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Power indices expressed in terms of minimal winning coalitions

Author

Listed:
  • Fabien Lange

    (GREThA, Universit‚ Montesquieu Bordeaux 4.)

  • Laszlo A. Koczy

    (Institute of Economics, Research Centre for Economic and Regional Studies, Hungarian Academy of Sciences)

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 in a voting situation and are calculated by looking at marginal contributions in a simple game consisting of winning and losing coalitions derived from the legislative rules. We introduce a new way to calculate these measures directly from the set of minimal winning coalitions and derive explicit formulae for the Shapley-Shubik and Banzhaf values. 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 the numerical calculations to obtain the indices. The technique generalises directly to all semivalues.

Suggested Citation

  • Fabien Lange & Laszlo A. Koczy, 2012. "Power indices expressed in terms of minimal winning coalitions," KRTK-KTI WORKING PAPERS 1220, Institute of Economics, Centre for Economic and Regional Studies.
    • Handle: RePEc:has:discpr:1220
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    References listed on IDEAS

    as
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    5. Saadia Obadi & Silvia Miquel, 2017. "Clan information market games," Theory and Decision, Springer, vol. 82(4), pages 501-517, April.

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    Keywords

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    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • D72 - Microeconomics - - Analysis of Collective Decision-Making - - - Political Processes: Rent-seeking, Lobbying, Elections, Legislatures, and Voting Behavior

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