Social Choice and Welfare

, Volume 28, Issue 2, pp 181–207 | Cite as

On the voting power of an alliance and the subsequent power of its members

  • Marc R. Feix
  • Dominique Lepelley
  • Vincent R. MerlinEmail author
  • Jean-Louis Rouet
Original Paper


Even, and in fact chiefly, if two or more players in a voting game have on a binary issue independent opinions, they may have interest to form a single voting alliance giving an average gain of influence for all of them. Here, assuming the usual independence of votes, we first study the alliance voting power and obtain new results in the so-called asymptotic limit for which the number of players is large enough and the alliance weight remains a small fraction of the total of the weights. Then, we propose to replace the voting game inside the alliance by a random game which allows new possibilities. The validity of the asymptotic limit and the possibility of new alliances are examined by considering the decision process in the Council of Ministers of the European Union.


Normal Approximation Power Index Asymptotic Limit Vote Power Approval Vote 
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Copyright information

© Springer-Verlag 2006

Authors and Affiliations

  • Marc R. Feix
    • 1
  • Dominique Lepelley
    • 2
  • Vincent R. Merlin
    • 3
    Email author
  • Jean-Louis Rouet
    • 4
    • 5
  1. 1.Ecole des Mines de NantesSUBATECHNantes cedex 3France
  2. 2.CERESUR, Department of EconomicsUniversité de la RéunionSaint-Denis cedex 9France
  3. 3.Centre de Recherche en Economie et Management (CREM)UMR6211 CNRS/Université de CaenCaen cedexFrance
  4. 4.Laboratoire de Mathématique, Applications et Physique Mathématique - UMR 6628Université d’Orléans, UFR des SciencesOrléans Cedex 2France
  5. 5.Institut des Sciences de la Terre d’Orléans (ISTO) UMR6113 CNRSUniversité d’Orléans 1AOrléans Cedex 2France

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