Comparing Electoral Systems: A Geometric Analysis

This paper constructs a game-theoretic model of elections inalternative electoral systems with three or four candidates.Each electoral system specifies how the platforms of thecandidates and their scores give rise to an outcome. Whengeometrical analysis shows that two outcomes can competeagainst each other for victory, a pivot probability isassociated to that pair. Each voter is rational and picks thecandidate that maximizes her expected utility, which resultsfrom the balancing of her preferences and beliefs about thepivot-probabilities. Candidate positioning is endogenous andthe result of a Nash game. The possible equilibria arecomputed for plurality and runoff majority systems.