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On strategy-proofness and semilattice single-peakedness

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  • Agustín G. Bonifacio
  • Jordi Massó

Abstract

We study social choice rules defined on the domain of semilattice single- peaked preferences. Semilattice single-peakedness has been identified as the necessary condition that a set of preferences must satisfy so that the set can be the domain of a strategy-proof, tops-only, anonymous and unanimous rule. We characterize the class of all such rules on that domain and show that they are deeply related to the supremum of the underlying semilattice structure.

Suggested Citation

  • Agustín G. Bonifacio & Jordi Massó, 2019. "On strategy-proofness and semilattice single-peakedness," UFAE and IAE Working Papers 965.19, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
    • Handle: RePEc:aub:autbar:965.19
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    References listed on IDEAS

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    1. Shurojit Chatterji & Jordi Massó, 2018. "On Strategy†Proofness And The Salience Of Single†Peakedness," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 59(1), pages 163-189, February.
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    13. John A. Weymark, 2008. "Strategy‐Proofness and the Tops‐Only Property," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 10(1), pages 7-26, February.
    14. Barbera, Salvador & Sonnenschein, Hugo & Zhou, Lin, 1991. "Voting by Committees," Econometrica, Econometric Society, vol. 59(3), pages 595-609, May.
    15. 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.
    16. Chatterji, Shurojit & Sanver, Remzi & Sen, Arunava, 2013. "On domains that admit well-behaved strategy-proof social choice functions," Journal of Economic Theory, Elsevier, vol. 148(3), pages 1050-1073.
    17. Barbera, Salvador & Sonnenschein, Hugo & Zhou, Lin, 1991. "Voting by Committees," Econometrica, Econometric Society, vol. 59(3), pages 595-609, May.
    18. Danilov, Vladimir I., 1994. "The structure of non-manipulable social choice rules on a tree," Mathematical Social Sciences, Elsevier, vol. 27(2), pages 123-131, April.
    19. Kim C. Border & J. S. Jordan, 1983. "Straightforward Elections, Unanimity and Phantom Voters," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 50(1), pages 153-170.
    20. T. Storcken & H. Peters & H. v. d. Stel & W. Peremans, 1997. "Strategy-proofness on Euclidean spaces," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 14(3), pages 379-401.
    21. Yves Sprumont, 1995. "Strategyproof Collective Choice in Economic and Political Environments," Canadian Journal of Economics, Canadian Economics Association, vol. 28(1), pages 68-107, February.
    22. H. Moulin, 1980. "On strategy-proofness and single peakedness," Public Choice, Springer, vol. 35(4), pages 437-455, January.
    23. Ehlers, Lars & Peters, Hans & Storcken, Ton, 2002. "Strategy-Proof Probabilistic Decision Schemes for One-Dimensional Single-Peaked Preferences," Journal of Economic Theory, Elsevier, vol. 105(2), pages 408-434, August.
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    Cited by:

    1. Chatterji, Shurojit & Zeng, Huaxia, 2023. "A taxonomy of non-dictatorial unidimensional domains," Games and Economic Behavior, Elsevier, vol. 137(C), pages 228-269.
    2. 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.
    3. Shurojit Chatterji & Huaxia Zeng, 2022. "A Taxonomy of Non-dictatorial Unidimensional Domains," Papers 2201.00496, arXiv.org, revised Oct 2022.
    4. Ernesto Savaglio & Stefano Vannucci, 2022. "Strategy-proof aggregation rules in median semilattices with applications to preference aggregation," Papers 2208.12732, arXiv.org.
    5. Bonifacio, Agustín G. & Massó, Jordi & Neme, Pablo, 2023. "Preference restrictions for simple and strategy-proof rules: Local and weakly single-peaked domains," Journal of Mathematical Economics, Elsevier, vol. 106(C).
    6. 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).
    7. Ernesto Savaglio & Stefano Vannucci, 2021. "Strategy-Proof Aggregation Rules in Median Semilattices with Applications to Preference Aggregation," Department of Economics University of Siena 867, Department of Economics, University of Siena.

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    More about this item

    Keywords

    Strategy-proofness; Unanimity; Anonymity; Tops-onlyness; Single-peakedness.;
    All these keywords.

    JEL classification:

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

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