Electoral Outcomes and Social Log-Likelihood Maxima

Abstract

Abstract : This paper is concerned with the public policies that occur in economies with elections when political candidates estimate voting behavior with log-concave probabilistic voting estimators (e.g., normal estimators). We establish that, for a vector of policies to be the outcome of an election, it is both necessary and sufficient that these policies maximize the society's mean (or social) log-likelihood function. This implies: First, the set of possible electoral outcomes is convex. Second, there is an electoral equilibrium whenever the set of social alternatives is compact. This property which holds for all multi-dimensional policy spaces does not use any special symmetry requirements on voter preferences. Third, under 'cardinal probabilistic voting,' every electoral outcome is also a maximum of a Nash type Social Welfare function. Fourth, in a finite population of m voters with independent probabilistic voting density functions a vector of policies is an electoral outcome if any only if it has the maximum estimated likelihood of receiving unanimous support.