A Well-Behaved Index of a Priori P-Power for Simple N-Person Games
Tóm tắt
As far as we know, all previously suggested indices of a priori P-power for simple n-person games violate one or more postulates that are considered compelling for a reasonable P-power index. A new index is proposed in this paper which satisfies all these postulates.
Tài liệu tham khảo
Alonso-Meijide, J. M., & Freixas, J. (2010). A new index based on minimal winning coalitions without any surplus. Decision Support Systems, 49, 70–76.
Alonso-Meijide, J. M., Freixas, J., & Molinero, X. (2012). Computation of several power indices by generating functions. Applied Mathematics and Computation, 219, 3395–3402.
Banzhaf, J. F. (1965). Weighted voting doesn’t work: A mathematical analysis. Rutgers Law Review, 19, 317–343.
Coleman, J. S. (1971). Control of collectivities and the power of a collectivity to act. In B. Lieberman (Ed.), Social choice (pp. 269–300). New York: Gordon and Breach.
Deegan, J., & Packel, E. W. (1978). A new index of power for simple N-person games. International Journal of Game Theory, 7, 113–123.
Deegan, J., & Packel, E. W. (1982). To the (minimal winning) victors go the (equally divided) spoils: A new index of power for simple N-person games. In S. J. Brams, W. F. Lucas, & P. D. Straffin (Eds.), Political and related models (pp. 239–255). New York: Springer.
Felsenthal, D. S., & Machover, M. (1995). Postulates and paradoxes of relative voting power—a critical appraisal. Theory and Decision, 38, 196–229.
Felsenthal, D. S., & Machover, M. (1996). Alternative forms of the Shapley value and the Shapley–Shubik index. Public Choice, 87, 315–318.
Felsenthal, D. S., & Machover, M. (1998). The measurement of voting power: theory and practice problems and paradoxes. Cheltenham: Edward Elgar.
Felsenthal, D. S., Machover, M., & Zwicker, W. S. (1998). The bicameral postulates and indices of a priori voting power. Theory and Decision, 44, 83–116.
Freixas, J., & Kaniovsky, S. (2014). The minimum sum representation as an index of voting power. European Journal of Operational Research, 233, 739–748.
Freixas, J., & Kurz, S. (2016). The cost of getting local monotonicity. European Journal of Operational Research, 251, 600–612.
Holler, M. J. (1978). A priori power and government formation. Munich Social Science Review, 4, 25–41.
Holler, M. J. (1982). Forming coalitions and measuring voting power. Political Studies, 30, 262–271.
Holler, M. J., & Napel, S. (2004). Monotonicity of power and power measures. Theory and Decision, 56, 93–111.
Holler, M. J., Ono, R., & Steffen, F. (2001). Constrained monotonicity and the measurement of power. Theory and Decision, 50, 385–397.
Isbell, J. R. (1958). A class of simple games. Duke Mathematics Journal, 25, 423–439.
Johnston, R. J. (1978). On the measurement of power: some reactions to Laver. Environment and Planning A, 10, 907–914.
Laver, M., & Schofield, N. (1990). Multiparty government: The politics of coalition in Europe. Oxford: Oxford University Press.
Penrose, L. S. (1946). The elementary statistics of majority voting. Journal of the Royal Statistical Society, 109, 53–57.
Penrose, L. S. (1952). On the objective study of crowd behaviour. London: H.K. Lewis & Co.
Riker, W. H. (1962). The theory of political coalitions. New Haven: Yale University Press.
Shapley, L. S. (1953). A value for n-person games. In H. W. Kuhn and A. W. Tucker (Eds.), Contributions to the theory of games, volume II (Annals of mathematics studies 28) (pp. 307–318). Princeton: Princeton University Press.
Shapley, L. S., & Shubik, M. (1954). A method for evaluating the distribution of power in a committee system. American Political Science Review, 48, 787–792.
Taylor, A. D., & Zwicker, W. S. (1999). Simple games: Desirability relations, trading, Pseudoweightings. Princeton: Princeton University Press.