Comparing Electoral Systems: A Geometric Analysis

Abstract

This paper constructs a game-theoretic model of elections in alternative electoral systems with three or four candidates. Each electoral system specifies how the platforms of the candidates and their scores give rise to an outcome. When geometrical analysis shows that two outcomes can compete against each other for victory, a pivot probability is associated to that pair. Each voter is rational and picks the candidate that maximizes her expected utility, which results from the balancing of her preferences and beliefs about the pivot-probabilities. Candidate positioning is endogenous and the result of a Nash game. The possible equilibria are computed for plurality and runoff majority systems.