnalternatives. For supermajority voting at any levelτ>.5286... they show that the probability of Condorcet cycles (intransitivity of the aggregate preference) tends quickly to 0 asnincreases. This paper offers an alternative analysis that relates voting outcomes to the behavior of sample medians. Condorcet cycles turn out to be asymptotically rare for allτ> 1 2 , but for the disappointing reason that preferences are rare. In contrast, for simple majority voting,τ= 1 2 , cycles occur with probability converging to 1 asn→∞.Journal of Economic LiteratureClassification Number: D71.