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Condorcet domains on at most seven alternatives

Author

Listed:
  • Akello-Egwel, Dolica
  • Leedham-Green, Charles
  • Litterick, Alastair
  • Markström, Klas
  • Riis, Søren

Abstract

A Condorcet domain is a collection of linear orders which avoid Condorcet’s paradox for majority voting. We have developed a new algorithm for complete enumeration of all maximal Condorcet domains and, using a supercomputer, obtained the first enumeration of all maximal Condorcet domains on n≤7 alternatives.

Suggested Citation

  • Akello-Egwel, Dolica & Leedham-Green, Charles & Litterick, Alastair & Markström, Klas & Riis, Søren, 2025. "Condorcet domains on at most seven alternatives," Mathematical Social Sciences, Elsevier, vol. 133(C), pages 23-33.
  • Handle: RePEc:eee:matsoc:v:133:y:2025:i:c:p:23-33
    DOI: 10.1016/j.mathsocsci.2024.12.002
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    References listed on IDEAS

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    1. Chatterji, Shurojit & Zeng, Huaxia, 2023. "A taxonomy of non-dictatorial unidimensional domains," Games and Economic Behavior, Elsevier, vol. 137(C), pages 228-269.
    2. Puppe, Clemens, 2018. "The single-peaked domain revisited: A simple global characterization," Journal of Economic Theory, Elsevier, vol. 176(C), pages 55-80.
    3. Bernard Monjardet, 2009. "Acyclic Domains of Linear Orders: A Survey," Studies in Choice and Welfare, in: Steven J. Brams & William V. Gehrlein & Fred S. Roberts (ed.), The Mathematics of Preference, Choice and Order, pages 139-160, Springer.
    4. Inada, Ken-Ichi, 1969. "The Simple Majority Decision Rule," Econometrica, Econometric Society, vol. 37(3), pages 490-506, July.
    5. Puppe, Clemens & Slinko, Arkadii, 2024. "Maximal Condorcet domains. A further progress report," Games and Economic Behavior, Elsevier, vol. 145(C), pages 426-450.
    6. 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.
    7. 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.
    8. Dominik Peters & Lan Yu & Hau Chan & Edith Elkind, 2022. "Preferences Single-Peaked on a Tree: Multiwinner Elections and Structural Results," Post-Print hal-03834509, HAL.
    9. 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.
    10. Demange, Gabrielle, 1982. "Single-peaked orders on a tree," Mathematical Social Sciences, Elsevier, vol. 3(4), pages 389-396, December.
    11. Partha Dasgupta & Eric Maskin, 2008. "On The Robustness of Majority Rule," Journal of the European Economic Association, MIT Press, vol. 6(5), pages 949-973, September.
    12. Jean-Marie Blin, 1972. "The General Concept of Multidimensional Consistency: Some Algebraic Aspects of the Aggregation Problem," Discussion Papers 12, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    13. Danilov, Vladimir I., 1994. "The structure of non-manipulable social choice rules on a tree," Mathematical Social Sciences, Elsevier, vol. 27(2), pages 123-131, April.
    14. H. Moulin, 1980. "On strategy-proofness and single peakedness," Public Choice, Springer, vol. 35(4), pages 437-455, January.
    15. Navin Aswal & Shurojit Chatterji & Arunava Sen, 2003. "Dictatorial domains," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 22(1), pages 45-62, August.
    16. Gibbard, Allan, 1973. "Manipulation of Voting Schemes: A General Result," Econometrica, Econometric Society, vol. 41(4), pages 587-601, July.
    17. Miguel Ballester & Guillaume Haeringer, 2011. "A characterization of the single-peaked domain," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 36(2), pages 305-322, February.
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