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An efficient heuristic search algorithm for discovering large Condorcet domains

Author

Listed:
  • Bei Zhou

    (Imperial College London)

  • Søren Riis

    (Queen Mary University of London)

Abstract

We explore large peak-pit Condorcet domains (CD), an active research area in voting theory. The search for large CDs, defined combinatorially, serves as a benchmark for heuristic-based optimisation algorithms. Since 1996, Fishburn’s alternating scheme produced the largest known CDs for $$n \le 15$$ n ≤ 15 alternatives until recent discoveries surpassed it for $$n = 8$$ n = 8 and $$n \ge 13$$ n ≥ 13 . For $$8

Suggested Citation

  • Bei Zhou & Søren Riis, 2025. "An efficient heuristic search algorithm for discovering large Condorcet domains," 4OR, Springer, vol. 23(2), pages 193-216, June.
    • Handle: RePEc:spr:aqjoor:v:23:y:2025:i:2:d:10.1007_s10288-025-00583-1
    DOI: 10.1007/s10288-025-00583-1
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    References listed on IDEAS

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    1. 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.
    2. Peter C. Fishburn, 2002. "Acyclic sets of linear orders: A progress report," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 19(2), pages 431-447.
    3. Peter Fishburn, 1996. "Acyclic sets of linear orders," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 14(1), pages 113-124.
    4. Juho Lauri & Sourav Dutta & Marco Grassia & Deepak Ajwani, 2023. "Learning fine-grained search space pruning and heuristics for combinatorial optimization," Journal of Heuristics, Springer, vol. 29(2), pages 313-347, June.
    5. 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.
    6. Arkadii Slinko, 2024. "A family of condorcet domains that are single-peaked on a circle," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 63(1), pages 57-67, August.
    7. Alhussein Fawzi & Matej Balog & Aja Huang & Thomas Hubert & Bernardino Romera-Paredes & Mohammadamin Barekatain & Alexander Novikov & Francisco J. R. Ruiz & Julian Schrittwieser & Grzegorz Swirszcz & , 2022. "Discovering faster matrix multiplication algorithms with reinforcement learning," Nature, Nature, vol. 610(7930), pages 47-53, October.
    8. 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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