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Stable Voting Procedures for Committees in Economic Environments

Author

Listed:
  • 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).

Suggested Citation

  • Hans Keiding & Bezalel Peleg, 1999. "Stable Voting Procedures for Committees in Economic Environments," Discussion Papers 99-20, University of Copenhagen. Department of Economics.
    • Handle: RePEc:kud:kuiedp:9920
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    File URL: http://www.econ.ku.dk/english/research/publications/wp/1999/9920.pdf/
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    References listed on IDEAS

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    1. Holzman, Ron, 1986. "The capacity of a committee," Mathematical Social Sciences, Elsevier, vol. 12(2), pages 139-157, October.
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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. Clempner, Julio B. & Poznyak, Alexander S., 2015. "Computing the strong Nash equilibrium for Markov chains games," Applied Mathematics and Computation, Elsevier, vol. 265(C), pages 911-927.
    3. Bezalel Peleg, 2002. "Complete Characterization of Acceptable Game Forms by Effectivity Functions," Discussion Paper Series dp283, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem.
    4. 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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    More about this item

    Keywords

    committees; simple games; representation; effectivity functions;
    All these keywords.

    JEL classification:

    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations
    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games

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