Power indices expressed in terms of minimal winning coalitions

Fabien Lange () and László Kóczy ()
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Fabien Lange: GREThA, Universit‚ Montesquieu Bordeaux 4.

No 1220, CERS-IE WORKING PAPERS from Institute of Economics, Centre for Economic and Regional Studies

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.

Keywords: Shapley-Shubik index; Banzhaf index; semivalue; minimal winning coalition; M”bius transform (search for similar items in EconPapers)
JEL-codes: C71 D72 (search for similar items in EconPapers)
Pages: 20 pages
Date: 2012-06
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Related works:
Journal Article: Power indices expressed in terms of minimal winning coalitions (2013)
Working Paper: Power indices expressed in terms of minimal winning coalitions (2012)
Working Paper: Power indices expressed in terms of minimal winning coalitions (2010)
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