Social Choice and Welfare

, Volume 41, Issue 2, pp 281–292 | Cite as

Power indices expressed in terms of minimal winning coalitions

  • Fabien Lange
  • László Á. KóczyEmail author
Original Paper


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.


Cooperative Game Power Index Simple Game Vote Power Winning Coalition 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag 2012

Authors and Affiliations

  1. 1.GREThA, Université Montesquieu Bordeaux 4BordeauxFrance
  2. 2.Centre for Economic and Regional StudiesHungarian Academy of SciencesBudapestHungary
  3. 3.Óbuda UniversityBudapestHungary

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