Social utility functions for strategic decisions in probabilistic voting models

This paper studies societies which have probabilistic voting that is smooth, scalable and unbiased. Its results establish that, in such societies, the decisions of vote-seeking candidates who start at a common location (such as the status quo for the society's policies and/or the same allocation of campaign resources) contain implicit rationality properties. In particular, it shows that in every such society there exist social utility functions which simultaneously rationalize the directional Nash behavior of candidates, the stationary electoral equilibria, and the non-degenerate local electoral equilibria which can occur at these locations. This is shown to be true both for unconstrained and for constrained sets of possible candidate locations. An example of such a utility function (which occurs in every one of the societies under consideration) is also provided.