IDEAS home Printed from https://ideas.repec.org/p/hal/psewpa/halshs-00581310.html
   My bibliography  Save this paper

Majority relation and median representative ordering

Author

Listed:
  • Gabrielle Demange

    (PSE - Paris-Jourdan Sciences Economiques - ENS-PSL - École normale supérieure - Paris - PSL - Université Paris Sciences et Lettres - INRA - Institut National de la Recherche Agronomique - EHESS - École des hautes études en sciences sociales - ENPC - École des Ponts ParisTech - CNRS - Centre National de la Recherche Scientifique, PSE - Paris School of Economics - UP1 - Université Paris 1 Panthéon-Sorbonne - ENS-PSL - École normale supérieure - Paris - PSL - Université Paris Sciences et Lettres - EHESS - École des hautes études en sciences sociales - ENPC - École des Ponts ParisTech - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement)

Abstract

This paper presents results on the transitivity of the majority relation and the existence of a median representative ordering. Building on the notion of intermediate preferences indexed by a median graph, the analysis extends well-known results obtained when the underlying graph is a line. In contrast with other types of restrictions such as single-peakedness, intermediate preferences allow for a clear distinction between restrictions on the set of preferences characteristics and those on the set of alternatives.

Suggested Citation

  • Gabrielle Demange, 2011. "Majority relation and median representative ordering," PSE Working Papers halshs-00581310, HAL.
    • Handle: RePEc:hal:psewpa:halshs-00581310
    Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-00581310
    as

    Download full text from publisher

    File URL: https://shs.hal.science/halshs-00581310/document
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Hansen, Pierre & Thisse, Jacques-Francois, 1981. "Outcomes of voting and planning : Condorcet, Weber and Rawls locations," Journal of Public Economics, Elsevier, vol. 16(1), pages 1-15, August.
    2. Gabrielle Demange, 1983. "Spatial Models of Collective Choice," Post-Print halshs-00576802, HAL.
    3. Demange, Gabrielle, 1982. "Single-peaked orders on a tree," Mathematical Social Sciences, Elsevier, vol. 3(4), pages 389-396, December.
    4. Demange, Gabrielle, 1994. "Intermediate preferences and stable coalition structures," Journal of Mathematical Economics, Elsevier, vol. 23(1), pages 45-58, January.
    5. Grandmont, Jean-Michel, 1978. "Intermediate Preferences and the Majority Rule," Econometrica, Econometric Society, vol. 46(2), pages 317-330, March.
    6. Nehring, Klaus & Puppe, Clemens, 2007. "The structure of strategy-proof social choice -- Part I: General characterization and possibility results on median spaces," Journal of Economic Theory, Elsevier, vol. 135(1), pages 269-305, July.
    7. H. Moulin, 1980. "On strategy-proofness and single peakedness," Public Choice, Springer, vol. 35(4), pages 437-455, January.
    8. Barberà, Salvador & Moreno, Bernardo, 2011. "Top monotonicity: A common root for single peakedness, single crossing and the median voter result," Games and Economic Behavior, Elsevier, vol. 73(2), pages 345-359.
    9. Bandelt, Hans-Jurgen, 1985. "Networks with condorcet solutions," European Journal of Operational Research, Elsevier, vol. 20(3), pages 314-326, June.
    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. Bhattacharya, Mihir & Gravel, Nicolas, 2021. "Is the preference of the majority representative ?," Mathematical Social Sciences, Elsevier, vol. 114(C), pages 87-94.
    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. Demange, Gabrielle, 2024. "Stable outcomes in simple cooperative games," Journal of Mathematical Economics, Elsevier, vol. 111(C).
    4. Gabrielle Demange, 2017. "The stability of group formation," Revue d'économie politique, Dalloz, vol. 127(4), pages 495-516.
    5. Slinko, Arkadii, 2019. "Condorcet domains satisfying Arrow’s single-peakedness," Journal of Mathematical Economics, Elsevier, vol. 84(C), pages 166-175.
    6. Mihir Bhattacharya & Nicolas Gravel, 2019. "Is the Preference of the Majority Representative?," Working Papers 1028, Ashoka University, Department of Economics.
    7. Berno Buechel, 2014. "Condorcet winners on median spaces," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 42(3), pages 735-750, March.
    8. Slinko, Arkadii & Wu, Qinggong & Wu, Xingye, 2021. "A characterization of preference domains that are single-crossing and maximal Condorcet," Economics Letters, Elsevier, vol. 204(C).
    9. 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.

    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. Demange, Gabrielle, 2024. "Stable outcomes in simple cooperative games," Journal of Mathematical Economics, Elsevier, vol. 111(C).
    2. Roy, Souvik & Sadhukhan, Soumyarup, 2021. "A unified characterization of the randomized strategy-proof rules," Journal of Economic Theory, Elsevier, vol. 197(C).
    3. Salvador Barberà & Dolors Berga & Bernardo Moreno, 2020. "Arrow on domain conditions: a fruitful road to travel," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 54(2), pages 237-258, March.
    4. Chatterji, Shurojit & Zeng, Huaxia, 2023. "A taxonomy of non-dictatorial unidimensional domains," Games and Economic Behavior, Elsevier, vol. 137(C), pages 228-269.
    5. Chatterji, Shurojit & Zeng, Huaxia, 2019. "Random mechanism design on multidimensional domains," Journal of Economic Theory, Elsevier, vol. 182(C), pages 25-105.
    6. Robert Bredereck & Jiehua Chen & Gerhard Woeginger, 2013. "A characterization of the single-crossing domain," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 41(4), pages 989-998, October.
    7. Ernesto Savaglio & Stefano Vannucci, 2014. "Strategy-proofness and single-peackedness in bounded distributive lattices," Papers 1406.5120, arXiv.org.
    8. Gopakumar Achuthankutty & Souvik Roy, 2018. "On single-peaked domains and min–max rules," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 51(4), pages 753-772, December.
    9. Hans Peters & Souvik Roy & Soumyarup Sadhukhan, 2021. "Unanimous and Strategy-Proof Probabilistic Rules for Single-Peaked Preference Profiles on Graphs," Mathematics of Operations Research, INFORMS, vol. 46(2), pages 811-833, May.
    10. 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).
    11. Madhuparna Karmokar & Souvik Roy & Ton Storcken, 2021. "Necessary and sufficient conditions for pairwise majority decisions on path-connected domains," Theory and Decision, Springer, vol. 91(3), pages 313-336, October.
    12. Edith Elkind & Piotr Faliszewski & Piotr Skowron, 2020. "A characterization of the single-peaked single-crossing domain," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 54(1), pages 167-181, January.
    13. Shurojit Chatterji & Huaxia Zeng, 2022. "A Taxonomy of Non-dictatorial Unidimensional Domains," Papers 2201.00496, arXiv.org, revised Oct 2022.
    14. 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.
    15. Bossert, Walter & Sprumont, Yves, 2014. "Strategy-proof preference aggregation: Possibilities and characterizations," Games and Economic Behavior, Elsevier, vol. 85(C), pages 109-126.
    16. Haeringer, Guillaume & Hałaburda, Hanna, 2016. "Monotone strategyproofness," Games and Economic Behavior, Elsevier, vol. 98(C), pages 68-77.
    17. Chatterji, Shurojit & Sanver, Remzi & Sen, Arunava, 2013. "On domains that admit well-behaved strategy-proof social choice functions," Journal of Economic Theory, Elsevier, vol. 148(3), pages 1050-1073.
    18. Vannucci, Stefano, 2020. "Single peaked domains with tree-shaped spectra," Mathematical Social Sciences, Elsevier, vol. 108(C), pages 74-80.
    19. Chatterji, Shurojit & Sen, Arunava & Zeng, Huaxia, 2016. "A characterization of single-peaked preferences via random social choice functions," Theoretical Economics, Econometric Society, vol. 11(2), May.
    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.

    More about this item

    Keywords

    majority rule; median graph; tree; Condorcet winner; intermediate preferences;
    All these keywords.

    JEL classification:

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    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:psewpa:halshs-00581310. 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.