Equilibrium Equivalence under Expected Plurality and Probability of Winning Maximization∗ INCOMPLETE: ONE SECTION MISSING

This paper studies competition between two office-motivated candidates when voters vote probabilistically and candidates maximize expected plurality or they maximize probability of winning. Every symmetric equilibrium under probability of winning is an equilibrium under expected plurality, but the converse hinges on some subtle issues. In a standard model of probabilistic voting, equilibria under probability of winning — if any — must be symmetric and must occur at the utilitarian welfare maximizing policy position. If the utility functions of voters are negative definite at that point, then it is indeed a local equilibrium under probability of winning. If negative definiteness is weakened to strict concavity (a seemingly innocuous move), this implication breaks down, and pure strategy equilibria under probability of winning need not exist. This possibility is examined in detail.