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Voting Power Derives from the Poll Distribution. Shedding Light on Contentious Issues of Weighted Votes and the Constitutional Treaty

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  • Paterson, Iain

    (Department of Economics and Finance, Institute for Advanced Studies, Vienna, Austria)

Abstract

Analysis of the Constitutional Treaty of the European Union shows that there is a serious discrepancy between the voting power gradient of Member States computed by the Shapley-Shubik and Banzhaf indices. Given the lack of compelling arguments to choose between these indices on purely axiomatic grounds, we turn to a probabilistic approach as pioneered by Straffin (1977) focusing on the probability distribution of voting poll outcomes. We present a unifying model of power indices as expected decisiveness, which shows that the defining feature of each approach is a particular distribution of the voting poll. Empirical evidence drawn from voting situations, in addition to a consideration of first principles, leads us to reject one of these approaches. The unified formulation allows us to develop useful related concepts of efficiency and blocking leverage, previously used solely by a 'Banzhaf' approach, for the case of Shapley-Shubik, and a comparison of results is shown.

Suggested Citation

  • Paterson, Iain, 2006. "Voting Power Derives from the Poll Distribution. Shedding Light on Contentious Issues of Weighted Votes and the Constitutional Treaty," Economics Series 187, Institute for Advanced Studies.
    • Handle: RePEc:ihs:ihsesp:187
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    File URL: https://irihs.ihs.ac.at/id/eprint/1693
    File Function: First version, 2006
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    References listed on IDEAS

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    1. Philip Straffin, 1977. "Homogeneity, independence, and power indices," Public Choice, Springer, vol. 30(1), pages 107-118, June.
    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. 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.
    4. Brams, Steven J. & Davis, Morton D., 1974. "The 3/2's Rule in Presidential Campaigning," American Political Science Review, Cambridge University Press, vol. 68(1), pages 113-134, March.
    5. Paterson, Iain, 1998. "Vote Weighting in the European Union," East European Series 54, Institute for Advanced Studies.
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    Cited by:

    1. Sreejith Das, 2011. "Criticality in games with multiple levels of approval," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 37(3), pages 373-395, September.

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    More about this item

    Keywords

    Voting power indices; Power gradient; Coefficient of representation; Expected decisiveness; Efficiency; Blocking leverage; Constitution of the European Union;
    All these keywords.

    JEL classification:

    • C43 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Index Numbers and Aggregation
    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • D02 - Microeconomics - - General - - - Institutions: Design, Formation, Operations, and Impact
    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty

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