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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

Abstract

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.

Keywords

Normal Approximation Power Index Asymptotic Limit Vote Power Approval Vote 
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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References

  1. Banzhaf JF III (1965) Weighted voting doesn’t work. Rutgers Law Review Winter: 317–343Google Scholar
  2. Felsenthal DS, Machover M (1998) The measurement of voting power: theory and practice, problems and paradoxes. Edward Elgar, LondonGoogle Scholar
  3. Felsenthal DS, Machover M (2001) The treaty of nice and qualified majority voting. Soc Choice Welf 18:431–464CrossRefGoogle Scholar
  4. Felsenthal DS, Machover M (2002) Annexations and alliances: when are blocs advantageous a priori? Soc Choice Welf 19:295–312CrossRefGoogle Scholar
  5. Fristedt B, Gray L (1996) A modern approach to probability theory. Birkhauser, BostonGoogle Scholar
  6. Huang K (1963) Statistical mecanics. J Wiley, New-YorkGoogle Scholar
  7. Kittel C (1988) Elementary statistical physics. Krieger, Reprint editionGoogle Scholar
  8. Leech D (2003) Computing Power indices for large voting games. Manag Sci 49:831–837CrossRefGoogle Scholar
  9. Lindner I, Machover M (2004) LS Penrose’s limit theorem: proof of some special cases. Math Soc Sc 47:37–49CrossRefGoogle Scholar
  10. Owen G (1972) Multilinear extensions of games. Manag Sci 18:64–79CrossRefGoogle Scholar
  11. Owen G (1975) Multilinear extensions and the Banzhaf value. Nav Res Logist Q 22:741–750CrossRefGoogle Scholar
  12. Penrose LS (1946) The elementary statistics of majority voting. J R Stat Soc 109:53–57CrossRefGoogle Scholar
  13. Penrose LS (1952) On the objective study of crowd behavior. H.K. Lewis, LondonGoogle Scholar
  14. Rae D (1969) Decision rules and individual values in constitutional choice. Am Polit Sci Rev 63:40–56CrossRefGoogle Scholar
  15. Tribelsky MI (2002) General solution to the problem of the probability density for sums of random variables. Phys Rev Lett. 89, 7:070201-1–070201-4CrossRefGoogle Scholar

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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