Optimality in Social Choice

Marengo and Settepanella (2010) have developed a geometric model of social choice when it takes place among bundles of interdependent elements, showing that by bundling and unbundling the same set of constituent elements an authority has the power of determining the social outcome. In this article, we will tie the model above to tournament theory, solving some of the mathematical problems arising in their work and opening new questions which are interesting from both a mathematical and social choice point of view. In particular, we will introduce the notion of u-local optima and study it from both a theoretical and a numerically probabilistic point of view; we will also describe an algorithm that computes the universal basin of attraction of a social outcome in O(M 3log M) time (where M is the number of social outcomes).