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Nash implementable domains for the Borda count

Author

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  • Puppe, Clemens
  • Tasnádi, Attila

Abstract

We characterize the preference domains on which the Borda count satisfies Maskin monotonicity. The basic concept is the notion of a "cyclic permutation domain" which arises by fixing one particular ordering of alternatives and including all its cyclic permutations. The cyclic permutation domains are exactly the maximal domains on which the Borda count is strategy-proof (when combined with every tie breaking rule). It turns out that the Borda count is monotonic on a larger class of domains. We show that the maximal domains on which the Borda count satisfies Maskin monotonicity are the "cyclically nested permutation domains." These are the preference domains which can be obtained from the cyclic permutation domains in an appropriate recursive way.

Suggested Citation

  • Puppe, Clemens & Tasnádi, Attila, 2006. "Nash implementable domains for the Borda count," MPRA Paper 775, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:775
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    File URL: https://mpra.ub.uni-muenchen.de/775/1/MPRA_paper_775.pdf
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    References listed on IDEAS

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    1. Kalai, Ehud & Ritz, Zvi, 1980. "Characterization of the private alternatives domains admitting arrow social welfare functions," Journal of Economic Theory, Elsevier, vol. 22(1), pages 23-36, February.
    2. Gaertner,Wulf, 2006. "Domain Conditions in Social Choice Theory," Cambridge Books, Cambridge University Press, number 9780521028745, April.
    3. Eric Maskin, 1999. "Nash Equilibrium and Welfare Optimality," Review of Economic Studies, Oxford University Press, vol. 66(1), pages 23-38.
    4. Muller, Eitan & Satterthwaite, Mark A., 1977. "The equivalence of strong positive association and strategy-proofness," Journal of Economic Theory, Elsevier, vol. 14(2), pages 412-418, April.
    5. Martin Barbie & Clemens Puppe & Attila Tasnádi, 2006. "Non-manipulable domains for the Borda count," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 27(2), pages 411-430, January.
    6. M. Sanver, 2009. "Strategy-proofness of the plurality rule over restricted domains," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 39(3), pages 461-471, June.
    7. Orhan Erdem & M. Sanver, 2005. "Minimal monotonic extensions of scoring rules," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 25(1), pages 31-42, October.
    8. Kalai, Ehud & Muller, Eitan, 1977. "Characterization of domains admitting nondictatorial social welfare functions and nonmanipulable voting procedures," Journal of Economic Theory, Elsevier, vol. 16(2), pages 457-469, December.
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    Cited by:

    1. Sanver, M. Remzi, 2008. "Nash implementability of the plurality rule over restricted domains," Economics Letters, Elsevier, vol. 99(2), pages 298-300, May.
    2. Ollár, Mariann, 2010. "Monotonicity and robustness of majority rule," Economics Letters, Elsevier, vol. 107(2), pages 288-290, May.
    3. Battal Doğan & Semih Koray, 2015. "Maskin-monotonic scoring rules," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 44(2), pages 423-432, February.

    More about this item

    Keywords

    Maskin monotonicity; Borda count; restricted preference domains;

    JEL classification:

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

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