IDEAS home Printed from https://ideas.repec.org/p/bge/wpaper/273.html
   My bibliography  Save this paper

A Characterization of Single-Peaked Preferences

Author

Listed:
  • Miguel Ángel Ballester
  • Guillaume Haeringer

Abstract

We identify in this paper two conditions that characterize the domain of single-peaked preferences on the line in the following sense: a preference profile satisfies these two properties if and only if there exists a linear order L over the set of alternatives such that these preferences are single-peaked with respect L. The first property states that for any subset of alternatives the set of alternatives considered as the worst by all agents cannot contains more than 2 elements. The second property states that two agents cannot disagree on the relative ranking of two alternatives with respect to a third alternative but agree on the (relative) ranking of a fourth one.

Suggested Citation

  • Miguel Ángel Ballester & Guillaume Haeringer, 2006. "A Characterization of Single-Peaked Preferences," Working Papers 273, Barcelona School of Economics.
    • Handle: RePEc:bge:wpaper:273
    as

    Download full text from publisher

    File URL: https://www.barcelonagse.eu/sites/default/files/working_paper_pdfs/273.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Inada, Ken-Ichi, 1969. "The Simple Majority Decision Rule," Econometrica, Econometric Society, vol. 37(3), pages 490-506, July.
    2. Demange, Gabrielle, 1982. "Single-peaked orders on a tree," Mathematical Social Sciences, Elsevier, vol. 3(4), pages 389-396, December.
    3. Barbera, Salvador & Sonnenschein, Hugo & Zhou, Lin, 1991. "Voting by Committees," Econometrica, Econometric Society, vol. 59(3), pages 595-609, May.
    4. Barbera, Salvador & Sonnenschein, Hugo & Zhou, Lin, 1991. "Voting by Committees," Econometrica, Econometric Society, vol. 59(3), pages 595-609, May.
    5. H. Moulin, 1980. "On strategy-proofness and single peakedness," Public Choice, Springer, vol. 35(4), pages 437-455, January.
    6. Unknown, 1986. "Letters," Choices: The Magazine of Food, Farm, and Resource Issues, Agricultural and Applied Economics Association, vol. 1(4), pages 1-9.
    7. Klaus, Bettina & Peters, Hans & Storcken, Ton, 1997. "Strategy-proof division of a private good when preferences are single-dipped," Economics Letters, Elsevier, vol. 55(3), pages 339-346, September.
    8. Haluk I. Ergin, 2002. "Efficient Resource Allocation on the Basis of Priorities," Econometrica, Econometric Society, vol. 70(6), pages 2489-2497, November.
    9. 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.
    10. Trick, Michael A., 1989. "Recognizing single-peaked preferences on a tree," Mathematical Social Sciences, Elsevier, vol. 17(3), pages 329-334, 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. Walter Bossert & Hans Peters, 2009. "Single-peaked choice," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 41(2), pages 213-230, November.
    2. Vicki Knoblauch, 2008. "Recognizing a Single-Issue Spatial Election," Working papers 2008-26, University of Connecticut, Department of Economics.
    3. 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.
    4. Knoblauch, Vicki, 2010. "Recognizing one-dimensional Euclidean preference profiles," Journal of Mathematical Economics, Elsevier, vol. 46(1), pages 1-5, 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. 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.
    2. 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.
    3. 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.
    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 & 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.
    6. 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.
    7. Tobias Rachidi, 2020. "Optimal Voting Mechanisms on Generalized Single-Peaked Domains," CRC TR 224 Discussion Paper Series crctr224_2020_214, University of Bonn and University of Mannheim, Germany.
    8. Moulin, Hervé, 2017. "One dimensional mechanism design," Theoretical Economics, Econometric Society, vol. 12(2), May.
    9. Chatterji, Shurojit & Zeng, Huaxia, 2019. "Random mechanism design on multidimensional domains," Journal of Economic Theory, Elsevier, vol. 182(C), pages 25-105.
    10. Ernesto Savaglio & Stefano Vannucci, 2014. "Strategy-proofness and single-peackedness in bounded distributive lattices," Papers 1406.5120, arXiv.org.
    11. Shurojit Chatterji & Huaxia Zeng, 2022. "A Taxonomy of Non-dictatorial Unidimensional Domains," Papers 2201.00496, arXiv.org, revised Oct 2022.
    12. Bonifacio, Agustín G. & Massó, Jordi & Neme, Pablo, 2023. "Preference restrictions for simple and strategy-proof rules: Local and weakly single-peaked domains," Journal of Mathematical Economics, Elsevier, vol. 106(C).
    13. 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.
    14. M. Sanver, 2009. "Strategy-proofness of the plurality rule over restricted domains," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 39(3), pages 461-471, June.
    15. repec:spo:wpmain:info:hdl:2441/4ccevsvsdm96qpv5fgamlf1p1p is not listed on IDEAS
    16. Shurojit Chatterji & Arunava Sen, 2011. "Tops-only domains," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 46(2), pages 255-282, February.
    17. Block, Veronica, 2010. "Efficient and strategy-proof voting over connected coalitions: A possibility result," Economics Letters, Elsevier, vol. 108(1), pages 1-3, July.
    18. Sidartha Gordon, 2015. "Unanimity in attribute-based preference domains," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 44(1), pages 13-29, January.
    19. Vannucci, Stefano, 2020. "Single peaked domains with tree-shaped spectra," Mathematical Social Sciences, Elsevier, vol. 108(C), pages 74-80.
    20. Salvador Barberà & Dolors Berga & Bernardo Moreno, 2012. "Domains, ranges and strategy-proofness: the case of single-dipped preferences," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 39(2), pages 335-352, July.
    21. repec:spo:wpecon:info:hdl:2441/4ccevsvsdm96qpv5fgamlf1p1p is not listed on IDEAS
    22. Arribillaga, R. Pablo & Massó, Jordi & Neme, Alejandro, 2020. "On obvious strategy-proofness and single-peakedness," Journal of Economic Theory, Elsevier, vol. 186(C).

    More about this item

    Keywords

    Single-peaked preferences; lineal order;

    JEL classification:

    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations
    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory

    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:bge:wpaper:273. 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: Bruno Guallar (email available below). General contact details of provider: https://edirc.repec.org/data/bargses.html .

    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.