The Probability of a Cyclical Majority

Frank R DeMeyer · Charles R. Plott

123 citations0/0 files storedEconometrica

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Game Theory and Voting Systems Game Theory and Applications Opinion Dynamics and Social Influence

Abstract

Consider a committee or society attempting to order the alternatives (X_1, X_2, X_3) by use of majority rule. Each individual is assumed to have a strong ordering (called a profile) on the alternatives. "Indifference" is not a property of the profiles. The committee is said to "prefer" X_i to X_j, denoted X_iCX_j if X_i is preferred to X_j on a majority of the individual profiles. It is well known that if certain individual profiles are chosen, the resulting "social ordering" may be cyclical, i.e., X_iCX_j, X_jCX_k, X_kCX_i. Such a result is called a "cycle."

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1952A Set of Independent Necessary and Sufficient Conditions for Simple Majority Decision

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1985The vulnerability of point-voting schemes to preference variation and strategic manipulation 1974Voter Antagonism and the Paradox of Voting 2003The impartial culture maximizes the probability of majority cycles 1995Condorcet Winners and the Paradox of Voting: Probability Calculations for Weak Preference Orders 2001An Empirical Example of the Condorcet Paradox of Voting in a Large Electorate 1974Two Preference Paradoxes

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