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On Ehrhart Polynomials and Probability Calculations in Voting Theory

Dominique Lepelley, Ahmed Louichi and Hatem Smaoui
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Ahmed Louichi: CREM – CNRS
Hatem Smaoui: CREM – CNRS

Economics Working Paper Archive (University of Rennes 1 & University of Caen) from Center for Research in Economics and Management (CREM), University of Rennes 1, University of Caen and CNRS

Abstract: In voting theory, analyzing how frequent is an event (e.g. a voting paradox) is, under some specific but widely used assumptions, equivalent to computing the exact number of integer solutions in a system of linear constraints. Recently, some algorithms for computing this number have been proposed in social choice literature by Huang and Chua [17] and by Gehrlein ([12, 14]). The purpose of this paper is threefold. Firstly, we want to do justice to Eugène Ehrhart, who, more than forty years ago, discovered the theoretical foundations of the above mentioned algorithms. Secondly, we present some efficient algorithms that have been recently developed by computer scientists, independently from voting theorists. Thirdly, we illustrate the use of these algorithms by providing some original results in voting theory.

Keywords: voting rules; manipulability; polytopes; lattice points; algorithms. (search for similar items in EconPapers)
JEL-codes: D70 D71 (search for similar items in EconPapers)
New Economics Papers: this item is included in nep-cdm, nep-dcm and nep-pol
Date: 2006
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Related works:
Journal Article: On Ehrhart polynomials and probability calculations in voting theory (2008) Downloads
Working Paper: On Ehrhart polynomials and probability calculations in voting theory (2007)
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