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A unified approach to strategy-proofness for single-peaked preferences

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  • John Weymark

Abstract

This article establishes versions of Moulin's [On strategy-proofness and single peakedness, Public Choice 35 (1980), 31--38] characterizations of various classes of strategy-proof social choice functions when the domain consists of all profiles of single-peaked preferences on an arbitrary subset of the real line. Two results are established that show that the median of 2n+1 numbers can be expressed using a combination of minimization and maximization operations applied to subsets of these numbers when either these subsets or the numbers themselves are restricted in a particular way. These results are used to show how Moulin's characterizations of generalized median social choice functions can be obtained as corollaries of his characterization of min-max social choice functions.
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  • John Weymark, 2011. "A unified approach to strategy-proofness for single-peaked preferences," SERIEs: Journal of the Spanish Economic Association, Springer;Spanish Economic Association, vol. 2(4), pages 529-550, December.
  • Handle: RePEc:spr:series:v:2:y:2011:i:4:p:529-550
    DOI: 10.1007/s13209-011-0064-5
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    3. Roy, Souvik & Sadhukhan, Soumyarup, 2021. "A unified characterization of the randomized strategy-proof rules," Journal of Economic Theory, Elsevier, vol. 197(C).
    4. 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.
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    6. 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.
    7. Peters, Hans & Roy, Souvik & Sen, Arunava & Storcken, Ton, 2014. "Probabilistic strategy-proof rules over single-peaked domains," Journal of Mathematical Economics, Elsevier, vol. 52(C), pages 123-127.
    8. 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.
    9. Chatterji, Shurojit & Zeng, Huaxia, 2023. "A taxonomy of non-dictatorial unidimensional domains," Games and Economic Behavior, Elsevier, vol. 137(C), pages 228-269.
    10. Ernesto Savaglio & Stefano Vannucci, 2019. "Strategy-proof aggregation rules and single peakedness in bounded distributive lattices," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 52(2), pages 295-327, February.
    11. Mridu Prabal Goswami, 2022. "Non-dictatorial public distribution rules," Review of Economic Design, Springer;Society for Economic Design, vol. 26(2), pages 165-183, June.
    12. Bonifacio, Agustín G. & Massó, Jordi, 2020. "On strategy-proofness and semilattice single-peakedness," Games and Economic Behavior, Elsevier, vol. 124(C), pages 219-238.
    13. Achuthankutty, Gopakumar & Roy, Souvik, 2017. "Strategy-proof Rules on Partially Single-peaked Domains," MPRA Paper 82267, University Library of Munich, Germany.
    14. Dolors Berga & Bernardo Moreno & Antonio Nicolò, 2023. "Undominated rules with three alternatives in an almost unrestricted domain," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 60(1), pages 65-74, January.
    15. 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).
    16. Haris Aziz & Alexander Lam & Barton E. Lee & Toby Walsh, 2021. "Strategyproof and Proportionally Fair Facility Location," Papers 2111.01566, arXiv.org, revised Nov 2023.
    17. Powers, Robert C. & Wells, Flannery, 2023. "Another strategy-proofness characterization of majority rule," Mathematical Social Sciences, Elsevier, vol. 122(C), pages 42-49.
    18. Achuthankutty, Gopakumar & Roy, Souvik, 2017. "On Top-connected Single-peaked and Partially Single-peaked Domains," MPRA Paper 78102, University Library of Munich, Germany.
    19. 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.

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    More about this item

    Keywords

    Generalized median social choice functions; Moulin min–max rules; Single-peaked preferences; Strategy-proofness; D71; D82;
    All these keywords.

    JEL classification:

    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design

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