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Power Indices And Probabilistic Voting Assumptions


  • 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.

Suggested Citation

  • Leech, D., 1989. "Power Indices And Probabilistic Voting Assumptions," The Warwick Economics Research Paper Series (TWERPS) 325, University of Warwick, Department of Economics.
  • Handle: RePEc:wrk:warwec:325

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    References listed on IDEAS

    1. Harrison, M., 1989. "Soviet National Income And The Burden Of Defence, 1937 And 1940-1944," The Warwick Economics Research Paper Series (TWERPS) 320, University of Warwick, Department of Economics.
    2. Guillermo Owen, 1972. "Multilinear Extensions of Games," Management Science, INFORMS, vol. 18(5-Part-2), pages 64-79, January.
    3. 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.
    4. 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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    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. 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. Sutter, Matthias, 2000. "Flexible Integration, EMU and Relative Voting Power in the EU," Public Choice, Springer, vol. 104(1-2), pages 41-62, July.

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    voting ; social behaviour ; probability;


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