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A characterization of single-peaked preferences via random social choice functions

Author

Listed:
  • Chatterji, Shurojit

    (School of Economics, Singapore Management University)

  • Sen, Arunava

    (Planning Unit, Indian Statistical Institute, New Delhi)

  • Zeng, Huaxia

    (School of Economics, Singapore Management University)

Abstract

The paper proves the following result: every path-connected domain of preferences that admits a strategy-proof, unanimous, tops-only random social choice function satisfying a compromise property, is single-peaked. Conversely, every single-peaked domain admits a random social choice function satisfying these properties. Single-peakedness is defined with respect to arbitrary trees. The paper provides a justification of the salience of single-peaked preferences and evidence in favour of the Gul conjecture (\citet{barbsurvey}).

Suggested Citation

  • 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.
    • Handle: RePEc:the:publsh:1972
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    References listed on IDEAS

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    Citations

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    Cited by:

    1. Stefano Vannucci, 2017. "Tree-Wise Single Peaked Domains," Department of Economics University of Siena 770, Department of Economics, University of Siena.
    2. 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).
    3. Shurojit Catterji & Jordi Massó, 2015. "On Strategy-proofness and the Salience of Single-peakedness," Working Papers 828, Barcelona School of Economics.
    4. Peters, Hans & Roy, Souvik & Sadhukhan, Soumyarup, 2018. "Random social choice functions for single-peaked domains on trees," Research Memorandum 004, Maastricht University, Graduate School of Business and Economics (GSBE).
    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. Vannucci, Stefano, 2020. "Single peaked domains with tree-shaped spectra," Mathematical Social Sciences, Elsevier, vol. 108(C), pages 74-80.
    7. 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.
    8. Morimoto, Shuhei, 2022. "Group strategy-proof probabilistic voting with single-peaked preferences," Journal of Mathematical Economics, Elsevier, vol. 102(C).
    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 & Zeng, Huaxia, 2019. "Random mechanism design on multidimensional domains," Journal of Economic Theory, Elsevier, vol. 182(C), pages 25-105.
    11. Matías Núñez & Carlos Pimienta & Dimitrios Xefteris, 2018. "Implementing the Median," Discussion Papers 2018-11, School of Economics, The University of New South Wales.
    12. Yan Long, 2019. "Strategy-proof group selection under single-peaked preferences over group size," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 68(3), pages 579-608, October.
    13. Núñez, Matías & Pimienta, Carlos & Xefteris, Dimitrios, 2022. "On the implementation of the median," Journal of Mathematical Economics, Elsevier, vol. 99(C).

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    More about this item

    Keywords

    Random social choice functions; strategy-proofness; compromise; single-peaked preferences;
    All these keywords.

    JEL classification:

    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations

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