Abstract
In this paper we discuss the meaning of Owen’s coalitional extension of the Banzhaf index in the context of voting situations. It is discussed the possibility of accommodating this index within the following model: in order to evaluate the likelihood of a voter to be crucial in making a decision by means of a voting rule a second input (apart from the rule itself) is necessary: an estimate of the probability of different vote configurations. It is shown how Owen’s coalitional extension can be seen as three different normative variations of this model.
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References
Aumann, R.J. and Drèze, J. (1975), Solutions of cooperative games with coalitional structure, International Journal of Game Theory 4, 167–176.
Banzhaf, J. (1965), Weighted voting doesn’t work: a mathematical analysis, Rutgers Law Review 19, 317–343.
Dubey, P. and Shapley, L.S. (1979), Mathematical properties of the Banzhaf power index, Mathematics of Operations Research 4, 99–131.
Laruelle, A. and Valenciano, F. (forthcoming), Assessing success and decisiveness in voting situations, Social Choice and Welfare
Owen, G. (1975), Multilinear extensions and the Banzhaf value, Naval Research Logistics Quarterly 22, 741–750.
Owen, G. (1977), Values of games with a priori unions, in R. Hein and O. Moeschlin (eds), Essays in Mathematical Economics and Game Theory New York: Springer-Verlag, 76–88.
Owen, G. (1982), Modification of the Banzhaf—Coleman index for games with a priori unions, in M.J. Holler (ed.), Power, Voting, and Voting Power. Würzbürg: Physica-Verlag, 232–238.
Shapley, L.S. (1953), A value for n-person games, Annals of Mathematical Studies 28, 307–317.
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© 2004 Springer Science+Business Media New York
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Laruelle, A., Valenciano, F. (2004). On the Meaning of Owen—Banzhaf Coalitional Value in Voting Situations. In: Gambarelli, G. (eds) Essays in Cooperative Games. Theory and Decision Library, vol 36. Springer, Boston, MA. https://doi.org/10.1007/978-1-4020-2936-3_9
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DOI: https://doi.org/10.1007/978-1-4020-2936-3_9
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