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Strategy-proof social choice on multiple and multi-dimensional single-peaked domains

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  • Reffgen, Alexander

Abstract

We generalize the traditional concept of single-peaked preference domains in two ways. First, we introduce the concept of a multiple single-peaked domain, where the set of alternatives is equipped with several underlying orderings with respect to which a preference can be single-peaked, and we argue that these domains are appropriate to represent preferences over political parties. Second, we define a domain of multi-dimensional single-peaked preferences based on the condition of value-restricted preferences by Sen [34]. We provide complete characterizations of the strategy-proof social choice functions on both multiple and multi-dimensional single-peaked domains. For both domains, we also identify the subclasses consisting of all anonymous strategy-proof social choice functions.

Suggested Citation

  • Reffgen, Alexander, 2015. "Strategy-proof social choice on multiple and multi-dimensional single-peaked domains," Journal of Economic Theory, Elsevier, vol. 157(C), pages 349-383.
    • Handle: RePEc:eee:jetheo:v:157:y:2015:i:c:p:349-383
    DOI: 10.1016/j.jet.2014.12.010
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    Cited by:

    1. 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.
    2. Mishra, Debasis, 2016. "Ordinal Bayesian incentive compatibility in restricted domains," Journal of Economic Theory, Elsevier, vol. 163(C), pages 925-954.
    3. Bonifacio, Agustín G. & Massó, Jordi, 2020. "On strategy-proofness and semilattice single-peakedness," Games and Economic Behavior, Elsevier, vol. 124(C), pages 219-238.
    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. Karmokar, Madhuparna & Roy, Souvik, 2020. "The structure of (local) ordinal Bayesian incentive compatible random rules," MPRA Paper 103494, University Library of Munich, Germany.
    6. Chatterji, Shurojit & Zeng, Huaxia, 2023. "A taxonomy of non-dictatorial unidimensional domains," Games and Economic Behavior, Elsevier, vol. 137(C), pages 228-269.
    7. Aroon Narayanan, 2021. "Single-peaked domains with designer uncertainty," Papers 2108.11268, arXiv.org.
    8. Achuthankutty, Gopakumar & Roy, Souvik, 2017. "On Top-connected Single-peaked and Partially Single-peaked Domains," MPRA Paper 78102, University Library of Munich, Germany.
    9. 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.
    10. Shurojit Chatterji & Huaxia Zeng, 2022. "A Taxonomy of Non-dictatorial Unidimensional Domains," Papers 2201.00496, arXiv.org, revised Oct 2022.
    11. Achuthankutty, Gopakumar & Roy, Souvik, 2017. "Strategy-proof Rules on Partially Single-peaked Domains," MPRA Paper 82267, University Library of Munich, Germany.
    12. Mishra, Debasis & Pramanik, Anup & Roy, Souvik, 2016. "Local incentive compatibility with transfers," Games and Economic Behavior, Elsevier, vol. 100(C), pages 149-165.
    13. Aroon Narayanan, 2023. "Single-peaked domains with designer uncertainty," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 60(4), pages 561-578, May.
    14. Shurojit Chatterji & Souvik Roy & Soumyarup Sadhukhan & Arunava Sen & Huaxia Zeng, 2021. "Probabilistic Fixed Ballot Rules and Hybrid Domains," Papers 2105.10677, arXiv.org, revised Jan 2022.
    15. Karmokar, Madhuparna & Roy, Souvik & Storcken, Ton, 2019. "A characterization of possibility domains under Pareto optimality and group strategy-proofness," Economics Letters, Elsevier, vol. 183(C), pages 1-1.

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    More about this item

    Keywords

    Social choice function; Strategy-proofness; Single-peakedness; Spatial voting;
    All these keywords.

    JEL classification:

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

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