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Estimating the Efficiency of Voting in Big Size Committees

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Abstract

In a simple voting committee with a finite number of members, in which each member has a voting weight, the voting rule is defined by the quota (a minimal number of voting weights is required to approve a proposal), and the efficiency of voting in the committee is defined as the ratio of the number of winning coalitions (subsets of the set of members with total voting weights no less than the quota) to the number of all possible coalitions. A straightforward way of calculating the efficiency is based on the full enumeration of all coalitions and testing whether or not they are winning. The enumeration of all coalitions is NP-complete problem (the time required to find the solution grows exponentially with the size of the committee) and is unusable for big size committees. In this paper we are developing three algorithms (two exact and one heuristic) to compute the efficiency for committees with high number of voters within a reasonable timeframe. Algorithms are applied for evaluating the voting effi ciency in the Lower House of the Czech Parliament, in the European Parliament and in the Council of Ministers of the EU.

Suggested Citation

  • 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.
  • Handle: RePEc:fau:aucocz:au2011_172
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    References listed on IDEAS

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    1. Madeleine O. Hosli, 2008. "Council Decision Rules and European Union Constitutional Design," Czech Economic Review, Charles University Prague, Faculty of Social Sciences, Institute of Economic Studies, vol. 2(1), pages 076-096, March.
    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. Aleskerov, Fuad, 2009. "Power indices taking into account agents' preferences," The Warwick Economics Research Paper Series (TWERPS) 898, University of Warwick, Department of Economics.
    4. 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.
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    More about this item

    Keywords

    Efficiency of voting; committee; European Parliament; EU Council of Ministers;

    JEL classification:

    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations
    • D72 - Microeconomics - - Analysis of Collective Decision-Making - - - Political Processes: Rent-seeking, Lobbying, Elections, Legislatures, and Voting Behavior

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