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Power Indices And Probabilistic Voting Assumptions


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  • LEECH, D.


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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Bibliographic Info

Paper provided by University of Warwick, Department of Economics in its series The Warwick Economics Research Paper Series (TWERPS) with number 325.

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Length: 9 pages
Date of creation: 1989
Date of revision:
Handle: RePEc:wrk:warwec:325

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Keywords: voting ; social behaviour ; probability;

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Cited by:
  1. WidgrÉn, Mika, 2002. "On the Probabilistic Relationship between the Public Good Index and the Normalized Banzhaf Index," Discussion Papers 707, The Research Institute of the Finnish Economy.
  2. 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.
  3. Matthias Sutter, 2000. "Flexible Integration, EMU and Relative Voting Power in the EU," Public Choice, Springer, vol. 104(1), pages 41-62, July.


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