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Computing Power Indices For Large Voting Games

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  • Leech, Dennis

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, based on co-operative game theory, has been known for a long time its empirical application has been to some extent limited, in part by the difficulty of computing the indices when there are many players. This paper presents new algorithms for computing the power indices of Shapley and Shubik and of Banzhaf, that are essentially modifications of approximation methods due to Owen, and have been shown to work well in real applications. They are of most utility in situations where both the number of players is large and their voting weights are very concentrated, some members having considerably larger numbers of votes than others, where Owen's approximation methods are least accurate.

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  • Leech, Dennis, 2002. "Computing Power Indices For Large Voting Games," Economic Research Papers 269350, University of Warwick - Department of Economics.
    • Handle: RePEc:ags:uwarer:269350
    DOI: 10.22004/ag.econ.269350
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    References listed on IDEAS

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    1. Widgren, Mika, 1994. "Voting power in the EC decision making and the consequences of two different enlargements," European Economic Review, Elsevier, vol. 38(5), pages 1153-1170, May.
    2. Dan Felsenthal & Moshé Machover & William Zwicker, 1998. "The Bicameral Postulates and Indices of a Priori Voting Power," Theory and Decision, Springer, vol. 44(1), pages 83-116, January.
    3. 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.
    4. Rafael La Porta & Florencio Lopez‐De‐Silanes & Andrei Shleifer, 1999. "Corporate Ownership Around the World," Journal of Finance, American Finance Association, vol. 54(2), pages 471-517, April.
    5. Jan-Erik Lane & Sven Berg, 1999. "Relevance of Voting Power," Journal of Theoretical Politics, , vol. 11(3), pages 309-320, July.
    6. 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.
    7. 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.
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    Cited by:

    1. Tomislav Marošević & Ivan Soldo, 2018. "Modified indices of political power: a case study of a few parliaments," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 26(3), pages 645-657, September.
    2. Daphne Cornelisse & Thomas Rood & Mateusz Malinowski & Yoram Bachrach & Tal Kachman, 2022. "Neural Payoff Machines: Predicting Fair and Stable Payoff Allocations Among Team Members," Papers 2208.08798, arXiv.org.
    3. de Mouzon, Olivier & Laurent, Thibault & Le Breton, Michel & Moyouwou, Issofa, 2020. "“One Man, One Vote” Part 1: Electoral Justice in the U.S. Electoral College: Banzhaf and Shapley/Shubik versus May," TSE Working Papers 20-1074, Toulouse School of Economics (TSE).
    4. Wilms, Ingo, 2020. "Dynamic programming algorithms for computing power indices in weighted multi-tier games," Mathematical Social Sciences, Elsevier, vol. 108(C), pages 175-192.
    5. 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.

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