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

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Author Info
M.R. Feix (SUBATECH/EMN)
D. Lepelley (CERESUR)
V. Merlin (CREM – CNRS)
J.L. Rouet (MAPMO – CNRS)

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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.

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Paper provided by Center for Research in Economics and Management (CREM), University of Rennes 1, University of Caen and CNRS in its series Economics Working Paper Archive (University of Rennes 1 & University of Caen) with number 200605.

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Date of creation: 2006
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Handle: RePEc:tut:cremwp:200605

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  1. Moshé Machover & Dan S. Felsenthal, 2001. "The Treaty of Nice and qualified majority voting," Social Choice and Welfare, Springer, vol. 18(3), pages 431-464. [Downloadable!] (restricted)
  2. Moshé Machover & Dan S. Felsenthal, 2002. "Annexations and alliances: When are blocs advantageous a priori?," Social Choice and Welfare, Springer, vol. 19(2), pages 295-312. [Downloadable!] (restricted)
  3. Leech, D., 1998. "Computing Power Indices for Large Voting Games: A New Algorithm," The Warwick Economics Research Paper Series (TWERPS) 510, University of Warwick, Department of Economics.
  4. Lindner, Ines & Machover, Moshe, 2004. "L.S. Penrose's limit theorem: proof of some special cases," Mathematical Social Sciences, Elsevier, vol. 47(1), pages 37-49, January. [Downloadable!] (restricted)
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  1. 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. [Downloadable!]
  2. Michel Grabisch & Agnieszka Rusinowska, 2009. "A model of influence in a social network," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00308741_v1, HAL. [Downloadable!]
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