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Acyclic domains of linear orders: a survey

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  • Bernard Monjardet

    (CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique)

Abstract
Among the many significant contributions that Fishburn made to social choice theory some have focused on what he has called "acyclic sets", i.e. the sets of linear orders where majority rule applies without the "Condorcet effect" (majority relation never has cycles). The search for large domains of this type is a fascinating topic. I review the works in this field and in particular consider a recent one that allows to show the connections between some of them that have been unrelated up to now.

Suggested Citation

  • Bernard Monjardet, 2009. "Acyclic domains of linear orders: a survey," Post-Print halshs-00198635, HAL.
    • Handle: RePEc:hal:journl:halshs-00198635
    DOI: 10.1007/978-3-540-79128-7_8
    Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-00198635
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    References listed on IDEAS

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    1. B. Monjardet, 1978. "An Axiomatic Theory of Tournament Aggregation," Mathematics of Operations Research, INFORMS, vol. 3(4), pages 334-351, November.
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    Cited by:

    1. Chatterji, Shurojit & Zeng, Huaxia, 2018. "On random social choice functions with the tops-only property," Games and Economic Behavior, Elsevier, vol. 109(C), pages 413-435.
    2. Liu, Peng, 2020. "Random assignments on sequentially dichotomous domains," Games and Economic Behavior, Elsevier, vol. 121(C), pages 565-584.
    3. Liu, Peng & Zeng, Huaxia, 2019. "Random assignments on preference domains with a tier structure," Journal of Mathematical Economics, Elsevier, vol. 84(C), pages 176-194.
    4. Roy, Souvik & Sadhukhan, Soumyarup, 2021. "A unified characterization of the randomized strategy-proof rules," Journal of Economic Theory, Elsevier, vol. 197(C).
    5. Puppe, Clemens, 2018. "The single-peaked domain revisited: A simple global characterization," Journal of Economic Theory, Elsevier, vol. 176(C), pages 55-80.
    6. Chatterji, Shurojit & Zeng, Huaxia, 2023. "A taxonomy of non-dictatorial unidimensional domains," Games and Economic Behavior, Elsevier, vol. 137(C), pages 228-269.
    7. Alexander Karpov & Arkadii Slinko, 2023. "Constructing large peak-pit Condorcet domains," Theory and Decision, Springer, vol. 94(1), pages 97-120, January.
    8. Gilbert Laffond & Jean Lainé, 2014. "Triple-consistent social choice and the majority rule," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(2), pages 784-799, July.
    9. Puppe, Clemens & Slinko, Arkadii, 2024. "Maximal Condorcet domains. A further progress report," Games and Economic Behavior, Elsevier, vol. 145(C), pages 426-450.
    10. Chatterji, Shurojit & Zeng, Huaxia, 2019. "Random mechanism design on multidimensional domains," Journal of Economic Theory, Elsevier, vol. 182(C), pages 25-105.
    11. Li, Guanhao, 2023. "A classification of peak-pit maximal Condorcet domains," Mathematical Social Sciences, Elsevier, vol. 125(C), pages 42-57.
    12. Bernard Monjardet, 2006. "Condorcet domains and distributive lattices," Post-Print halshs-00119141, HAL.
    13. Ping Zhan, 2019. "A simple construction of complete single-peaked domains by recursive tiling," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 90(3), pages 477-488, December.
    14. Saari, Donald G., 2014. "Unifying voting theory from Nakamura’s to Greenberg’s theorems," Mathematical Social Sciences, Elsevier, vol. 69(C), pages 1-11.
    15. Shurojit Chatterji & Souvik Roy & Soumyarup Sadhukhan & Arunava Sen & Huaxia Zeng, 2021. "Probabilistic Fixed Ballot Rules and Hybrid Domains," Papers 2105.10677, arXiv.org, revised Jan 2022.
    16. Olivier Hudry & Bernard Monjardet, 2010. "Consensus theories: an oriented survey," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00504974, HAL.
    17. Bredereck, Robert & Chen, Jiehua & Woeginger, Gerhard J., 2016. "Are there any nicely structured preference profiles nearby?," Mathematical Social Sciences, Elsevier, vol. 79(C), pages 61-73.
    18. Chatterji, Shurojit & Roy, Souvik & Sadhukhan, Soumyarup & Sen, Arunava & Zeng, Huaxia, 2022. "Probabilistic fixed ballot rules and hybrid domains," Journal of Mathematical Economics, Elsevier, vol. 100(C).
    19. Bernard Monjardet, 2008. ""Mathématique Sociale" and Mathematics. A case study: Condorcet's effect and medians," Post-Print halshs-00309825, HAL.
    20. 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.
    21. Li, Guanhao & Puppe, Clemens & Slinko, Arkadii, 2021. "Towards a classification of maximal peak-pit Condorcet domains," Mathematical Social Sciences, Elsevier, vol. 113(C), pages 191-202.
    22. Shurojit Chatterji & Huaxia Zeng, 2022. "A Taxonomy of Non-dictatorial Unidimensional Domains," Papers 2201.00496, arXiv.org, revised Oct 2022.
    23. Alexander Karpov, 2019. "On the Number of Group-Separable Preference Profiles," Group Decision and Negotiation, Springer, vol. 28(3), pages 501-517, June.
    24. Slinko, Arkadii, 2019. "Condorcet domains satisfying Arrow’s single-peakedness," Journal of Mathematical Economics, Elsevier, vol. 84(C), pages 166-175.
    25. Li, Guanhao & Puppe, Clemens & Slinko, Arkadii, 2020. "Towards a classification of maximal peak-pit Condorcet domains," Working Paper Series in Economics 144, Karlsruhe Institute of Technology (KIT), Department of Economics and Management.

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