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- Shapley-Shubik And Banzhaf Indices Revisited

  • Federico Valenciano

    ()

    (Universidad del País Vasco)

  • Annick Laruelle

    (Universidad de Alicante)

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 Function: Fisrt version / Primera version, 2000
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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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  1. Annick Laruelle, 1999. "- On The Choice Of A Power Index," Working Papers. Serie AD 1999-10, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
  2. Feltkamp, V., 1993. "Alternative Axiomatic Characterizations of the Shapley and Banzhaf Values," Papers 9353, Tilburg - Center for Economic Research.
  3. Robert J. Weber, 1977. "Probabilistic Values for Games," Cowles Foundation Discussion Papers 471R, Cowles Foundation for Research in Economics, Yale University.
  4. 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.
  5. 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.
  6. Robert J. Weber, 1979. "Subjectivity in the Valuation of Games," Cowles Foundation Discussion Papers 515, Cowles Foundation for Research in Economics, Yale University.
  7. E. Calvo & Juan Carlos Santos, 2000. "Weighted weak semivalues," International Journal of Game Theory, Springer, vol. 29(1), pages 1-9.
  8. 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).
  9. Roth, Alvin E., 1977. "Utility functions for simple games," Journal of Economic Theory, Elsevier, vol. 16(2), pages 481-489, December.
  10. Lehrer, E, 1988. "An Axiomatization of the Banzhaf Value," International Journal of Game Theory, Springer, vol. 17(2), pages 89-99.
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