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On the performance of the Shapley Shubik and Banzhaf power indices for the allocations of mandates

Author

Listed:
  • Fabrice Barthélémy

    (THEMA, Université de Cergy-Pontoise)

  • Mathieu MARTIN

    (THEMA, Université de Cergy-Pontoise)

  • Vincent MERLIN

    (CREM, CNRS and Université de Caen, Faculté de sciences économiques et de gestion,)

Abstract

A classical problem in the power index literature is to design a voting mechanism such as the distribution of power of the different players is equal (or closer) to a pre established target. This tradition is especially popular when considering two tiers voting mechanisms: each player votes in his own jurisdiction to designate a delegate for the upper tier; and the question is to assign a certain number of mandates for each delegate according the population of the jurisdiction he or she represents. Unfortunately, there exist several measures of power, which in turn imply different distributions of the mandates for the same pre established target. The purposes of this paper are twofold: first, we calculate the probability that the two most important power indices, the Banzhaf index and the Shapley-Shubik index, lead to the same voting rule when the target is the same. Secondly, we determine which index on average comes closer to the pre established target.

Suggested Citation

  • Fabrice Barthélémy & Mathieu MARTIN & Vincent MERLIN, 2007. "On the performance of the Shapley Shubik and Banzhaf power indices for the allocations of mandates," THEMA Working Papers 2007-25, THEMA (THéorie Economique, Modélisation et Applications), Université de Cergy-Pontoise.
    • Handle: RePEc:ema:worpap:2007-25
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    File URL: http://thema.u-cergy.fr/IMG/documents/2007-25.pdf
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    Cited by:

    1. Fabrice Barthelemy & Mathieu Martin, 2011. "A Comparison Between the Methods of Apportionment Using Power Indices: the Case of the US Presidential Elections," Annals of Economics and Statistics, GENES, issue 101-102, pages 87-106.

    More about this item

    Keywords

    Banzhaf; Shapley-Shubik; power indices;
    All these keywords.

    JEL classification:

    • C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory
    • D7 - Microeconomics - - Analysis of Collective Decision-Making

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