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Condorcet domains and distributive lattices

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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

Condorcet domains are sets of linear orders where Condorcet's effect can never occur. Works of Abello, Chameni-Nembua, Fishburn and Galambos and Reiner have allowed a strong understanding of a significant class of Condorcet domains which are distributive lattices -in fact covering distributive sublattices of the permutoèdre lattice- and which can be obtained from a maximal chain of this lattice. We describe this class and we study three particular types of such Condorcet domains.

Suggested Citation

  • Bernard Monjardet, 2006. "Condorcet domains and distributive lattices," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00119141, HAL.
    • Handle: RePEc:hal:cesptp:halshs-00119141
    Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-00119141
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    References listed on IDEAS

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    1. 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.
    2. Duquenne, Vincent & Cherfouh, Ameziane, 1994. "On permutation lattices," Mathematical Social Sciences, Elsevier, vol. 27(1), pages 73-89, February.
    3. Pierre Barthelemy, Jean & Monjardet, Bernard, 1981. "The median procedure in cluster analysis and social choice theory," Mathematical Social Sciences, Elsevier, vol. 1(3), pages 235-267, May.
    4. Kenneth J. Arrow & Herve Raynaud, 1986. "Social Choice and Multicriterion Decision-Making," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262511754, April.
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    Cited by:

    1. Puppe, Clemens, 2018. "The single-peaked domain revisited: A simple global characterization," Journal of Economic Theory, Elsevier, vol. 176(C), pages 55-80.
    2. Alexander Karpov & Arkadii Slinko, 2023. "Constructing large peak-pit Condorcet domains," Theory and Decision, Springer, vol. 94(1), pages 97-120, January.
    3. Slinko, Arkadii, 2019. "Condorcet domains satisfying Arrow’s single-peakedness," Journal of Mathematical Economics, Elsevier, vol. 84(C), pages 166-175.
    4. Li, Guanhao, 2023. "A classification of peak-pit maximal Condorcet domains," Mathematical Social Sciences, Elsevier, vol. 125(C), pages 42-57.

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