Exploiting Polyhedral Symmetries in Social Choice

Details Exploiting Polyhedral Symmetries in Social Choice Exploiting Polyhedral Symmetries in Social Choice

2011-09-07

arxiv.org/abs/1109.1545v2

Mathematics

Optimization and Control

14 pages; with minor improvements; to be published in Social Choice and Welfare

Scientific paper

A large amount of literature in social choice theory deals with quantifying the probability of certain election outcomes. One way of computing the probability of a specific voting situation under the Impartial Anonymous Culture assumption is via counting integral points in polyhedra. Here, Ehrhart theory can help, but unfortunately the dimension and complexity of the involved polyhedra grows rapidly with the number of candidates. However, if we exploit available polyhedral symmetries, some computations become possible that previously were infeasible. We show this in three well known examples: Condorcet's paradox, Condorcet efficiency of plurality voting and in Plurality voting vs Plurality Runoff.

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