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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.

Suggested Citation

  • Leech, Dennis, 1989. "Power Indices And Probabilistic Voting Assumptions," Economic Research Papers 268359, University of Warwick - Department of Economics.
    • Handle: RePEc:ags:uwarer:268359
    DOI: 10.22004/ag.econ.268359
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    1. 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.
    2. Dennis Leech, 1988. "The Relationship Between Shareholding Concentration and Shareholder Voting Power in British Companies: A Study of the Application of Power Indices for Simple Games," Management Science, INFORMS, vol. 34(4), pages 509-527, April.
    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.
    4. Harrison, Mark, 1989. "Soviet National Income and the Burden of Defence, 1937 and 1940-1944," Economic Research Papers 268354, University of Warwick - Department of Economics.
    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.
    6. Guillermo Owen, 1972. "Multilinear Extensions of Games," Management Science, INFORMS, vol. 18(5-Part-2), pages 64-79, January.
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