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Power indices expressed in terms of minimal winning coalitions

Author

Listed:
  • Fabien Lange

    (GREThA - Groupe de Recherche en Economie Théorique et Appliquée - UB - Université de Bordeaux - CNRS - Centre National de la Recherche Scientifique)

  • Laszlo A Koczy

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

Suggested Citation

  • Fabien Lange & Laszlo A Koczy, 2012. "Power indices expressed in terms of minimal winning coalitions," Post-Print hal-00780511, HAL.
    • Handle: RePEc:hal:journl:hal-00780511
    DOI: 10.1007/s00355.012.0685.z
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    Cited by:

    1. is not listed on IDEAS
    2. Antônio Francisco Neto & Carolina Rodrigues Fonseca, 2019. "An approach via generating functions to compute power indices of multiple weighted voting games with incompatible players," Annals of Operations Research, Springer, vol. 279(1), pages 221-249, August.
    3. Aleksei Y. Kondratev & Vladimir V. Mazalov, 2020. "Tournament solutions based on cooperative game theory," International Journal of Game Theory, Springer;Game Theory Society, vol. 49(1), pages 119-145, March.
    4. Debabrata Pal, 2021. "Does everyone have equal voting power?," Indian Economic Review, Springer, vol. 56(2), pages 515-525, December.
    5. Saadia Obadi & Silvia Miquel, 2017. "Clan information market games," Theory and Decision, Springer, vol. 82(4), pages 501-517, April.

    More about this item

    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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