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Hierarchy of players in swap robust voting games

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  • Monisankar Bishnu

    ()

  • Sonali Roy

    ()

Abstract

Ordinarily, the process of decision making by a committee through voting is modelled by a monotonic game the range of whose characteristic function is restricted to {0,1}. The decision rule that governs the collective action of a voting body induces a hierarchy in the set of players in terms of the a-priori influence that the players have over the decision making process. In order to determine this hierarchy in a swap robust game, one has to either evaluate a number-based power index (e.g., the Shapley-Shubik index, the Banzhaf-Coleman index) for each player or conduct a pairwise comparison between players in order to find out whether there exists a coalition in which player i is desirable over another player j as a coalition partner. In this paper we outline a much simpler and more elegant mechanism to determine the ranking of players in terms of their a-priori power using only minimal winning coalitions, rather than the entire set of winning coalitions.

(This abstract was borrowed from another version of this item.)

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File URL: http://hdl.handle.net/10.1007/s00355-010-0504-3
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Bibliographic Info

Article provided by Springer in its journal Social Choice and Welfare.

Volume (Year): 38 (2012)
Issue (Month): 1 (January)
Pages: 11-22

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Handle: RePEc:spr:sochwe:v:38:y:2012:i:1:p:11-22

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  1. Lawrence Diffo Lambo & Joël Moulen, 2002. "Ordinal equivalence of power notions in voting games," Theory and Decision, Springer, vol. 53(4), pages 313-325, December.
  2. Saari, Donald G. & Sieberg, Katri K., 2001. "Some Surprising Properties of Power Indices," Games and Economic Behavior, Elsevier, vol. 36(2), pages 241-263, August.
  3. Werner Kirsch & Jessica Langner, 2010. "Power indices and minimal winning coalitions," Social Choice and Welfare, Springer, vol. 34(1), pages 33-46, January.
  4. Josep Freixas, 2010. "On ordinal equivalence of the Shapley and Banzhaf values for cooperative games," International Journal of Game Theory, Springer, vol. 39(4), pages 513-527, October.
  5. Carreras, Francesc & Freixas, Josep, 1996. "Complete simple games," Mathematical Social Sciences, Elsevier, vol. 32(2), pages 139-155, October.
  6. Taylor Alan & Zwicker William, 1993. "Weighted Voting, Multicameral Representation, and Power," Games and Economic Behavior, Elsevier, vol. 5(1), pages 170-181, January.
  7. Moshé Machover & Dan S. Felsenthal, 2001. "The Treaty of Nice and qualified majority voting," Social Choice and Welfare, Springer, vol. 18(3), pages 431-464.
  8. Carreras, Francesc & Freixas, Josep, 2008. "On ordinal equivalence of power measures given by regular semivalues," Mathematical Social Sciences, Elsevier, vol. 55(2), pages 221-234, March.
  9. Josep Freixas & Montserrat Pons, 2010. "Hierarchies achievable in simple games," Theory and Decision, Springer, vol. 68(4), pages 393-404, April.
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