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Compound Voting and the Banzhaf Power Index

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Author Info

  • Pradeep Dubey

    ()

  • Ezra Einy

    ()

  • Ori Haimanko

    ()

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    Abstract

    We present three axioms for a power index defined on the domain of simple (voting) games. Positivity requires that no voter has negative power, and at least one has positive power. Transfer requires that, when winning coalitions are enhanced in a game, the change in voting power depends only on the change in the game, i.e., on the set of new winning coalitions. The most crucial axiom is composition: the value of a player in a compound voting game is the product of his power in the relevant first-tier game and the power of his delegate in the second-tier game. We prove that these three axioms categorically determine the Banzhaf index.

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    File URL: http://ratio.huji.ac.il/sites/default/files/publications/Haimanko333.pdf
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    Bibliographic Info

    Paper provided by The Center for the Study of Rationality, Hebrew University, Jerusalem in its series Discussion Paper Series with number dp333.

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    Length: 12 pages
    Date of creation: Aug 2003
    Date of revision:
    Handle: RePEc:huj:dispap:dp333

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    Related research

    Keywords: voting games; Banzhaf power index; compound games; composition axiom;

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    References

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    1. Federico Valenciano & Annick Laruelle, 2000. "- Shapley-Shubik And Banzhaf Indices Revisited," Working Papers. Serie AD 2000-02, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
    2. Lehrer, E, 1988. "An Axiomatization of the Banzhaf Value," International Journal of Game Theory, Springer, vol. 17(2), pages 89-99.
    3. M. Josune Albizuri & Luis M. Ruiz, 2001. "A new axiomatization of the Banzhaf semivalue," Spanish Economic Review, Springer, vol. 3(2), pages 97-109.
    4. Pradeep Dubey & Abraham Neyman & Robert J. Weber, 1979. "Value Theory without Efficiency," Cowles Foundation Discussion Papers 513, Cowles Foundation for Research in Economics, Yale University.
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    Cited by:
    1. Crama, Yves & Leruth, Luc, 2007. "Control and voting power in corporate networks: Concepts and computational aspects," European Journal of Operational Research, Elsevier, vol. 178(3), pages 879-893, May.

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