Voter Turnout, Ideological Candidates, and Platform Setting with Non-Quadratic Preferences

In the framework of the median voter theorem, an ideologically driven candidate can fully alter policy when running against a vote-maximizing opponent. When turnout is allowed to depend on the relative positioning of the ideal points of the candidates relative to the voter, this result need not hold. This paper develops a model of turnout in which voters are assumed to abstain due to “indifference” and “alienation,” the politician faces a trade-off when moving his platform toward his opponent: the total number of voters aligning themselves with the candidates increases, but the number of abstensions also increases. Depending upon the distribution of voters across the policy space, this may or may not lead to a net incease in the vote share. The main implications of this model are that the inclusion of platform-dependent turnout (1) lessens the ability of ideological candidates to alter policy, (2) may lead to multiple platform equilibria, and (3) significantly alters the shape of the electoral landscape. The effect of the third result is demonstrated by simulating candidates that have limited information about the effects of a change in policy, and that can only move within a small neighborhood of their current position in a given period. Policy convergence with less than full turnout is slower and less complete than in the full turnout case.