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Exploiting polyhedral symmetries in social choice

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  • Achill Schürmann

Abstract

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. Copyright Springer-Verlag 2013

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  • Achill Schürmann, 2013. "Exploiting polyhedral symmetries in social choice," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 40(4), pages 1097-1110, April.
    • Handle: RePEc:spr:sochwe:v:40:y:2013:i:4:p:1097-1110
    DOI: 10.1007/s00355-012-0667-1
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    References listed on IDEAS

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    1. William Gehrlein & Michel Breton & Dominique Lepelley, 2017. "The likelihood of a Condorcet winner in the logrolling setting," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 49(2), pages 315-327, August.

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