Power Indices in Large Voting Bodies
AbstractThere is no consensus on the properties of voting power indices when there are a large number of voters in a weighted voting body. On the one hand, in some real-world cases that have been studied the power indices have been found to be nearly proportional to the weights (eg the EUCM, US Electoral College). This is true for both the PenroseBanzhaf and the Shapley-Shubik indices. It has been suggested that this is a manifestation of a conjecture by Penrose (known subsequently as the Penrose limit theorem, that has been shown to hold under certain conditions). On the other hand, we have the older literature from cooperative game theory, due to Shapley and his collaborators, showing that, where there are a nite number of voters whose weights remain constant in relative terms, and where the quota remains constant in relative terms, while the total number of voters increases without limit - so called oceanic games - the powers of the voters with nite weight tend to limiting values that are, in general, not proportional to the weights. These results, too, are supported by empirical studies of large voting bodies (eg. the IMF/WB boards, corporate shareholder control). This paper proposes a restatement of the Penrose Limit theorem and shows that, for both the power indices, convergence occurs in general, in the limit as the Laakso-Taagepera index of political fragmentation increases. This new version reconciles the di erent theoretical and empirical results that have been found for large voting bodies
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Bibliographic InfoPaper provided by University of Warwick, Department of Economics in its series The Warwick Economics Research Paper Series (TWERPS) with number 942.
Date of creation: 2010
Date of revision:
This paper has been announced in the following NEP Reports:
- NEP-ALL-2010-09-03 (All new papers)
- NEP-CDM-2010-09-03 (Collective Decision-Making)
- NEP-GTH-2010-09-03 (Game Theory)
- NEP-POL-2010-09-03 (Positive Political Economics)
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- Leech, D., 1998. "Computing Power Indices for Large Voting Games: A New Algorithm," The Warwick Economics Research Paper Series (TWERPS) 510, University of Warwick, Department of Economics.
- Leech, Dennis & Aziz, Haris, 2007. "The Double Majority Voting Rule of the EU Reform Treaty as a Democratic Ideal for an Enlarging Union : an Appraisal Using Voting Power Analysis," The Warwick Economics Research Paper Series (TWERPS) 824, University of Warwick, Department of Economics.
- Dennis Leech, 2002.
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Political Studies Association, vol. 50(1), pages 1-22, 03.
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- Leech, D., 2000. "Members' Voting Power in the Governance of the International Monetary Fund," The Warwick Economics Research Paper Series (TWERPS) 583, University of Warwick, Department of Economics.
- Nicholas Miller, 2012. "Why the Electoral College is good for political science (and public choice)," Public Choice, Springer, vol. 150(1), pages 1-25, January.
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