Conditions for Voting Equilibria in Continuous Voter Distributions
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.
Additional Information© 1980 Society for Industrial and Applied Mathematics. Received by the editors July 5, 1977, and in final revised form April 25, 1979. We acknowledge the thorough reading and helpful comments of an anonymous referee of this journal.
Published - MCKsiamjam80.pdf