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Condorcet Domains of Degree at most Seven

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  • Dolica Akello-Egwell
  • Charles Leedham-Green
  • Alastair Litterick
  • Klas Markstrom
  • S{o}ren Riis

Abstract

In this paper we give the first explicit enumeration of all maximal Condorcet domains on $n\leq 7$ alternatives. This has been accomplished by developing a new algorithm for constructing Condorcet domains, and an implementation of that algorithm which has been run on a supercomputer. We follow this up by the first survey of the properties of all maximal Condorcet domains up to degree 7, with respect to many properties studied in the social sciences and mathematical literature. We resolve several open questions posed by other authors, both by examples from our data and theorems. We give a new set of results on the symmetry properties of Condorcet domains which unify earlier works. Finally we discuss connections to other domain types such as non-dictatorial domains and generalisations of single-peaked domains. All our data is made freely available for other researches via a new website.

Suggested Citation

  • Dolica Akello-Egwell & Charles Leedham-Green & Alastair Litterick & Klas Markstrom & S{o}ren Riis, 2023. "Condorcet Domains of Degree at most Seven," Papers 2306.15993, arXiv.org, revised Dec 2023.
    • Handle: RePEc:arx:papers:2306.15993
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    References listed on IDEAS

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    1. Ádám Galambos & Victor Reiner, 2008. "Acyclic sets of linear orders via the Bruhat orders," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 30(2), pages 245-264, February.
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