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- On The Choice Of A Power Index

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Author Info

  • Annick Laruelle

    (Universidad de Alicante)

Abstract

In this paper, we review and compare the main power indices to be found in the literature, that is to say, the Shapley-Shubik index, the Banzhaf index, the Johnston index, the Deegan-Packel index, and the Holler-Packel index. Three diferent approaches are used. First, the power indices are compared on the basis of a priori properties that they should satisfy. Second, a players power indices are compared on the basis of a priori properties that they shoud satisfy. Second, a players power is interpreted as the probability of her or his vote being necessary to pass a proposal. We present two models consistent with this approach: a model in which this probability arises from the assumptions made on the coalition formation and model, in which it arises from the assumptions made on the players voting behavior. Third, a players power is dened as her or his probability of playing a crucial role. Some power indices are derived from diferent assessments concerning the probability of playing such a role. Illustrations of the choice of an index are given for actual decision-making processes.

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File URL: http://www.ivie.es/downloads/docs/wpasad/wpasad-1999-10.pdf
File Function: Fisrt version / Primera version, 1999
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Bibliographic Info

Paper provided by Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie) in its series Working Papers. Serie AD with number 1999-10.

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Length: 27 pages
Date of creation: May 1999
Date of revision:
Publication status: Published by Ivie
Handle: RePEc:ivi:wpasad:1999-10

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Related research

Keywords: Collective Decision Making; Power Indices;

References

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  1. M Laver, 1978. "The problems of measuring power in Europe," Environment and Planning A, Pion Ltd, London, vol. 10(8), pages 901-905, August.
  2. Edelman, Paul H., 1997. "A note on voting," Mathematical Social Sciences, Elsevier, vol. 34(1), pages 37-50, August.
  3. Annick Laruelle & Mika Widgrén, 1998. "Is the allocation of voting power among EU states fair?," Public Choice, Springer, vol. 94(3), pages 317-339, March.
  4. Federico Valenciano & Annick Laruelle, 2000. "- On The Measurement Of Inequality In The Distribution Of Power In Voting Procedures," Working Papers. Serie AD 2000-10, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
  5. 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.
  6. Dan Felsenthal & Moshé Machover & William Zwicker, 1998. "The Bicameral Postulates and Indices of a Priori Voting Power," Theory and Decision, Springer, vol. 44(1), pages 83-116, January.
  7. (*), Gerard van der Laan & RenÊ van den Brink, 1998. "Axiomatizations of the normalized Banzhaf value and the Shapley value," Social Choice and Welfare, Springer, vol. 15(4), pages 567-582.
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Citations

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Cited by:
  1. Donal G. Saari & Katri K. Sieberg, 1999. "Some Surprising Properties of Power Indices," Discussion Papers 1271, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  2. Carreras, Francesc, 2005. "A decisiveness index for simple games," European Journal of Operational Research, Elsevier, vol. 163(2), pages 370-387, June.
  3. J. Alonso-Meijide & F. Carreras & M. Fiestras-Janeiro, 2005. "The Multilinear Extension and the Symmetric Coalition Banzhaf Value," Theory and Decision, Springer, vol. 59(2), pages 111-126, 09.
  4. WidgrÉn, Mika, 2002. "On the Probabilistic Relationship between the Public Good Index and the Normalized Banzhaf Index," Discussion Papers 707, The Research Institute of the Finnish Economy.
  5. Harrie De Swart & Agnieszka Rusinowska, 2007. "On some properties of the Hoede-Bakker index," Post-Print halshs-00201414, HAL.
  6. Federico Valenciano & Annick Laruelle, 2000. "- Shapley-Shubik And Banzhaf Indices Revisited," Working Papers. Serie AD 2000-02, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).

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