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Stable voting procedures for committees in economic environments

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  • Keiding, Hans
  • Peleg, Bezalel

Abstract

A strong representation of a committee, formalized as a simple game, on a convex and closed set of alternatives is a game form with the members of the committee as players such that (i) the winning coalitions of the simple game are exactly those coalitions, which can get any given alternative independent of the strategies of the complement, and (ii) for any profile of continuous and convex preferences, the resulting game has a strong Nash equilibrium. In the paper, it is investigated whether committees have representations on convex and compact subsets of Rm. This is shown to be the case if there are vetoers; for committees with no vetoers the existence of strong representations depends on the structure of the alternative set as well as on that of the committee (its Nakamura-number). Thus, if A is strictly convex, compact, and has smooth boundary, then no committee can have a strong representation on A. On the other hand, if A has non-smooth boundary, representations may exist depending on the Nakamura-number (if it is at least 7).

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Bibliographic Info

Article provided by Elsevier in its journal Journal of Mathematical Economics.

Volume (Year): 36 (2001)
Issue (Month): 2 (November)
Pages: 117-140

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Handle: RePEc:eee:mateco:v:36:y:2001:i:2:p:117-140

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Web page: http://www.elsevier.com/locate/jmateco

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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. Holzman, Ron, 1986. "The capacity of a committee," Mathematical Social Sciences, Elsevier, vol. 12(2), pages 139-157, October.
  3. 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).
  4. Greenberg, Joseph, 1979. "Consistent Majority Rules over Compact Sets of Alternatives," Econometrica, Econometric Society, vol. 47(3), pages 627-36, May.
  5. Dutta, Bhaskar & Pattanaik, Prasanta K, 1978. "On Nicely Consistent Voting Systems," Econometrica, Econometric Society, vol. 46(1), pages 163-70, January.
  6. Gibbard, Allan, 1973. "Manipulation of Voting Schemes: A General Result," Econometrica, Econometric Society, vol. 41(4), pages 587-601, July.
  7. Peleg, Bezalel, 1978. "Consistent Voting Systems," Econometrica, Econometric Society, vol. 46(1), pages 153-61, January.
  8. Moulin, H. & Peleg, B., 1982. "Cores of effectivity functions and implementation theory," Journal of Mathematical Economics, Elsevier, vol. 10(1), pages 115-145, June.
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Cited by:
  1. Keiding, Hans & Peleg, Bezalel, 2006. "On the continuity of representations of effectivity functions," Journal of Mathematical Economics, Elsevier, vol. 42(7-8), pages 827-842, November.
  2. Bezalel Peleg, 2002. "Complete Characterization of Acceptable Game Forms by Effectivity Functions," Discussion Paper Series dp283, The Center for the Study of Rationality, Hebrew University, Jerusalem.
  3. Peleg, Bezalel, 2004. "Representation of effectivity functions by acceptable game forms: a complete characterization," Mathematical Social Sciences, Elsevier, vol. 47(3), pages 275-287, May.

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