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Nash implementable domains for the Borda count

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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.

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Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 775.

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Date of creation: 07 Nov 2006
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Handle: RePEc:pra:mprapa:775

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Keywords: Maskin monotonicity; Borda count; restricted preference domains;

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  1. Martin Barbie & Clemens Puppe & Attila Tasnádi, 2006. "Non-manipulable domains for the Borda count," Economic Theory, Springer, vol. 27(2), pages 411-430, January.
  2. M. Sanver, 2009. "Strategy-proofness of the plurality rule over restricted domains," Economic Theory, Springer, vol. 39(3), pages 461-471, June.
  3. Gaertner,Wulf, 2006. "Domain Conditions in Social Choice Theory," Cambridge Books, Cambridge University Press, number 9780521028745.
  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. Maskin, Eric, 1999. "Nash Equilibrium and Welfare Optimality," Review of Economic Studies, Wiley Blackwell, vol. 66(1), pages 23-38, January.
  6. Ehud Kalai & Zvi Ritz, 1978. "Characterization of the Private Alternative Domains Admitting Arrow Social Welfare Functions," Discussion Papers 341, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  7. Ehud Kalai & Eitan Muller, 1977. "Characterization of Domains Admitting Nondictatorial Social Welfare Functions and Nonmanipulable Voting Procedures," Discussion Papers 234, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  8. Orhan Erdem & M. Sanver, 2005. "Minimal monotonic extensions of scoring rules," Social Choice and Welfare, Springer, vol. 25(1), pages 31-42, October.
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