Two Papers on Majority Rule: Continuity Properties of Majority Rule with Intermediate Preferences. Electoral Outcomes with Probabilistic Voting and Nash Social Welfare Maxima

摘要

This technical report contains two joint (or co-authored) papers on aspects of majority rule. The first (with Kuan-Pin Lin) studies the continuity properties of majority rule. Specifically, it shows that certain conditions which have previously been shown (by Grandmont) to be sufficient for a society's majority rule relation to be transitive or acyclic are also sufficient for the map from distributions of voter preferences to indices identified with their majority rule relations to be continuous. Applications of this result to societies with certain classical assumptions on preferences reveal that, in such societies, the map from distributions of voter preferences to their majority rule equilibria is also continuous. The second (with Shmuel Nitzan) analyzes outcomes from electoral competitions with a Luce model of probabilistic voting. These outcomes are shown to be precisely the social alternatives that maximize a Nash-type social welfare function. These outcomes are also shown to be unanimity likelihood maxima when voting is independent. Finally, we show that the model's assumptions also imply the existence and uniqueness of electoral equilibria. (Author)