Power indices expressed in terms of minimal winning coalitions
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.
|Date of creation:||2010|
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- Márkus, Judit & Pintér, Miklós & Radványi, Anna, 2011.
"The Shapley value for airport and irrigation games,"
30031, University Library of Munich, Germany.
- Judit Markus & Anna Radvanyi & Miklos Pinter, 2012. "The Shapley Value for Airport and Irrigation Games," IEHAS Discussion Papers 1207, Institute of Economics, Centre for Economic and Regional Studies, Hungarian Academy of Sciences.
- Billot, Antoine & Thisse, Jacques-Francois, 2005.
"How to share when context matters: The Mobius value as a generalized solution for cooperative games,"
Journal of Mathematical Economics,
Elsevier, vol. 41(8), pages 1007-1029, December.
- BILLOT, Antoine & THISSE, Jean-François, 2002. "How to share when context matters: The Möbius value as a generalized solution for cooperative games," CORE Discussion Papers 2002025, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
- Jacques-François Thisse & Antoine Billot, 2005. "How to share when context matters : The Mobius value as a generalized solution for cooperative games," Post-Print halshs-00754051, HAL.
- Kóczy, László Á., 2012. "Beyond Lisbon: Demographic trends and voting power in the European Union Council of Ministers," Mathematical Social Sciences, Elsevier, vol. 63(2), pages 152-158.
- Lehrer, E, 1988. "An Axiomatization of the Banzhaf Value," International Journal of Game Theory, Springer;Game Theory Society, vol. 17(2), pages 89-99.
- 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).
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