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Power indices expressed in terms of minimal winning coalitions

Author

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  • László Á. Kóczy

    (Óbuda University)

  • Fabien Lange

    (Óbuda University)

Abstract

A voting situation is given by a set of voters and the rules of legislation that determine minimal requirements for a group of voters to pass a motion. A priori measures of voting power, such as the Shapley-Shubik index and the Banzhaf value, show the influence of the individual players. We used to calculate them by looking at marginal contributions in a simple game consisting of winning and losing coalitions derived from the rules of the legislation. We introduce a new way to calculate these measures directly from the set of minimal winning coalitions. This new approach logically appealing as it writes measures as functions of the rules of the legislation. For certain classes of games that arise naturally in applications the logical shortcut drastically simplifies calculations. The technique generalises directly to all semivalues. Keywords. Shapley-Shubik index, Banzhaf index, semivalue, minimal winning coalition, Möbius transform.

Suggested Citation

  • László Á. Kóczy & Fabien Lange, 2010. "Power indices expressed in terms of minimal winning coalitions," Working Paper Series 0909, Óbuda University, Keleti Faculty of Business and Management.
    • Handle: RePEc:pkk:wpaper:0909.rdf
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    File URL: http://uni-obuda.hu/users/vecseya/RePEc/pkk/wpaper/0909.pdf
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    Keywords

    Shapley-Shubik index; Banzhaf index; semivalue; minimal winning coalition; Möbius transform.;
    All these keywords.

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