Policy convergence in a two-candidate probabilistic voting model

I propose a generalization of the probabilistic voting model in two-candidate elections. Unlike in all previous works, I assume that the candidates have general von Neumann-Morgenstern utility functions defined over the voting outcomes. For a finite number of voters, I derive necessary and sufficient conditions for the existence of a local Nash equilibrium in which the policy platforms of the candidates are identical. The convergent equilibrium exists only if a certain condition on the probability of voting functions is satisfied, and/or a strict symmetry condition on the candidate utility functions is satisfied. Both widely studied special cases — probability of win-maximizers and voteshare-maximizers — satisfy the latter condition. Hence, policy coincidence will not exist in the general case, although Banks and Duggan (2005) have shown that every pure-strategy Nash equilibrium will exhibit convergence for voteshare-maximizing candidates and a broad class of probability of voting functions. ∗Central Economics and Mathematics Institute, Moscow, Russia. [email protected], www.politecon.ru/zakharov