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Tops-Only Domains

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  • Shurojit Chatterji

    (SMU)

  • Arunava Sen

Abstract

In this paper we consider the standard voting model with a finite set of alternatives A and n voters and address the following question : what are the characteristics of domains D that induce the property that every strategy-proof social choice function f : Dn -> A satisfying unanimity, has the tops-only property? We first impose a minimal richness condition which ensures that for every alternative a, there exists an admissible ordering where a is maximal. We identify conditions on D that are sufficient for strategy-proofness and unanimity to imply tops onlyness in the general case of n voters and in the special case, n = 2. We provide an algorithm for constructing tops-only domains from connected graphs with elements of A as nodes. We provide several applications of our results. Finally, we relax the minimal richness assumption and partially extend our results.

Suggested Citation

  • Shurojit Chatterji & Arunava Sen, 2009. "Tops-Only Domains," Macroeconomics Working Papers 22064, East Asian Bureau of Economic Research.
  • Handle: RePEc:eab:macroe:22064
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    Citations

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    Cited by:

    1. Sato, Shin, 2013. "A sufficient condition for the equivalence of strategy-proofness and nonmanipulability by preferences adjacent to the sincere one," Journal of Economic Theory, Elsevier, vol. 148(1), pages 259-278.
    2. Puppe, Clemens, 2016. "The single-peaked domain revisited: A simple global characterization," Working Paper Series in Economics 97, Karlsruhe Institute of Technology (KIT), Department of Economics and Business Engineering.
    3. Azrieli, Yaron & Kim, Semin, 2016. "On the self-(in)stability of weighted majority rules," Games and Economic Behavior, Elsevier, pages 376-389.
    4. Chatterji, Shurojit & Sen, Arunava & Zeng, Huaxia, 2016. "A characterization of single-peaked preferences via random social choice functions," Theoretical Economics, Econometric Society, vol. 11(2), May.
    5. Chatterji, Shurojit & Sen, Arunava & Zeng, Huaxia, 2014. "Random dictatorship domains," Games and Economic Behavior, Elsevier, vol. 86(C), pages 212-236.
    6. Youngsub Chun & Manipushpak Mitra & Suresh Mutuswami, 2014. "Egalitarian equivalence and strategyproofness in the queueing problem," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), pages 425-442.
    7. Alex Gershkov & Benny Moldovanu & Xianwen Shi, 2013. "Optimal Mechanism Design without Money," Working Papers tecipa-481, University of Toronto, Department of Economics.
    8. Matías Núñez, 2014. "The strategic sincerity of Approval voting," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), pages 157-189.
    9. 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.
    10. Mishra, Debasis, 2016. "Ordinal Bayesian incentive compatibility in restricted domains," Journal of Economic Theory, Elsevier, vol. 163(C), pages 925-954.
    11. Alex Gershkov & Benny Moldovanu & Xianwen Shi, 2017. "Optimal Voting Rules," Review of Economic Studies, Oxford University Press, vol. 84(2), pages 688-717.
    12. Mishra, Debasis & Roy, Souvik, 2012. "Strategy-proof partitioning," Games and Economic Behavior, Elsevier, vol. 76(1), pages 285-300.
    13. Barberà, Salvador & Berga, Dolors & Moreno, Bernardo, 2012. "Two necessary conditions for strategy-proofness: On what domains are they also sufficient?," Games and Economic Behavior, Elsevier, pages 490-509.
    14. 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.
    15. Shin Sato, 2010. "Circular domains," Review of Economic Design, Springer;Society for Economic Design, vol. 14(3), pages 331-342, September.
    16. Gersbach, Hans, 2017. "Flexible Majority Rules in democracyville: A guided tour," Mathematical Social Sciences, Elsevier, vol. 85(C), pages 37-43.
    17. Shurojit Chatterji & Arunava Sen & Huaxia Zeng, 2012. "Random Dictatorship Domains," Working Papers 27-2012, Singapore Management University, School of Economics.
    18. Shurojit Chatterji & Arunava Sen & Huaxia Zeng, 2014. "A CHaracterization of Single-Peaked Preferences via Random Social Choice Functions," Working Papers 13-2014, Singapore Management University, School of Economics.

    More about this item

    Keywords

    Voting; social choice; tops-only domain;

    JEL classification:

    • D72 - Microeconomics - - Analysis of Collective Decision-Making - - - Political Processes: Rent-seeking, Lobbying, Elections, Legislatures, and Voting Behavior
    • D70 - Microeconomics - - Analysis of Collective Decision-Making - - - General

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