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Tops-Only Domains

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Author Info

  • Shurojit Chatterji

    ()
    (School of Economics, Singapore Management University)

  • Arunava Sen

    ()
    (Indian Statistical Institute)

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.

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File URL: https://mercury.smu.edu.sg/rsrchpubupload/14580/topsfeb09(2).pdf
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Bibliographic Info

Paper provided by Singapore Management University, School of Economics in its series Working Papers with number 06-2009.

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Length: 32 pages
Date of creation: Feb 2009
Date of revision:
Publication status: Published in SMU Economics and Statistics Working Paper Series
Handle: RePEc:siu:wpaper:06-2009

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References

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  1. H. Moulin, 1980. "On strategy-proofness and single peakedness," Public Choice, Springer, vol. 35(4), pages 437-455, January.
  2. Barbera, Salvador & Masso, Jordi & Neme, Alejandro, 2005. "Voting by committees under constraints," Journal of Economic Theory, Elsevier, vol. 122(2), pages 185-205, June.
  3. Barbera, S. & Gul, F. & Stacchetti, E., 1992. "Generalized Median Voter Schemes and Committees," UFAE and IAE Working Papers 184.92, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
  4. Barbera, S. & Peleg, B., 1988. "Strategy-Proof Voting Schemes With Continuous Preferences," UFAE and IAE Working Papers 91.88, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
  5. Benoit, Jean-Pierre, 2002. "Strategic Manipulation in Voting Games When Lotteries and Ties Are Permitted," Journal of Economic Theory, Elsevier, vol. 102(2), pages 421-436, February.
  6. John Duggan & Thomas Schwartz, 2000. "Strategic manipulability without resoluteness or shared beliefs: Gibbard-Satterthwaite generalized," Social Choice and Welfare, Springer, vol. 17(1), pages 85-93.
  7. Selçuk Özyurt & M. Sanver, 2008. "Strategy-proof resolute social choice correspondences," Social Choice and Welfare, Springer, vol. 30(1), pages 89-101, January.
  8. Özyurt, Selçuk & Sanver, M. Remzi, 2009. "A general impossibility result on strategy-proof social choice hyperfunctions," Games and Economic Behavior, Elsevier, vol. 66(2), pages 880-892, July.
  9. Demange, Gabrielle, 1982. "Single-peaked orders on a tree," Mathematical Social Sciences, Elsevier, vol. 3(4), pages 389-396, December.
  10. Barbera, Salvador & Dutta, Bhaskar & Sen, Arunava, 2001. "Strategy-proof Social Choice Correspondences," Journal of Economic Theory, Elsevier, vol. 101(2), pages 374-394, December.
  11. Lars-Gunnar Svensson & Pär Torstensson, 2008. "Strategy-proof allocation of multiple public goods," Social Choice and Welfare, Springer, vol. 30(2), pages 181-196, February.
  12. Navin Aswal & Shurojit Chatterji & Arunava Sen, 2003. "Dictatorial domains," Economic Theory, Springer, vol. 22(1), pages 45-62, 08.
  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, 02.
  14. Kelly, Jerry S., 1989. "A new informational base for social choice," Mathematical Social Sciences, Elsevier, vol. 17(2), pages 177-188, April.
  15. Gibbard, Allan, 1973. "Manipulation of Voting Schemes: A General Result," Econometrica, Econometric Society, vol. 41(4), pages 587-601, July.
  16. Barbera, S. & Masso, J. & Neme, A., 1992. "Voting Under Constraints," UFAE and IAE Working Papers 200.92, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
  17. Lin Zhou & Stephen Ching, 2002. "Multi-valued strategy-proof social choice rules," Social Choice and Welfare, Springer, vol. 19(3), pages 569-580.
  18. Nehring, Klaus & Puppe, Clemens, 2007. "Efficient and strategy-proof voting rules: A characterization," Games and Economic Behavior, Elsevier, vol. 59(1), pages 132-153, April.
  19. Klaus, Bettina & Peters, Hans & Storcken, Ton, 1997. "Strategy-proof division of a private good when preferences are single-dipped," Economics Letters, Elsevier, vol. 55(3), pages 339-346, September.
  20. Nehring, Klaus & Puppe, Clemens, 2007. "The structure of strategy-proof social choice -- Part I: General characterization and possibility results on median spaces," Journal of Economic Theory, Elsevier, vol. 135(1), pages 269-305, July.
  21. Nicolas Gravel & Thierry Marchant & Arunava Sen, 2007. "Ranking Completely Uncertain Decisions by the Uniform Expected Utility Criterion," IDEP Working Papers 0705, Institut d'economie publique (IDEP), Marseille, France, revised 12 Jul 2007.
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Citations

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Cited by:
  1. Salvador Barberà & Dolors Berga & Bernardo Moreno, 2011. "Two Necessary Conditions for Strategy-Proofness: on What Domains are they also Sufficient?," UFAE and IAE Working Papers 892.11, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
  2. Shin Sato, 2010. "Circular domains," Review of Economic Design, Springer, vol. 14(3), pages 331-342, September.
  3. Debasis Mishra & Souvik Roy, 2011. "Strategy-proof partitioning," Indian Statistical Institute, Planning Unit, New Delhi Discussion Papers 11-06, Indian Statistical Institute, New Delhi, India.
  4. 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.
  5. Alex Gershkov & Benny Moldovanu & Xianwen Shi, 2013. "Optimal Mechanism Design without Money," Working Papers tecipa-481, University of Toronto, Department of Economics.
  6. 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.
  7. Shurojit Chatterji & Arunava Sen & Huaxia Zeng, 2012. "Random Dictatorship Domains," Working Papers 27-2012, Singapore Management University, School of Economics.

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