Computations of volumes and Ehrhart series in four candidates elections

Winfried Bruns (), Bogdan Ichim () and Christof Söger ()
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Winfried Bruns: Universität Osnabrück
Bogdan Ichim: Simion Stoilow Institute of Mathematics of the Romanian Academy
Christof Söger: Universität Osnabrück

Annals of Operations Research, 2019, vol. 280, issue 1, No 11, 265 pages

Abstract: Abstract We describe several analytical results obtained in four candidates social choice elections under the assumption of the Impartial Anonymous Culture. These include the Condorcet and Borda paradoxes, as well as the Condorcet efficiency of plurality voting with runoff. The computations are done by Normaliz. It finds precise probabilities as volumes of polytopes and counting functions encoded as Ehrhart series of polytopes.

Keywords: Rational polytope; Volume; Ehrhart series; Social choice; Condorcet paradox; Borda paradox; 52B20; 91B12 (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (14)

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DOI: 10.1007/s10479-019-03152-y

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