2013/21 LEM Working Paper Series

Decidability in complex social choices

Gennaro Amendola, Luigi Marengo, Davide Pirino, Simona Settepanella, Akimichi Takemura
Social choice, object construction, hyperplane arrangement, probability, tournament, algorithm

  JEL Classifications
D03, D71, D72

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.
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