Interdependent Voting in Two-Candidate Voting Games

The election of a political candidate is a public good for all those who prefer it and a public bad for those who are opposed. Given free-rider problems and other features of collective action, the probability that any one voter will vote for a preferred candidate is unlikely to be independent of the voting probabilities of all others with the same electoral preference, as is so often assumed. Interdependent voting probabilities are, therefore, likely to be the norm rather than the exception. We make no assumption about this interdependence other than a generalized concavity condition. The point of departure for this paper is independent voting in the context of a two-candidate, regular concave voting game. Such games always have a unique, asymptotically stable equilibrium platform. This platform is not the ideal point of the median voter, however. It is also, in general, not Pareto optimal. With interdependent voting, the unique equilibrium is preserved when candidates have the same initial endowments. If one candidate is advantaged (so the game is not symmetrical), however, plurality-maximizing candidates will cycle endlessly. A candidate advantage creates a convex set of platform choices, none of which can be defeated by the disadvantaged opponent. An equilibrium without convergence is achieved if we assume that the advantaged candidate chooses from an undefeatable set a platform that maximizes utility while an opponent maximizes her plurality. The set of undefeatable platforms collapses on a unique winning platform as the advantage disappears.