Generic difference of expected vote share and probability of victory maximization in simple plurality elections with probabilistic voters

Abstract

In this paper I examine single member, simple plurality elections with n ≥ 3 probabilistic voters and show that the maximization of expected vote share and maximization of probability of victory are “generically different” in a specific sense. More specifically, I first describe finite shyness (Anderson and Zame in Adv Theor Econ 1:1–62, 2000), a notion of genericity for infinite dimensional spaces. Using this notion, I show that, for any policy \(x^{*}\) in the interior of the policy space and any candidate j, the set of n-dimensional profiles of twice continuously differentiable probabilistic voting functions for which \(x^{*}\) simultaneously satisfies the first and second order conditions for maximization of j’s probability of victory and j’s expected vote share at \(x^{*}\) is finitely shy with respect to the set of n-dimensional profiles of twice continuously differentiable probabilistic voting functions for which \(x^{*}\) satisfies the first and second order conditions for maximization of j’s expected vote share.