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Some conjectures on the two main power indices

Author

Listed:
  • Fabrice Barthelemy

    (THEMA, Universite de Cergy-Pontoise)

  • Mathieu Martin

    (THEMA, Universite de Cergy-Pontoise)

  • Bertrand Tchantcho

    (University of Yaounde I, Ecole Normale Superieure, Cameroon, PO Box 47 Yaounde)

Abstract

The purpose of this paper is to present a structural specification of the Shapley- Shubik and Banzhaf power indices in a weighted voting rule. We compare them in term of the cardinality of the sets of power vectors (PV). This is done in different situations where the quota or the number of seats are fixed or not.

Suggested Citation

  • Fabrice Barthelemy & Mathieu Martin & Bertrand Tchantcho, 2011. "Some conjectures on the two main power indices," THEMA Working Papers 2011-14, THEMA (THéorie Economique, Modélisation et Applications), Université de Cergy-Pontoise.
    • Handle: RePEc:ema:worpap:2011-14
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    File URL: http://thema.u-cergy.fr/IMG/documents/2011-14.pdf
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    References listed on IDEAS

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    1. Straffin, Philip Jr., 1994. "Power and stability in politics," Handbook of Game Theory with Economic Applications, in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 2, chapter 32, pages 1127-1151, Elsevier.
    2. 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.
    3. Laruelle,Annick & Valenciano,Federico, 2011. "Voting and Collective Decision-Making," Cambridge Books, Cambridge University Press, number 9780521182638.
    4. Owen, Guillermo, 1975. "Evaluation of a Presidential Election Game," American Political Science Review, Cambridge University Press, vol. 69(3), pages 947-953, September.
    5. Dennis Leech, 2003. "Computing Power Indices for Large Voting Games," Management Science, INFORMS, vol. 49(6), pages 831-837, June.
    6. Dan S. Felsenthal & Moshé Machover, 1998. "The Measurement of Voting Power," Books, Edward Elgar Publishing, number 1489.
    7. Shapley, L. S. & Shubik, Martin, 1954. "A Method for Evaluating the Distribution of Power in a Committee System," American Political Science Review, Cambridge University Press, vol. 48(3), pages 787-792, September.
    8. Guillermo Owen, 1972. "Multilinear Extensions of Games," Management Science, INFORMS, vol. 18(5-Part-2), pages 64-79, January.
    9. Lawrence Diffo Lambo & Joël Moulen, 2002. "Ordinal equivalence of power notions in voting games," Theory and Decision, Springer, vol. 53(4), pages 313-325, December.
    10. Leech, Dennis, 2002. "Designing the Voting System for the Council of the European Union," Public Choice, Springer, vol. 113(3-4), pages 437-464, December.
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    Citations

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    Cited by:

    1. Boratyn, Daria & Kirsch, Werner & Słomczyński, Wojciech & Stolicki, Dariusz & Życzkowski, Karol, 2020. "Average weights and power in weighted voting games," Mathematical Social Sciences, Elsevier, vol. 108(C), pages 90-99.
    2. Fabrice Barthelemy & Dominique Lepelley & Mathieu Martin & Hatem Smaoui, 2021. "Dummy Players and the Quota in Weighted Voting Games," Group Decision and Negotiation, Springer, vol. 30(1), pages 43-61, February.
    3. Fabrice Barthélémy & Mathieu Martin, 2021. "Dummy Players and the Quota in Weighted Voting Games: Some Further Results," Studies in Choice and Welfare, in: Mostapha Diss & Vincent Merlin (ed.), Evaluating Voting Systems with Probability Models, pages 299-315, Springer.

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    More about this item

    Keywords

    Shapley-Shubik; Banzhaf; power index; power vectors.;
    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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