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Measuring voting power: The paradox of new members vs the null player axiom


  • László Á. Kóczy

    () (Budapest Tech)


Qualified majority voting is used when decisions are made by voters of different sizes. In such situations the voters' influence on decision making is far from obvious; power measures are used for an indication of the decision making ability. Several power measures have been proposed and characterised by simple axioms to help the choice between them. Unfortunately the power measures also feature a number of so-called paradoxes of voting power. In this paper we show that the Paradox of New Members follows from the Null Player Axiom. As a corollary of this result it follows that there does not exist a power measure that satisfies the axiom, while not exhibiting the Paradox.

Suggested Citation

  • László Á. Kóczy, 2009. "Measuring voting power: The paradox of new members vs the null player axiom," Working Paper Series 0903, Óbuda University, Keleti Faculty of Business and Management.
  • Handle: RePEc:pkk:wpaper:0903

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    References listed on IDEAS

    1. van Deemen, Adrian & Rusinowska, Agnieszka, 2003. "Paradoxes of Voting Power in Dutch Politics," Public Choice, Springer, vol. 115(1-2), pages 109-137, April.
    2. Julien Reynaud & Fabien Lange & Łukasz Gątarek & Christian Thimann, 2011. "Proximity in Coalition Building," Central European Journal of Economic Modelling and Econometrics, CEJEME, vol. 3(3), pages 111-132, September.
    3. Annick Laruelle & Federico Valenciano, 2005. "A critical reappraisal of some voting power paradoxes," Public Choice, Springer, vol. 125(1), pages 17-41, July.
    4. Diermeier, Daniel & Merlo, Antonio, 2004. "An empirical investigation of coalitional bargaining procedures," Journal of Public Economics, Elsevier, vol. 88(3-4), pages 783-797, March.
    5. Perez-Castrillo, David & Wettstein, David, 2001. "Bidding for the Surplus : A Non-cooperative Approach to the Shapley Value," Journal of Economic Theory, Elsevier, vol. 100(2), pages 274-294, October.
    6. repec:cup:apsrev:v:48:y:1954:i:03:p:787-792_00 is not listed on IDEAS
    7. R J Johnston, 1978. "On the measurement of power: some reactions to Laver," Environment and Planning A, Pion Ltd, London, vol. 10(8), pages 907-914, August.
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    Cited by:

    1. Kóczy Á., László, 2011. "Lisszaboni kilátások
      [Lisbon prospects]
      ," Közgazdasági Szemle (Economic Review - monthly of the Hungarian Academy of Sciences), Közgazdasági Szemle Alapítvány (Economic Review Foundation), vol. 0(12), pages 1045-1058.

    More about this item


    a priori voting power; paradox of new members; null player axiom;

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • D72 - Microeconomics - - Analysis of Collective Decision-Making - - - Political Processes: Rent-seeking, Lobbying, Elections, Legislatures, and Voting Behavior

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