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cooperative games; voting; power indices
Using players’ Shapley–Shubik power indices, Peleg [4] proved that voting by count and account is more egalitarian than voting by account. In this paper, we show that a stronger shift in power takes place when the voting power of players is measured by their Shapley–Shubik indices. Moreover, we prove that analogous power shifts also occur with respect to the absolute Banzhaf and the absolute Johnston power indices.
[1] Brams S. J., Lucas W. F., (eds.) P. D. Straffin: Political and Related Models. Springer–Verlag, New York 1983 MR 0682776 | Zbl 0503.00012
[2] Hirokawa M., Xu P.: Small Creditors’ Power in Civil Rehabilitation – A Compound Game of a Simple Majority and a Weighted Majority. Mimeo, Hosei University, 2005
[3] Lucas W. J.: Measuring power in weighted voting. In: Political and Related Models (S. J. Brams, W. F. Lucas, and P. D. Straffin, eds.), Springer–Verlag, New York 1983, pp. 183–238 Zbl 0514.90096
[4] Peleg B.: Voting by count and account. In: Rational Interaction: Essays in Honor of John C. Harsanyi (R. Selten, ed.), Springer–Verlag, New York 1992, pp. 41–51 Zbl 0856.90029
[5] Taylor A. D., Zwicker W. S.: Simple Games. Princeton University Press, Princeton, N. J. 1999 MR 1714706 | Zbl 0943.91005
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