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Combinatorial and computational aspects of multiple weighted voting games

Author

Listed:
  • Aziz, Haris

    (Computer Science Department, University of Warwick)

  • Paterson, Mike

    (Computer Science Department, University of Warwick)

  • Leech, Dennis

    (Economics Department, University of Warwick)

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. Among other results we extend the concept of amplitude to multiple weighted voting games. 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," The Warwick Economics Research Paper Series (TWERPS) 823, University of Warwick, Department of Economics.
    • Handle: RePEc:wrk:warwec:823
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    File URL: https://warwick.ac.uk/fac/soc/economics/research/workingpapers/2008/twerp_823.pdf
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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. 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.
    4. 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.
    5. 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.

    More about this item

    Keywords

    multi-agent systems ; multiple weighted ; voting games ; game theory ; algorithms and ; complexity ; voting power.;
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