Conditions for Voting Equilibria in Continuous Voter Distributions

Abstract

This paper extends Plott's necessary and sufficient conditions for the existence of majority rule equilibria to the case where there is a continuous distribution of voters. Plott's theorem extends in a natural way to this setting: It is shown that a point, x*, is a majority rule equilibrium if and only if, for every measurable cone originating at the origin, the measure of the voters whose gradients (at x*) lie in the cone is equal to the measure of the voters whose gradients lie in the negative cone.

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