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Computing Power Indices for Large Voting Games

Author

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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
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    File URL: http://dx.doi.org/10.1287/mnsc.49.6.831.16024
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    References listed on IDEAS

    as
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    Citations

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    Cited by:

    1. Pongou, Roland & Tchantcho, Bertrand & Tedjeugang, Narcisse, 2014. "Power theories for multi-choice organizations and political rules: Rank-order equivalence," Operations Research Perspectives, Elsevier, vol. 1(1), pages 42-49.
    2. Guemmegne, Juliette T. & Pongou, Roland, 2014. "A policy-based rationalization of collective rules: Dimensionality, specialized houses, and decentralized authority," Journal of Mathematical Economics, Elsevier, vol. 52(C), pages 182-193.
    3. Balsmeier, Benjamin & Bermig, Andreas & Dilger, Alexander, 2013. "Corporate governance and employee power in the boardroom: An applied game theoretic analysis," Journal of Economic Behavior & Organization, Elsevier, vol. 91(C), pages 51-74.
    4. Crama, Yves & Leruth, Luc, 2007. "Control and voting power in corporate networks: Concepts and computational aspects," European Journal of Operational Research, Elsevier, vol. 178(3), pages 879-893, May.
    5. Nguyen, Tri-Dung & Thomas, Lyn, 2016. "Finding the nucleoli of large cooperative games," European Journal of Operational Research, Elsevier, vol. 248(3), pages 1078-1092.
    6. José María Alonso-Meijide & Mikel Álvarez-Mozos & María Gloria Fiestras-Janeiro, 2015. "Power Indices and Minimal Winning Coalitions in Simple Games with Externalities Abstract: We propose a generalization of simple games to situations with coalitional externalities. The main novelty of ," UB Economics Working Papers 2015/328, Universitat de Barcelona, Facultat d'Economia i Empresa, UB Economics.
    7. Fabrice Barthelemy & Mathieu Martin & Bertrand Tchantcho, 2011. "Some conjectures on the two main power indices," THEMA Working Papers 2011-14, THEMA (THéorie Economique, Modélisation et Applications), Université de Cergy-Pontoise.
    8. Casajus, André & Huettner, Frank, 2015. "Potential, value, and the multilinear extension," Economics Letters, Elsevier, vol. 135(C), pages 28-30.
    9. Sreejith Das, 2011. "Criticality in games with multiple levels of approval," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 37(3), pages 373-395, September.
    10. Berghammer, Rudolf & Rusinowska, Agnieszka & de Swart, Harrie, 2010. "Applying relation algebra and RelView to measures in a social network," European Journal of Operational Research, Elsevier, vol. 202(1), pages 182-195, April.
    11. Marc Feix & Dominique Lepelley & Vincent Merlin & Jean-Louis Rouet, 2007. "On the voting power of an alliance and the subsequent power of its members," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 28(2), pages 181-207, February.
    12. Marc Levy & Ariane Szafarz, 2017. "Cross-Ownership: A Device for Management Entrenchment?," Review of Finance, European Finance Association, vol. 21(4), pages 1675-1699.
    13. Leech, Dennis & Leech, Robert, 2012. "A New Analysis of A Priori Voting Power in the IMF: Recent Quota Reforms Give Little Cause for Celebration," The Warwick Economics Research Paper Series (TWERPS) 1001, University of Warwick, Department of Economics.
    14. Pongou, Roland & Tchantcho, Bertrand & Tedjeugang, Narcisse, 2015. "Trial-Based Tournament: Rank and Earnings," MPRA Paper 65582, University Library of Munich, Germany.
    15. Nguyen, Tri-Dung, 2014. "A fast approximation algorithm for solving the complete set packing problem," European Journal of Operational Research, Elsevier, vol. 237(1), pages 62-70.
    16. Hamers, Herbert & Husslage, Bart & Lindelauf, R. & Campen, Tjeerd, 2016. "A New Approximation Method for the Shapley Value Applied to the WTC 9/11 Terrorist Attack," Discussion Paper 2016-042, Tilburg University, Center for Economic Research.
    17. Berezinets Irina & Ilina Yulia & Muravyev Alexander, 2011. "Owners, Boards, Managers and the Private Benefits of Control: A Study of Dual Class Stock Firms in an Emerging Market," EERC Working Paper Series 11/12e, EERC Research Network, Russia and CIS.
    18. Ines Lindner, 2012. "Annick Laruelle and Federico Valenciano: Voting and collective decision-making," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 38(1), pages 161-179, January.
    19. Dennis Leech, 2013. "Power indices in large voting bodies," Public Choice, Springer, vol. 155(1), pages 61-79, April.
    20. Benati, Stefano & Rizzi, Romeo & Tovey, Craig, 2015. "The complexity of power indexes with graph restricted coalitions," Mathematical Social Sciences, Elsevier, vol. 76(C), pages 53-63.
    21. Fabrice Barthélémy & Mathieu Martin, 2007. "Configurations study for the Banzhaf and the Shapley-Shubik indices of power," THEMA Working Papers 2007-07, THEMA (THéorie Economique, Modélisation et Applications), Université de Cergy-Pontoise.
    22. repec:eee:gamebe:v:105:y:2017:i:c:p:122-147 is not listed on IDEAS
    23. Rahhal Lahrach & Jérôme Le Tensorer & Vincent Merlin, 2005. "Who benefits from the US withdrawal of the Kyoto Protocol? An application of the MMEA method to measure power," Post-Print halshs-00010171, HAL.
    24. Berezinets, Irina & Ilina, Yulia & Muravyev, Alexander, 2011. "CEO and Board Characteristics as Determinants of Private Benefits of Control: Evidence from the Russian Stock Exchange," IZA Discussion Papers 6256, Institute for the Study of Labor (IZA).

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