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Configurations study for the Banzhaf and the Shapley-Shubik indices of power

Author

Listed:
  • Fabrice Barthélémy

    (THEMA, University of Cergy Pontoise)

  • Mathieu Martin

    (THEMA, University of Cergy Pontoise)

Abstract

How can we count and list all the Banzhaf or Shapley-Shubik index of power configurations for a given number of players? There is no formula in the literature that may give the cardinal of such a set, and moreover, even if this formula had existed, there is no formula which gives the configuration vectors. Even if we do not present such a formula, we present a methodology which enables to determine the set of configurations and its cardinality.

Suggested Citation

  • Fabrice Barthélémy & Mathieu Martin, 2007. "Configurations study for the Banzhaf and the Shapley-Shubik indices of power," THEMA Working Papers 2007-07, THEMA (THéorie Economique, Modélisation et Applications), Université de Cergy-Pontoise.
    • Handle: RePEc:ema:worpap:2007-07
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    References listed on IDEAS

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    1. Dennis Leech, 2003. "Computing Power Indices for Large Voting Games," Management Science, INFORMS, vol. 49(6), pages 831-837, June.
    2. Dan S. Felsenthal & Moshé Machover, 1998. "The Measurement of Voting Power," Books, Edward Elgar Publishing, number 1489.
    3. Shapley, L. S. & Shubik, Martin, 1954. "A Method for Evaluating the Distribution of Power in a Committee System," American Political Science Review, Cambridge University Press, vol. 48(3), pages 787-792, September.
    4. Guillermo Owen, 1972. "Multilinear Extensions of Games," Management Science, INFORMS, vol. 18(5-Part-2), pages 64-79, January.
    5. Leech, Dennis, 2002. "Computation of Power Indices," The Warwick Economics Research Paper Series (TWERPS) 644, University of Warwick, Department of Economics.
    6. Leech, Dennis, 2002. "Designing the Voting System for the Council of the European Union," Public Choice, Springer, vol. 113(3-4), pages 437-464, December.
    7. Leech, Dennis, 2002. "Computation Of Power Indices," Economic Research Papers 269457, University of Warwick - Department of Economics.
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    More about this item

    JEL classification:

    • C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory
    • D7 - Microeconomics - - Analysis of Collective Decision-Making

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