Abstract
In this paper we define and axiomatically characterize an extension of the Deegan–Packel index for simple games with a priori unions. A real-world example illustrates this extension.
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Albizuri M.J.: An axiomatization of the modified Banzhaf-Coleman index. Int. J. Game Theory 30, 167–176 (2001)
Alonso-Meijide J.M., Bowles C.: Generating functions for coalitional power indices: an application to IMF. Ann. Oper. Res. 137, 21–44 (2005)
Alonso-Meijide J.M., Fiestras-Janeiro M.G.: Modification of the Banzhaf value for games with a coalition structure. Ann. Oper. Res. 109, 213–227 (2002)
Alonso-Meijide J.M., Carreras F., Fiestras-Janeiro M.G.: The multilinear extension and the symmetric coalition Banzhaf value. Theory Decis. 59, 111–126 (2005)
Alonso-Meijide J.M., Carreras F., Fiestras-Janeiro M.G., Owen G.: A comparative axiomatic characterization of the Banzhaf-Owen coalitional value. Decis. Support Syst. 43, 701–712 (2007)
Amer R., Carreras F., Giménez J.M.: The modified Banzhaf value for games with a coalition structure: an axiomatic characterization. Math. Soc. Sci. 43, 45–54 (2002)
Aumann R.: Game theory. In: Eatwell, J., Milgate, M., Newman, P. (eds) The New Palgrave: A Dictionary of Economics, vol. 2, pp. 460–482. MacMillan, London (1977)
Banzhaf J.F.: Weighted voting doesn’t work: a mathematical analysis. Rutgers Law Rev. 19, 317–343 (1965)
Carreras F., Magaña A.: The multilinear extension and the modified Banzhaf-Coleman index. Math. Soc. Sci. 28, 215–222 (1994)
Carreras F., Llongueras D., Puente A.: Partnerships in politics. Homo Oecon. 24, 469–484 (2007)
Coleman J.S.: Control of collectivities and the power of a collectivity to act. In: Lieberman, B. (eds) Social Choice, pp. 269–300. Gordon and Breach, New York (1971)
Deegan J., Packel E.W.: A new index of power for simple n-person games. Int. J. Game Theory 7, 113–123 (1978)
Holler M.J.: Forming coalitions and measuring voting power. Polit. Stud. 30, 262–271 (1982)
Johnston R.J.: On the measurement of power: some reaction to Laver. Environ. Plan. A 10, 907–914 (1978)
Lorenzo-Freire S., Alonso-Meijide J.M., Casas-Méndez B., Fiestras-Janeiro M.G.: Characterization of the Deegan-Packel and Johnston power indices. Eur. J. Oper. Res. 177, 431–444 (2007)
Owen G.: Multilinear extensions of games. Manage. Sci. 18, 64–79 (1972)
Owen G.: Values of games with a priori unions. In: Henn, R., Moeschlin, O. (eds) Mathematical Economics and Game Theory, pp. 76–88. Springer Verlag, New York (1977)
Owen G.: Modification of the Banzhaf-Coleman index for games with a priori unions. In: Holler, M.J. (eds) Power, Voting and Voting Power, pp. 232–238. Physica-Verlag, Wuerzberg-Vienna (1982)
Owen G., Winter E.: Multilinear extensions and the coalition value. Games Econ. Behav. 4, 582–587 (1992)
Peleg B., Sudhölter P.: Introduction to the Theory of Cooperative Games. Kluwer Academic Publisher, Dordrecht (2003)
Shapley L.S., Shubik M.: A method for evaluating the distribution of power in a committee system. Am. Polit. Sci. Rev. 48, 787–792 (1954)
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Alonso-Meijide, J.M., Casas-Méndez, B., Fiestras-Janeiro, M.G. et al. The Deegan–Packel index for simple games with a priori unions. Qual Quant 45, 425–439 (2011). https://doi.org/10.1007/s11135-009-9306-z
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DOI: https://doi.org/10.1007/s11135-009-9306-z