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- Shapley-Shubik And Banzhaf Indices Revisited

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Author Info

  • Federico Valenciano

    ()
    (Universidad del País Vasco)

  • Annick Laruelle

    (Universidad de Alicante)

Abstract

We provide a new axiomatization of the Shapley-Shubik and the Banzhaf power indices in thedomain of simple superadditive games by means of transparent axioms. Only anonymity isshared with the former characterizations in the literature. The rest of the axioms are substitutedby more transparent ones in terms of power in collective decision-making procedures. Inparticular, a clear restatement and a compelling alternative for the transfer axiom are proposed.Only one axiom differentiates the characterization of either index, and these differentiatingaxioms provide a new point of comparison. In a first step both indices are characterized up to azero and a unit of scale. Then both indices are singled out by simple normalizing axioms.

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File URL: http://www.ivie.es/downloads/docs/wpasad/wpasad-2000-02.pdf
File Function: Fisrt version / Primera version, 2000
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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 2000-02.

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Length: 25 pages
Date of creation: Jan 2000
Date of revision:
Publication status: Published by Ivie
Handle: RePEc:ivi:wpasad:2000-02

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Related research

Keywords: Power indices; voting power; collective decision-making; simple games;

References

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  1. Robert J. Weber, 1977. "Probabilistic Values for Games," Cowles Foundation Discussion Papers 471R, Cowles Foundation for Research in Economics, Yale University.
  2. Feltkamp, Vincent, 1995. "Alternative Axiomatic Characterizations of the Shapley and Banzhaf Values," International Journal of Game Theory, Springer, vol. 24(2), pages 179-86.
  3. 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.
  4. E. Calvo & Juan Carlos Santos, 2000. "Weighted weak semivalues," International Journal of Game Theory, Springer, vol. 29(1), pages 1-9.
  5. Lehrer, E, 1988. "An Axiomatization of the Banzhaf Value," International Journal of Game Theory, Springer, vol. 17(2), pages 89-99.
  6. Andrzej S. Nowak, 1997. "note: On an Axiomatization of the Banzhaf Value without the Additivity Axiom," International Journal of Game Theory, Springer, vol. 26(1), pages 137-141.
  7. 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).
  8. Robert J. Weber, 1979. "Subjectivity in the Valuation of Games," Cowles Foundation Discussion Papers 515, Cowles Foundation for Research in Economics, Yale University.
  9. Roth, Alvin E., 1977. "Utility functions for simple games," Journal of Economic Theory, Elsevier, vol. 16(2), pages 481-489, December.
  10. Annick Laruelle, 1999. "- On The Choice Of A Power Index," Working Papers. Serie AD 1999-10, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
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Citations

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Cited by:
  1. Leech, Dennis, 2002. "Power Indices As An Aid To Institutional Design : The Generalised Apportionment Problem," The Warwick Economics Research Paper Series (TWERPS) 648, University of Warwick, Department of Economics.
  2. Jean-François Caulier, 2010. "On the measurement of Fragmentation," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-00633613, HAL.
  3. Kauppi, Heikki & Widgren, Mika, 2007. "Voting rules and budget allocation in the enlarged EU," European Journal of Political Economy, Elsevier, vol. 23(3), pages 693-706, September.
  4. Kauppi, Heikki & Widgrén, Mika, 2005. "Voting Rules and Budget Allocation in an Enlarged EU," CEPR Discussion Papers 5134, C.E.P.R. Discussion Papers.
  5. Fabien Lange & Laszlo A. Koczy, 2012. "Power indices expressed in terms of minimal winning coalitions," IEHAS Discussion Papers 1220, Institute of Economics, Centre for Economic and Regional Studies, Hungarian Academy of Sciences.
  6. Pradeep Dubey & Ezra Einy & Ori Haimanko, 2003. "Compound Voting and the Banzhaf Power Index," Discussion Paper Series dp333, The Center for the Study of Rationality, Hebrew University, Jerusalem.
  7. Jean-François Caulier, 2010. "On the measurement of Fragmentation," Working Papers hal-00633613, HAL.
  8. Heikki Kauppi & Mika Widgrén, 2008. "Do Benevolent Aspects Have Room in Explaining EU Budget Receipts?," Discussion Papers 38, Aboa Centre for Economics.
  9. Aleskerov, Fuad, 2009. "Power indices taking into account agents' preferences," The Warwick Economics Research Paper Series (TWERPS) 898, University of Warwick, Department of Economics.
  10. Kauppi, Heikki & Widgrén, Mika, 2008. "Do Benevolent Aspects Have Room Explaining EU Bydget Receipts?," Discussion Papers 1161, The Research Institute of the Finnish Economy.
  11. Barua, Rana & Chakravarty, Sanya R. & Roy, Sonali, 2007. "On the Coleman Indices of Voting Power," Staff General Research Papers 12810, Iowa State University, Department of Economics.
  12. Yan-An Hwang & Yu-Hsien Liao, 2010. "Consistency and dynamic approach of indexes," Social Choice and Welfare, Springer, vol. 34(4), pages 679-694, April.
  13. Robert E. Goodin & Werner Güth & Duncan Snidal, 2005. "Strategic Aspects of Hegemony," Papers on Strategic Interaction 2005-29, Max Planck Institute of Economics, Strategic Interaction Group.
  14. Roland Pongou & Bertrand Tchantcho & Lawrence Diffo Lambo, 2011. "Political influence in multi-choice institutions: cyclicity, anonymity, and transitivity," Theory and Decision, Springer, vol. 70(2), pages 157-178, February.
  15. Stefan Napel & Mika Widgrén, 2011. "Strategic versus non-strategic voting power in the EU Council of Ministers: the consultation procedure," Social Choice and Welfare, Springer, vol. 37(3), pages 511-541, September.
  16. Leech, Dennis, 2002. "The Use Of Coleman'S Power Indices To Inform The Choice Of Voting Rule With Reference To The Imf Governing Body And The Eu Council Of Ministers," The Warwick Economics Research Paper Series (TWERPS) 645, University of Warwick, Department of Economics.

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