IDEAS home Printed from https://ideas.repec.org/p/hal/cesptp/halshs-00119141.html
   My bibliography  Save this paper

Condorcet domains and distributive lattices

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: https://shs.hal.science/halshs-00119141/document
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. 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.
    2. 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.
    3. 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.
    4. Duquenne, Vincent & Cherfouh, Ameziane, 1994. "On permutation lattices," Mathematical Social Sciences, Elsevier, vol. 27(1), pages 73-89, February.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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. Slinko, Arkadii, 2019. "Condorcet domains satisfying Arrow’s single-peakedness," Journal of Mathematical Economics, Elsevier, vol. 84(C), pages 166-175.
    3. Li, Guanhao, 2023. "A classification of peak-pit maximal Condorcet domains," Mathematical Social Sciences, Elsevier, vol. 125(C), pages 42-57.
    4. Alexander Karpov & Arkadii Slinko, 2023. "Constructing large peak-pit Condorcet domains," Theory and Decision, Springer, vol. 94(1), pages 97-120, January.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Bernard Monjardet, 2008. ""Mathématique Sociale" and Mathematics. A case study: Condorcet's effect and medians," Post-Print halshs-00309825, HAL.
    2. Olivier Hudry & Bernard Monjardet, 2010. "Consensus theories: An oriented survey," Documents de travail du Centre d'Economie de la Sorbonne 10057, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
    3. William Gehrlein, 2002. "Condorcet's paradox and the likelihood of its occurrence: different perspectives on balanced preferences ," Theory and Decision, Springer, vol. 52(2), pages 171-199, March.
    4. Hudry, Olivier, 2009. "A survey on the complexity of tournament solutions," Mathematical Social Sciences, Elsevier, vol. 57(3), pages 292-303, May.
    5. Joey Au & Andrew Coleman & Trudy Sullivan, 2015. "A Practical Approach to Well-being Based Policy Development: What Do New Zealanders Want from Their Retirement Income Policies?," Treasury Working Paper Series 15/14, New Zealand Treasury.
    6. Hannu Salonen, 2014. "Aggregating and Updating Information," Czech Economic Review, Charles University Prague, Faculty of Social Sciences, Institute of Economic Studies, vol. 8(2), pages 55-67, October.
    7. Dias, Luis C. & Lamboray, Claude, 2010. "Extensions of the prudence principle to exploit a valued outranking relation," European Journal of Operational Research, Elsevier, vol. 201(3), pages 828-837, March.
    8. 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.
    9. Nehring, Klaus & Pivato, Marcus & Puppe, Clemens, 2014. "The Condorcet set: Majority voting over interconnected propositions," Journal of Economic Theory, Elsevier, vol. 151(C), pages 268-303.
    10. Nehring, Klaus & Pivato, Marcus & Puppe, Clemens, 2011. "Condorcet admissibility: Indeterminacy and path-dependence under majority voting on interconnected decisions," MPRA Paper 32434, University Library of Munich, Germany.
    11. Tangian, Andranik S., 2004. "Constructing the composite indicator "Quality of work" from the third European survey on working conditions," WSI Working Papers 132, The Institute of Economic and Social Research (WSI), Hans Böckler Foundation.
    12. 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.
    13. Marcus Pivato, 2013. "Voting rules as statistical estimators," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 40(2), pages 581-630, February.
    14. Dewan F. Wahid & Elkafi Hassini, 2022. "A Literature Review on Correlation Clustering: Cross-disciplinary Taxonomy with Bibliometric Analysis," SN Operations Research Forum, Springer, vol. 3(3), pages 1-42, September.
    15. 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.
    16. Zachary F. Lansdowne, 1996. "Ordinal ranking methods for multicriterion decision making," Naval Research Logistics (NRL), John Wiley & Sons, vol. 43(5), pages 613-627, August.
    17. Chatterji, Shurojit & Zeng, Huaxia, 2023. "A taxonomy of non-dictatorial unidimensional domains," Games and Economic Behavior, Elsevier, vol. 137(C), pages 228-269.
    18. Mala, Jozsef, 1999. "On [lambda]-majority voting paradoxes," Mathematical Social Sciences, Elsevier, vol. 37(1), pages 39-44, January.
    19. Pivato, Marcus, 2017. "Epistemic democracy with correlated voters," Journal of Mathematical Economics, Elsevier, vol. 72(C), pages 51-69.
    20. Bernard Monjardet, 2011. "G. Th. Guilbaud et la théorie du choix social," Documents de travail du Centre d'Economie de la Sorbonne 11047, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:hal:cesptp:halshs-00119141. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: CCSD (email available below). General contact details of provider: https://hal.archives-ouvertes.fr/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.