Computations of volumes in five candidates elections

We describe several analytical (i.e., precise) results obtained in five 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, negative plurality and Borda voting,...

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Bibliographic Details
Published in:Scientific reports 2023-08, Vol.13 (1), p.13266-13266, Article 13266
Main Authors: Bruns, Winfried, Ichim, Bogdan
Format: Article
Language:English
Subjects:
639/705/1042
639/705/794
Algorithms
Candidates
Efficiency
Election results
Humanities and Social Sciences
Mathematics
multidisciplinary
Probability
Science
Science (multidisciplinary)
Social behavior
Voters
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Summary:We describe several analytical (i.e., precise) results obtained in five 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, negative plurality and Borda voting, including their runoff versions. The computations are done by Normaliz. It finds precise probabilities as volumes of polytopes in dimension 119, using its recent implementation of the Lawrence algorithm.
ISSN:2045-2322
2045-2322
DOI:10.1038/s41598-023-39656-8