Probabilistic Voting and Equilibrium: An Impossibility Result

The introduction of voters' uncertainty alone is in no way sufficient to guarantee an equilibrium outcome of a voting process. What is needed in addition is the assumption that the voting probabilities depend strictly convex respectively concave of the utility losses caused by the proposed policies of the different parties. This assumption is, however, not compatible with an unrestricted policy space, and it has to be rejected for theoretical as well as empirical reasons. Thus, using models of probabilistic voting we still have to accept that cycles can arise and electoral outcomes are prone to manipulation via agenda setting.