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On the Voting Power of an Alliance and the Subsequent Power of its Members

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Author Info

  • Vincent Merlin

    ()
    (CREM - Centre de Recherche en Economie et Management - CNRS : UMR6211 - Université de Rennes I - Université de Caen)

  • Marc Feix

    (MAPMO - Mathématiques et Applications, Physique Mathématique d'Orléans - CNRS : UMR6628 - Université d'Orléans)

  • Dominique Lepelley

    (CREM - Centre de Recherche en Economie et Management - CNRS : UMR6211 - Université de Rennes I - Université de Caen, CERESUR - Centre d'Etudes et de Recherches Economique et Sociales de l'Université de La Réunion - Université de la Réunion)

  • Jean-Louis Rouet

    (MAPMO - Mathématiques et Applications, Physique Mathématique d'Orléans - CNRS : UMR6628 - Université d'Orléans)

Abstract

Even, and in fact chiefly, if two or more players in a voting gamehave on a binary issue independent opinions, they may haveinterest to form a single voting alliance giving an average gainof influence for all of them. Here, assuming the usualindependence of votes, we first study the alliance voting powerand obtain new results in the so-called asymptotic limit for whichthe number of players is large enough and the alliance weightremains a small fraction of the total of the weights. Then, wepropose to replace the voting game inside the alliance by a randomgame which allows new possibilities. The validity of theasymptotic limit and the possibility of new alliances are examinedby considering the decision process in the Council of Ministers ofthe European Union.

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Bibliographic Info

Paper provided by HAL in its series Post-Print with number halshs-00010168.

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Date of creation: 2007
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Publication status: Published, Social Choice and Welfare, 2007, 28, 2, 181--207
Handle: RePEc:hal:journl:halshs-00010168

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Keywords: Voting Power; Alliance;

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References

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  1. Moshé Machover & Dan S. Felsenthal, 2001. "The Treaty of Nice and qualified majority voting," Social Choice and Welfare, Springer, Springer, vol. 18(3), pages 431-464.
  2. Dan S. Felsenthal & Moshé Machover, 2002. "Annexations and alliances: When are blocs advantageous a priori?," Social Choice and Welfare, Springer, Springer, vol. 19(2), pages 295-312, April.
  3. Lindner, Ines & Machover, Moshe, 2004. "L.S. Penrose's limit theorem: proof of some special cases," Mathematical Social Sciences, Elsevier, Elsevier, vol. 47(1), pages 37-49, January.
  4. Guillermo Owen, 1972. "Multilinear Extensions of Games," Management Science, INFORMS, INFORMS, vol. 18(5-Part-2), pages 64-79, January.
  5. Dennis Leech, 2003. "Computing Power Indices for Large Voting Games," Management Science, INFORMS, INFORMS, vol. 49(6), pages 831-837, June.
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Cited by:
  1. repec:hal:journl:halshs-00344457 is not listed on IDEAS
  2. Michel Grabisch & Agnieszka Rusinowska, 2010. "A model of influence in a social network," Theory and Decision, Springer, Springer, vol. 69(1), pages 69-96, July.
  3. repec:hal:journl:halshs-00308741 is not listed on IDEAS
  4. Fabrice Barthélémy & Mathieu MARTIN, 2007. "A comparison between the methods of apportionment using power indices: the case of the U.S. presidential election," THEMA Working Papers 2007-26, THEMA (THéorie Economique, Modélisation et Applications), Université de Cergy-Pontoise.

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