Abstract
In this probabilistic generalization of the Deegan-Packel power index, a new family of power indices based on the notions of minimal winning coalitions and equal division of pay offs is developed. The family of indices is parameterized by allowing minimal winning coalitions to form in accordance with varying probability functions. These indices are axiomatically characterized and compared to other similarly characterized indices. Additionally, a dual family of minimal blocking coalition indices and their characterization axioms is presented.
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References
Banzhaf, J.F. (1965). ‘Weighted Voting Doesn't Work: A Mathematical Analysis.’ Rutgers Law Review, 19: 317–343.
Blair, D. (1976). Essays in Social Choice Theory. Unpublished Ph.D. dissertation, Yale University.
Brams, S.J. (1975). Game Theory and Politics. New York: Free Press.
Brams, S.J., and Affuso, P.J. (1976). ‘Power and Size: A New Paradox.’ Theory and Decision, 7: 29–56.
Caplow, T. (1968). Two Against One: Coalitions in Triads. Englewood Cliffs: Prentice-Hall.
Coleman, J.S. (1971). ‘Control of Collectivities and the Power of a Collectivity to Act.’ In B. Lieberman (Ed.), Social Choice. New York: Gordon and Breach. 277–287.
Deegan, J., Jr., and Packel, E.W. (1976). ‘To the (Minimal Winning) Victors Go the (Equally Divided) Spoils: A New Power Index for Simple n-Person Games.’ Module in Applied Mathematics, Mathematical Association of America, Cornell University. 17 pp.
Deegan, J., Jr., and Packel, E.W. (1979). ‘A New Index of Power for Simple n-Person Games.’ International Journal of Game Theory, 7 (2): 113–123.
Dubey, P. (1975). ‘On the Uniqueness of the Shapley Value.’ International Journal of Game Theory, 4: 131–139.
Dubey, P. (1976). ‘Probabilistic Generalizations of the Shapley Value.’ Cowles Foundation Discussion Paper No. 440. 29 pp.
Raanen, J. (1976). ‘The Inevitability of the Paradox of New Members.’ Department of Operations Research Technical Report 311, Cornell University.
Shapley, L.S., and Shubik, M. (1954). ‘A Method for Evaluating the Distribution of Power in a Committee System.’ American Political Science Review, 48: 787–792.
Straffin, P. (1976). ‘Power Indices in Politics.’ Module in Applied Mathematics, Mathematical Association of America, Cornell University.
Straffin, P. (1977). ‘Homogeneity, Independence, and Power Indices.’ Public Choice, 30: 107–118.
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Packel, E.W., Deegan, J. An axiomated family of power indices for simple n-person games. Public Choice 35, 229–239 (1980). https://doi.org/10.1007/BF00140846
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DOI: https://doi.org/10.1007/BF00140846