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Computing Power Indices for Large Voting Games

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  • Dennis Leech

    (Department of Economics, University of Warwick, Coventry CV47AL, United Kingdom)

Abstract

Voting power indices enable the analysis of the distribution of power in a legislature or voting body in which different members have different numbers of votes. Although this approach to the measurement of power has been known for a long time, its application to large games has been limited by the difficulty of computing these indices. This paper presents a new method for computing power indices that combines exact methods with an approximate method due to Owen. This method is of most utility in situations where the number of players is large and the voting weights are concentrated in the hands of a small number of members.

Suggested Citation

  • Dennis Leech, 2003. "Computing Power Indices for Large Voting Games," Management Science, INFORMS, vol. 49(6), pages 831-837, June.
    • Handle: RePEc:inm:ormnsc:v:49:y:2003:i:6:p:831-837
    DOI: 10.1287/mnsc.49.6.831.16024
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    References listed on IDEAS

    as
    1. R.J. Aumann & S. Hart (ed.), 2002. "Handbook of Game Theory with Economic Applications," Handbook of Game Theory with Economic Applications, Elsevier, edition 1, volume 3, number 3.
    2. Dennis Leech, 2002. "An Empirical Comparison of the Performance of Classical Power Indices," Political Studies, Political Studies Association, vol. 50(1), pages 1-22, March.
    3. Moshé Machover & Dan S. Felsenthal, 2001. "The Treaty of Nice and qualified majority voting," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 18(3), pages 431-464.
    4. Dennis Leech, 1988. "The Relationship Between Shareholding Concentration and Shareholder Voting Power in British Companies: A Study of the Application of Power Indices for Simple Games," Management Science, INFORMS, vol. 34(4), pages 509-527, April.
    5. Straffin, Philip Jr., 1994. "Power and stability in politics," Handbook of Game Theory with Economic Applications, in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 2, chapter 32, pages 1127-1151, Elsevier.
    6. ., 2000. "Notes on the theory of markets," Chapters, in: Macroeconomic Instability and Coordination, chapter 12, Edward Elgar Publishing.
    7. Dennis Leech, 2001. "Shareholder Voting Power and Corporate Governance: A Study of Large British Companies," Nordic Journal of Political Economy, Nordic Journal of Political Economy, vol. 27, pages 33-54.
    8. 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.
    9. Guillermo Owen, 1972. "Multilinear Extensions of Games," Management Science, INFORMS, vol. 18(5-Part-2), pages 64-79, January.
    10. J. Bilbao & J. Fernández & A. Losada & J. López, 2000. "Generating functions for computing power indices efficiently," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 8(2), pages 191-213, December.
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