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On Strategy†Proofness And The Salience Of Single†Peakedness

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  • Shurojit Chatterji
  • Jordi Massó

Abstract

We consider strategy†proof rules operating on a rich domain of preference profiles. We show that if the rule satisfies in addition tops†onlyness, anonymity, and unanimity, then the preferences in the domain have to satisfy a variant of single†peakedness (referred to as semilattice single†peakedness). We do so by deriving from the rule an endogenous partial order (a semilattice) from which the concept of a semilattice single†peaked preference can be defined. We also provide a converse of this main finding. Finally, we show how well†known restricted domains under which nontrivial strategy†proof rules are admissible are semilattice single†peaked domains.

Suggested Citation

  • 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.
    • Handle: RePEc:wly:iecrev:v:59:y:2018:i:1:p:163-189
    DOI: 10.1111/iere.12266
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    Citations

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    Cited by:

    1. Bonifacio, Agustín G. & Massó, Jordi, 2020. "On strategy-proofness and semilattice single-peakedness," Games and Economic Behavior, Elsevier, vol. 124(C), pages 219-238.
    2. 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).
    3. Salvador Barberà & Dolors Berga & Bernardo Moreno, 2020. "Arrow on domain conditions: a fruitful road to travel," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 54(2), pages 237-258, March.
    4. 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).
    5. Roy, Souvik & Sadhukhan, Soumyarup, 2021. "A unified characterization of the randomized strategy-proof rules," Journal of Economic Theory, Elsevier, vol. 197(C).
    6. Puppe, Clemens, 2018. "The single-peaked domain revisited: A simple global characterization," Journal of Economic Theory, Elsevier, vol. 176(C), pages 55-80.
    7. Chatterji, Shurojit & Zeng, Huaxia, 2023. "A taxonomy of non-dictatorial unidimensional domains," Games and Economic Behavior, Elsevier, vol. 137(C), pages 228-269.
    8. 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.
    9. Shurojit Chatterji & Huaxia Zeng, 2022. "A Taxonomy of Non-dictatorial Unidimensional Domains," Papers 2201.00496, arXiv.org, revised Oct 2022.
    10. Ernesto Savaglio & Stefano Vannucci, 2022. "Strategy-proof aggregation rules in median semilattices with applications to preference aggregation," Papers 2208.12732, arXiv.org.
    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.

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