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Power indices in large voting bodies\ud

By Dennis Leech

Abstract

There 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 \ud \u

Topics: H1, QA
Publisher: University of Warwick. Dept. of Economics
Year: 2010
OAI identifier: oai:wrap.warwick.ac.uk:3510

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Citations

  1. (2010). A priori voting power and the US Electoral College. In: Holler, doi
  2. (2002). An empirical comparison of the performance of classical power indices. doi
  3. (2007). Cases where the Penrose limit theorem does not hold. doi
  4. (2003). Computing power indices for large voting games. doi
  5. (1979). Eective number of parties: A measure with application to West Europe.
  6. (2004). LS Penrose's limit theorem: proof of some special cases. doi
  7. (2006). LS Penrose's limit theorem: Tests by simulation star, open. doi
  8. (1972). Multilinear extensions of games. doi
  9. (1952). On the objective study of crowd behavior. doi
  10. (1971). Probability Theory and its Applications, doi
  11. (2010). The Double Majority Voting Rule of the EU Reform Treaty as a Democratic Ideal for an Enlarging Union: an Appraisal Using Voting Power Analysis.
  12. (2007). The Jagellonian Compromise: An Alternative Voting System for the Council of the European Union.
  13. (2007). The Laakso-Taagepera index in a mean and variance framework. doi
  14. (1998). The Measurement of Voting Power. doi
  15. (1978). Values of large games II: Oceanic games. doi
  16. (1978). Values of large games, I: a limit theorem. doi
  17. (2002). Voting Power in the Governance of the International Monetary Fund.

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