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The largest Condorcet domain on 8 alternatives

Author

Listed:
  • Charles Leedham-Green

    (Queen Mary University of London)

  • Klas Markström

    (University of Umeå)

  • Søren Riis

    (Queen Mary University of London)

Abstract

In this note, we report on a Condorcet domain of record-breaking size for n = 8 alternatives. We show that there exists a Condorcet domain of size 224 and that this is the largest possible size for 8 alternatives. Our search also shows that this domain is unique up to isomorphism. In this note we investigate properties of the new domain and relate them to various open problems and conjectures.

Suggested Citation

  • Charles Leedham-Green & Klas Markström & Søren Riis, 2024. "The largest Condorcet domain on 8 alternatives," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 62(1), pages 109-116, February.
    • Handle: RePEc:spr:sochwe:v:62:y:2024:i:1:d:10.1007_s00355-023-01481-3
    DOI: 10.1007/s00355-023-01481-3
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    References listed on IDEAS

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    1. Clemens Puppe & Arkadii Slinko, 2019. "Condorcet domains, median graphs and the single-crossing property," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 67(1), pages 285-318, February.
    2. 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.
    3. 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.
    4. Marie-Louise Lackner & Martin Lackner, 2017. "On the likelihood of single-peaked preferences," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 48(4), pages 717-745, April.
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    Cited by:

    1. Bei Zhou & Søren Riis, 2025. "An efficient heuristic search algorithm for discovering large Condorcet domains," 4OR, Springer, vol. 23(2), pages 193-216, June.

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