Power indices expressed in terms of minimal winning coalitions
AbstractA 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.
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Bibliographic InfoPaper provided by Óbuda University, Keleti Faculty of Business and Management in its series Working Paper Series with number 1002.
Length: 14 pages
Date of creation: 2010
Date of revision:
Shapley-Shubik index; Banzhaf index; semivalue; minimal winning coalition; Möbius transform.;
Other versions of this item:
- Fabien Lange & LÃ¡szlÃ³ KÃ³czy, 2013. "Power indices expressed in terms of minimal winning coalitions," Social Choice and Welfare, Springer, Springer, vol. 41(2), pages 281-292, July.
- Fabien Lange & Laszlo A. Koczy, 2012. "Power indices expressed in terms of minimal winning coalitions," IEHAS Discussion Papers 1220, Institute of Economics, Centre for Economic and Regional Studies, Hungarian Academy of Sciences.
- 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
This paper has been announced in the following NEP Reports:
- NEP-ALL-2010-06-04 (All new papers)
- NEP-CDM-2010-06-04 (Collective Decision-Making)
- NEP-GTH-2010-06-04 (Game Theory)
- NEP-POL-2010-06-04 (Positive Political Economics)
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- MÃ¡rkus, Judit & PintÃ©r, MiklÃ³s & RadvÃ¡nyi, 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, Jean-FranÃ§ois, 2002.
"How to share when context matters: The MÃ¶bius value as a generalized solution for cooperative games,"
CORE Discussion Papers, UniversitÃ© catholique de Louvain, Center for Operations Research and Econometrics (CORE)
2002025, UniversitÃ© catholique de Louvain, Center for Operations Research and Econometrics (CORE).
- 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.
- Federico Valenciano & Annick Laruelle, 2000. "- Shapley-Shubik And Banzhaf Indices Revisited," Working Papers. Serie AD, Instituto Valenciano de Investigaciones EconÃ³micas, S.A. (Ivie) 2000-02, Instituto Valenciano de Investigaciones EconÃ³micas, S.A. (Ivie).
- KÃ³czy, LÃ¡szlÃ³ Ã., 2012. "Beyond Lisbon: Demographic trends and voting power in the European Union Council of Ministers," Mathematical Social Sciences, Elsevier, Elsevier, vol. 63(2), pages 152-158.
- Lehrer, E, 1988. "An Axiomatization of the Banzhaf Value," International Journal of Game Theory, Springer, Springer, vol. 17(2), pages 89-99.
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