The Library

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

Tools

Leech, Dennis (2002) 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. Working Paper. Coventry: University of Warwick, Department of Economics. Warwick economic research papers (No.645).

Preview

PDF
WRAP_Leech_twerp645.pdf - Requires a PDF viewer such as GSview, Xpdf or Adobe Acrobat Reader
Download (316Kb)

Official URL: http://www2.warwick.ac.uk/fac/soc/economics/resear...

Abstract

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.

Item Type:

Working or Discussion Paper (Working Paper)

Subjects:

H Social Sciences > HM Sociology

Divisions:

Faculty of Social Sciences > Economics

Library of Congress Subject Headings (LCSH):

Coleman, James Samuel, 1926-1995, Council of the European Union, International Monetary Fund. Executive Board, Rational choice theory, Voting research, Decision making, Mathematical sociology

Series Name:

Warwick economic research papers

Publisher:

University of Warwick, Department of Economics

Place of Publication:

Coventry

Official Date:

July 2002

Dates:

Date	Event
July 2002	Published

Number:

No.645

Number of Pages:

Status:

Not Peer Reviewed

Access rights to Published version:

Open Access

Description:

Paper prepared for the workshop "Modelling the European Decision Making", San Sebastian, Spain, July 12-14

References:

Banzhaf, John F (1965), “Weighted Voting Doesn’t Work: A Mathematical Analysis”, Rutgers Law Review, 19, 317-343
Brams, Steve (1975) Game Theory and Politics, New York, Free Press.
-----------------(1976) Voting Paradoxes, New York, Free Press.
-----------------P. J. Affuso (1976), “Power and Size: a New Paradox,” Theory and Decision, 7, 29-56.
Coleman, James S (1970) "The Benefits of Coalition", Public Choice, *, 45-61.
------------------------(1971) "Control of Collectivities and the Power of a Collectivity to Act," in B.Lieberman (ed), Social Choice, New York, Gordon and Breach; reprinted in J.S. Coleman, 1986, Individual Interests and Collective Action, Cambridge University Press.
-----------------------(1973), "Loss of Power", American Sociological Review, 38,1-17.
Cubbin, JohnS. and Dennis Leech (1983), "The Effect of Shareholding Dispersion on the Degree of Control in British Companies: Theory and Measurement," Economic Journal, 93, 351-369; reprinted in Kevin Keasey, Steve Thompson and Mike Wright (eds), Corporate Governance, Edward Elgar: Critical Writings in Economics vol 2 (of 4) May 1999, pp 61-80.
Deegan, J and W. H. Packel (1982), "The the (Minimal Winning) Victors Go the (Equally Divided) Spoils": a New Index of Power for Simple n-Person Games", in Steven J Brams, William F Lucas, and Phillip D Straffin (eds.) Political and Related Models, 1982, New York, Springer.
Dubey, Pradeep. and Lloyd.S. Shapley (1979), "Mathematical Properties of the Banzhaf Value," Mathematics of Operational Research, 4, 99-131.
Felsenthal, Dan S. and Moshé Machover, (1998),The Measurement of Voting Power, Cheltenham, Edward Elgar.
Galloway, David (2001), The Treaty of Nice and Beyond: Realities and Illusions of Power in the EU, Sheffield, Sheffield Academic Press.
Holler, Manfred (1981), (Ed.), Power, Voting and Voting Power, Physica-Verlag, Wurtzburg.
Johnston, R.J. (1978), "On the Measurement of Power: Some Reactions to Laver", Environment and Planning, A,10, 907-914.
Keynes, John M. (1943a), Speech to House of Lords, 18 May 1943, in D. Moggridge, The Collected Writings of John Maynard Keynes, Cambridge University Press, 1980, vol. XXV, p. 278.
---------------------(1943b), Letter to J Viner, 12 July 1943, in D. Moggridge, The Collected Writings of John Mynard Keynes, Cambridge University Press, 1980, vol. XXV, p. 328.
Laruelle, Annick and Federico Valenciano (2001), “Shapley-Shubik and Banzhaf Indices Revisited”, Mathematics of Operations Research, 26, 89-104.
Leech, Dennis (2002), "Voting Power in the Governance of the International Monetary Fund", Annals of Operations Research, 109, 373-395. (Available for download from www.warwick.ac.uk/fac/soc/Economics/leech.)
--------------- (forthcoming), “Designing the Voting System for the Council of the European Union,” Public Choice, in press. (Available for download from www.warwick.ac.uk/fac/soc/Economics/leech.)
Lucas, William F. (1983), “Measuring Power in Weighted Voting Systems,” in S. Brams, W. Lucas and P. Straffin (eds.), Political and Related Models, Springer.
Nurmi, H.(1987), Comparing Voting Systems, Dordrecht,, Reidel Publishing.
Ordeshook, Peter C. (1986), Game theory and Political Theory, Cambridge UP.
Owen, Guillermo (1995), Game Theory,(3rd Edition) , Academic Press.
Penrose, L.S. (1946), "The Elementary Statistics of Majority Voting," Journal of the Royal Statistical Society, 109, 53-57.
Shapley, Lloyd and Martin Shubik (1954), “A Method for Evaluation the Distribution of Power in a Committee System”, American Political Science Review, 48, 787-92.
Straffin, Philip D. (1994), "Power and Stability in Politics," chapter 32 of Aumann, Robert J and Sergiu Hart (eds.), Handbook of Game Theory, Volume 2, North-Holland.