Amendola, Gennaro Marengo, Luigi Pirino, Davide Settepanella, Simona Takemura, Akimichi
Year of Publication:
LEM Working Paper Series 2013/21
In this paper we develop on a geometric model of social choice among bundles of interdependent elements (objects). Social choice can be seen as a process of search for optima in a complex multi-dimensional space and objects determine a decomposition of such a space into subspaces. We present a series of numerical and probabilistic results which show that such decompositions in objects can greatly increase decidability, as new kind of optima (called local and u-local) are very likely to appear also in cases in which no generalized Condorcet winner exists in the original search space.
social choice object construction hyperplane arrangement probability tournament algorithm