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Combinatorial and computational aspects of multiple weighted voting games

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  • Aziz, Haris
  • Paterson, Mike
  • Leech, Dennis

Abstract

Weighted voting games are ubiquitous mathematical models which are used in economics, political science, neuroscience, threshold logic, reliability theory and distributed systems. They model situations where agents with variable voting weight vote in favour of or against a decision. A coalition of agents is winning if and only if the sum of weights of the coalition exceeds or equals a specified quota. We provide a mathematical and computational characterization of multiple weighted voting games which are an extension of weighted voting games1 . We analyse the structure of multiple weighted voting games and some of their combinatorial properties especially with respect to dictatorship, veto power, dummy players and Banzhaf indices. An illustrative Mathematica program to compute voting power properties of multiple weighted voting games is also provided.

Suggested Citation

  • Aziz, Haris & Paterson, Mike & Leech, Dennis, 2007. "Combinatorial and computational aspects of multiple weighted voting games," Economic Research Papers 269772, University of Warwick - Department of Economics.
    • Handle: RePEc:ags:uwarer:269772
    DOI: 10.22004/ag.econ.269772
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    References listed on IDEAS

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    1. Bilbao, J. M. & Fernandez, J. R. & Jimenez, N. & Lopez, J. J., 2002. "Voting power in the European Union enlargement," European Journal of Operational Research, Elsevier, vol. 143(1), pages 181-196, November.
    2. Dennis Leech, 2002. "Voting Power in the Governance of the International Monetary Fund," Annals of Operations Research, Springer, vol. 109(1), pages 375-397, January.
    3. Laruelle, Annick & Widgren, Mika, 1998. "Is the Allocation of Voting Power among EU States Fair?," Public Choice, Springer, vol. 94(3-4), pages 317-339, March.
    4. Dan S Felsenthal & Moshé Machover, 2004. "Analysis of QM rules in the draft constitution for Europe proposed by the European Convention, 2003," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 23(1), pages 1-20, August.
    5. Algaba, E. & Bilbao, J.M. & Fernandez, J.R., 2007. "The distribution of power in the European Constitution," European Journal of Operational Research, Elsevier, vol. 176(3), pages 1752-1766, February.
    6. Leech, Dennis, 2002. "Voting Power In The Governance Of The International Monetary Fund," Economic Research Papers 269354, University of Warwick - Department of Economics.
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    Cited by:

    1. Leech, Dennis, 2007. "The Double Majority Voting Rule Of The Eu Reform Treaty As A Democratic Ideal For An Enlarging Union: An Appraisal Using Voting Power Analysis," Economic Research Papers 269773, University of Warwick - Department of Economics.
    2. Leech, Dennis & Aziz, Haris, 2007. "The Double Majority Voting Rule of the EU Reform Treaty as a Democratic Ideal for an Enlarging Union : an Appraisal Using Voting Power Analysis," The Warwick Economics Research Paper Series (TWERPS) 824, University of Warwick, Department of Economics.
    3. 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.
    4. Pavel Doležel, 2011. "Estimating the Efficiency of Voting in Big Size Committees," Czech Economic Review, Charles University Prague, Faculty of Social Sciences, Institute of Economic Studies, vol. 5(2), pages 172-190, August.
    5. Pavel Doležel, 2011. "Optimizing the Efficiency of Weighted Voting Games," Czech Economic Review, Charles University Prague, Faculty of Social Sciences, Institute of Economic Studies, vol. 5(3), pages 306-323, November.

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