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Stable Voting Procedures for Committees in Economic Environments

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  • Hans Keiding

    (Institute of Economics, University of Copenhagen)

  • Bezalel Peleg

    (Hebrew University of Jerusalem)

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

Paper provided by University of Copenhagen. Department of Economics in its series Discussion Papers with number 99-20.

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Length: 26 pages
Date of creation: Jul 1999
Date of revision:
Handle: RePEc:kud:kuiedp:9920

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Keywords: committees; simple games; representation; effectivity functions;

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  1. Zhou, Lin, 1991. "Impossibility of Strategy-Proof Mechanisms in Economies with Pure Public Goods," Review of Economic Studies, Wiley Blackwell, vol. 58(1), pages 107-19, January.
  2. Greenberg, Joseph, 1979. "Consistent Majority Rules over Compact Sets of Alternatives," Econometrica, Econometric Society, vol. 47(3), pages 627-36, May.
  3. Satterthwaite, Mark Allen, 1975. "Strategy-proofness and Arrow's conditions: Existence and correspondence theorems for voting procedures and social welfare functions," Journal of Economic Theory, Elsevier, vol. 10(2), pages 187-217, April.
  4. Holzman, Ron, 1986. "The capacity of a committee," Mathematical Social Sciences, Elsevier, vol. 12(2), pages 139-157, October.
  5. Peleg, Bezalel, 1978. "Consistent Voting Systems," Econometrica, Econometric Society, vol. 46(1), pages 153-61, January.
  6. 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).
  7. Moulin, H. & Peleg, B., 1982. "Cores of effectivity functions and implementation theory," Journal of Mathematical Economics, Elsevier, vol. 10(1), pages 115-145, June.
  8. Dutta, Bhaskar & Pattanaik, Prasanta K, 1978. "On Nicely Consistent Voting Systems," Econometrica, Econometric Society, vol. 46(1), pages 163-70, January.
  9. Yves Sprumont, 1995. "Strategyproof Collective Choice in Economic and Political Environments," Canadian Journal of Economics, Canadian Economics Association, vol. 28(1), pages 68-107, February.
  10. Gibbard, Allan, 1973. "Manipulation of Voting Schemes: A General Result," Econometrica, Econometric Society, vol. 41(4), pages 587-601, July.
  11. H. Moulin, 1980. "On strategy-proofness and single peakedness," Public Choice, Springer, vol. 35(4), pages 437-455, January.
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Cited by:
  1. 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.
  2. Hans Keiding & Bezalel Peleg, 2003. "On the Continuity of Representations of Effectivity Functions," Discussion Papers 03-30, University of Copenhagen. Department of Economics.
  3. 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.

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