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Power Indices and Probabilistic Voting Assumptions

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  • Leech, Dennis

Abstract

This paper compares the theoretical bases of the Shapley-Shubik and Banzhaf indices of voting power for a legislature with weighted voting. Definitions based on probabilistic-voting assumptions, useful both as behavioral descriptions and for computation in empirical applications, are compared in terms of necessary and sufficient conditions on the choice of voting probabilities. It is shown that the Shapley-Shubik index requires stronger conditions than the Banzhaf index : the former that voting probabilities be chosen by all players from a common uniform distribution on the unit interval, the latter only that voting probabilities be selected independently from any set of distributions (on the unit interval) which have a common mean of 1/2. This result haS a bearing on the theoretical criteria by which one may choose between the two indices in a voting context.
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  • Leech, Dennis, 1990. "Power Indices and Probabilistic Voting Assumptions," Public Choice, Springer, vol. 66(3), pages 293-299, September.
    • Handle: RePEc:kap:pubcho:v:66:y:1990:i:3:p:293-99
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    1. Guillermo Owen, 1972. "Multilinear Extensions of Games," Management Science, INFORMS, vol. 18(5-Part-2), pages 64-79, January.
    2. Harrison, M., 1989. "Total Output And The Productivity Of Labour In Soviet Industry, 1940-1945," The Warwick Economics Research Paper Series (TWERPS) 319, University of Warwick, Department of Economics.
    3. Miller, M. & Weller, P. & Williamson, J., 1989. "The Stabilizing Properties Of Target Zones," The Warwick Economics Research Paper Series (TWERPS) 318, University of Warwick, Department of Economics.
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    5. Shapley, L. S. & Shubik, Martin, 1954. "A Method for Evaluating the Distribution of Power in a Committee System," American Political Science Review, Cambridge University Press, vol. 48(3), pages 787-792, September.
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    Cited by:

    1. Mika WidgrÚn, 2002. "On the Probablistic Relationship between the Public Good Index and the Normalized Bannzhaf Index," Homo Oeconomicus, Institute of SocioEconomics, vol. 19, pages 373-386.
    2. Leech, Dennis, 1999. "Minority Control: An Analysis of British Companies using Voting Power Indices," Economic Research Papers 269251, University of Warwick - Department of Economics.
    3. Matthias Sutter, 2000. "Flexible Integration, EMU and Relative Voting Power in the EU," Public Choice, Springer, vol. 104(1), pages 41-62, July.
    4. Arnold Cédrick SOH VOUTSA, 2021. "The Public Good spatial power index in political games," THEMA Working Papers 2021-01, THEMA (THéorie Economique, Modélisation et Applications), Université de Cergy-Pontoise.
    5. Dan Felsenthal & Moshé Machover & William Zwicker, 1998. "The Bicameral Postulates and Indices of a Priori Voting Power," Theory and Decision, Springer, vol. 44(1), pages 83-116, January.
    6. Arash Abizadeh & Adrian Vetta, 2021. "A Recursive Measure of Voting Power that Satisfies Reasonable Postulates," Papers 2105.03006, arXiv.org, revised May 2022.
    7. Arash Abizadeh & Adrian Vetta, 2022. "The Blocker Postulates for Measures of Voting Power," Papers 2205.08368, arXiv.org.

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