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On random social choice functions with the tops-only property

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  • Chatterji, Shurojit
  • Zeng, Huaxia

Abstract

We study the standard voting model with randomization. A Random Social Choice Function (or RSCF) satisfies the tops-only property if the social lottery under each preference profile depends only on the peaks of voters' preferences. We identify a general condition on domains of preferences (the Interior Property and the Exterior Property) which ensures that every strategy-proof RSCF satisfying unanimity has the tops-only property. We show that our condition applies to important classes of voting domains which include restricted connected domains (Sato, 2013) and the multi-dimensional single-peaked domain (Barberà et al., 1993). As an application of our result, we show that every ex-post efficient and strategy-proof RSCF defined on the multi-dimensional single-peaked domain is a random dictatorship.

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  • 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.
    • Handle: RePEc:eee:gamebe:v:109:y:2018:i:c:p:413-435
    DOI: 10.1016/j.geb.2017.11.011
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    2. Roy, Souvik & Sadhukhan, Soumyarup, 2021. "A unified characterization of the randomized strategy-proof rules," Journal of Economic Theory, Elsevier, vol. 197(C).
    3. Souvik Roy & Soumyarup Sadhukhan, 2019. "A characterization of random min–max domains and its applications," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 68(4), pages 887-906, November.
    4. 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.
    5. Roy, Souvik & Sadhukhan, Soumyarup, 2022. "On the equivalence of strategy-proofness and upper contour strategy-proofness for randomized social choice functions," Journal of Mathematical Economics, Elsevier, vol. 99(C).
    6. Chatterji, Shurojit & Zeng, Huaxia, 2019. "Random mechanism design on multidimensional domains," Journal of Economic Theory, Elsevier, vol. 182(C), pages 25-105.
    7. Bonifacio, Agustín G. & Massó, Jordi, 2020. "On strategy-proofness and semilattice single-peakedness," Games and Economic Behavior, Elsevier, vol. 124(C), pages 219-238.
    8. 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).
    9. Morimoto, Shuhei, 2022. "Group strategy-proof probabilistic voting with single-peaked preferences," Journal of Mathematical Economics, Elsevier, vol. 102(C).
    10. Madhuparna Karmokar & Souvik Roy, 2023. "The structure of (local) ordinal Bayesian incentive compatible random rules," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 76(1), pages 111-152, July.
    11. Felix Brand & Patrick Lederer & Sascha Tausch, 2023. "Strategyproof Social Decision Schemes on Super Condorcet Domains," Papers 2302.12140, arXiv.org.
    12. 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.

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    More about this item

    Keywords

    Random social choice functions; Unanimity; Strategy-proofness; The tops-only property; The interior property; The exterior property;
    All these keywords.

    JEL classification:

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

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