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

Author

Listed:
  • Shurojit Chatterji

    (School of Economics, Singapore Management University)

  • Arunava Sen

    (Indian Statistical Institute)

  • Huaxia Zeng

    (School of Economics, Singapore Management University)

Abstract

This 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 favor of the Gul conjecture (Barberà 2010).

Suggested Citation

  • Shurojit Chatterji & Arunava Sen & Huaxia Zeng, 2016. "A characterization of single-peaked preferences via random social choice functions," Economics and Statistics Working Papers 11-2016, Singapore Management University, School of Economics.
    • Handle: RePEc:ris:smuesw:2016_011
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    Cited by:

    1. Patrick Lederer, 2025. "Robust Voting Rules on the Interval Domain," Papers 2509.04874, arXiv.org.
    2. Stefano Vannucci, 2017. "Tree-Wise Single Peaked Domains," Department of Economics University of Siena 770, Department of Economics, University of Siena.
    3. Hatzivelkos, Aleksandar, 2024. "Note on compromise axiom," Mathematical Social Sciences, Elsevier, vol. 130(C), pages 38-47.
    4. 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).
    5. Shurojit Chatterji & Jordi Massó, 2015. "On Strategy-proofness and the Salience of Single-peakedness," Working Papers 828, Barcelona School of Economics.
    6. 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).
    7. Puppe, Clemens, 2018. "The single-peaked domain revisited: A simple global characterization," Journal of Economic Theory, Elsevier, vol. 176(C), pages 55-80.
    8. Vannucci, Stefano, 2020. "Single peaked domains with tree-shaped spectra," Mathematical Social Sciences, Elsevier, vol. 108(C), pages 74-80.
    9. 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.
    10. Morimoto, Shuhei, 2022. "Group strategy-proof probabilistic voting with single-peaked preferences," Journal of Mathematical Economics, Elsevier, vol. 102(C).
    11. 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.
    12. Chatterji, Shurojit & Zeng, Huaxia, 2019. "Random mechanism design on multidimensional domains," Journal of Economic Theory, Elsevier, vol. 182(C), pages 25-105.
    13. Matías Núñez & Carlos Pimienta & Dimitrios Xefteris, 2018. "Implementing the Median," Discussion Papers 2018-11, School of Economics, The University of New South Wales.
    14. 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.
    15. Núñez, Matías & Pimienta, Carlos & Xefteris, Dimitrios, 2022. "On the implementation of the median," Journal of Mathematical Economics, Elsevier, vol. 99(C).
    16. Karmokar, Madhuparna & Majumdar, Dipjyoti & Roy, Souvik, 2024. "Some further results on random OBIC rules," Mathematical Social Sciences, Elsevier, vol. 131(C), pages 102-112.

    More about this item

    Keywords

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    JEL classification:

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

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