Geodesic
Power analysis of voting by count and account
Kybernetika, Tome 42 (2006) no. 4, pp. 483-493 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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.
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.
Classification : 91A12, 91B12, 91B14
Keywords: cooperative games; voting; power indices 
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Hirokawa, Midori; Vlach, Milan. Power analysis of voting by count and account. Kybernetika, Tome 42 (2006) no. 4, pp. 483-493. http://geodesic.mathdoc.fr/item/KYB_2006_42_4_a7/

[1] Brams S. J., Lucas W. F., (eds.) P. D. Straffin: Political and Related Models. Springer–Verlag, New York 1983 | MR | Zbl

[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

[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

[5] Taylor A. D., Zwicker W. S.: Simple Games. Princeton University Press, Princeton, N. J. 1999 | MR | Zbl