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The use of Coleman's power indices to inform the choice of voting rule with reference to the IMF governing body and the EU Council of Ministers

By Dennis Leech


In his well known 1971 paper the mathematical sociologist James S. Coleman, proposed three measures of voting power: (1) "the power of a collectivity to act", (2) "the power to prevent action" and (3) "the power to initiate action". (1) is a measure of the overall decisiveness of a voting body taking into account its size, decision rule and the weights of its members, while (2) and (3) are separate indices of the power of individual members, in being able to block or achieve decisions. These measures seem to have been little used for a variety of reasons, although the paper itself is widely cited. First, much of the power indices literature has focused on normalised indices which gives no role to (1) and means that (2) and (3) are identical. Second, Coleman's coalition model is different from that of Shapley and Shubik which has sometimes tended to dominate in discussions of voting power. Third, (2) and (3) are indistinguishable when the decision quota is a simple majority, the distinction becoming important in other voting situations. In this paper I propose that these indices, which are based on a fundamentally different notion of power than that assumed by game-theoretic approaches, have a useful role in aiding a better understanding of collective institutions in which decisions are taken by voting. I use them to illustrate different aspects of the design of a weighted voting system such as the governing body of the IMF or World Bank, or the system of QMV in the European Council

Topics: HM
Publisher: University of Warwick, Department of Economics
Year: 2002
OAI identifier:

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  1. (1954). A Method for Evaluation the Distribution of Power in a Committee System”, doi
  2. Comparing Voting Systems, doi
  3. (1971). Control of Collectivities and the Power of a Collectivity to Act," in B.Lieberman (ed), Social Choice,
  4. (1986). Game theory and Political Theory, doi
  5. (1995). Game Theory,(3rd Edition) doi
  6. (1943). in D. Moggridge, The Collected Writings of John Mynard Keynes, doi
  7. (1973). Loss of Power",
  8. (1979). Mathematical Properties of the Banzhaf Value," doi
  9. (1998). Measurement of Voting Power, doi
  10. (1978). On the Measurement of Power: Some Reactions to Laver", Environment and Planning, doi
  11. (1976). Power and Size: a New Paradox,” Theory and Decision, doi
  12. (1994). Power and Stability in Politics," chapter 32 of Aumann, Robert doi
  13. (1981). Power, Voting and Voting Power, doi
  14. (1943). Speech to House of Lords,
  15. (1970). The Benefits of Coalition", doi
  16. (1983). The Effect of Shareholding Dispersion on the Degree of Control in British Companies: Theory and Measurement," doi
  17. (1946). The Elementary Statistics of Majority Voting," doi
  18. (1982). The the (Minimal Winning) Victors Go the (Equally Divided) Spoils": a New Index of Power for Simple n-Person Games", doi
  19. (1976). Voting Paradoxes, doi
  20. (2002). Voting Power in the Governance of the International Monetary Fund", doi
  21. (1965). Weighted Voting Doesn’t Work: A Mathematical Analysis”,

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