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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References
Banzhaf JF III (1965) Weighted voting doesn’t work. Rutgers Law Review Winter: 317–343
Felsenthal DS, Machover M (1998) The measurement of voting power: theory and practice, problems and paradoxes. Edward Elgar, London
Felsenthal DS, Machover M (2001) The treaty of nice and qualified majority voting. Soc Choice Welf 18:431–464
Felsenthal DS, Machover M (2002) Annexations and alliances: when are blocs advantageous a priori? Soc Choice Welf 19:295–312
Fristedt B, Gray L (1996) A modern approach to probability theory. Birkhauser, Boston
Huang K (1963) Statistical mecanics. J Wiley, New-York
Kittel C (1988) Elementary statistical physics. Krieger, Reprint edition
Leech D (2003) Computing Power indices for large voting games. Manag Sci 49:831–837
Lindner I, Machover M (2004) LS Penrose’s limit theorem: proof of some special cases. Math Soc Sc 47:37–49
Owen G (1972) Multilinear extensions of games. Manag Sci 18:64–79
Owen G (1975) Multilinear extensions and the Banzhaf value. Nav Res Logist Q 22:741–750
Penrose LS (1946) The elementary statistics of majority voting. J R Stat Soc 109:53–57
Penrose LS (1952) On the objective study of crowd behavior. H.K. Lewis, London
Rae D (1969) Decision rules and individual values in constitutional choice. Am Polit Sci Rev 63:40–56
Tribelsky MI (2002) General solution to the problem of the probability density for sums of random variables. Phys Rev Lett. 89, 7:070201-1–070201-4
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Feix, M.R., Lepelley, D., Merlin, V.R. et al. On the voting power of an alliance and the subsequent power of its members. Soc Choice Welfare 28, 181–207 (2007). https://doi.org/10.1007/s00355-006-0171-6
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DOI: https://doi.org/10.1007/s00355-006-0171-6