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- Shapley-Shubik And Banzhaf Indices Revisited

Author

Listed:
  • 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.

Suggested Citation

  • 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).
    • Handle: RePEc:ivi:wpasad:2000-02
    as

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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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    References listed on IDEAS

    as
    1. Lehrer, E, 1988. "An Axiomatization of the Banzhaf Value," International Journal of Game Theory, Springer;Game Theory Society, vol. 17(2), pages 89-99.
    2. Andrzej S. Nowak, 1997. "note: On an Axiomatization of the Banzhaf Value without the Additivity Axiom," International Journal of Game Theory, Springer;Game Theory Society, vol. 26(1), pages 137-141.
    3. Robert J. Weber, 1979. "Subjectivity in the Valuation of Games," Cowles Foundation Discussion Papers 515, Cowles Foundation for Research in Economics, Yale University.
    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. Roth, Alvin E., 1977. "Utility functions for simple games," Journal of Economic Theory, Elsevier, vol. 16(2), pages 481-489, December.
    6. Pradeep Dubey & Lloyd S. Shapley, 1979. "Mathematical Properties of the Banzhaf Power Index," Mathematics of Operations Research, INFORMS, vol. 4(2), pages 99-131, May.
    7. E. Calvo & Juan Carlos Santos, 2000. "Weighted weak semivalues," International Journal of Game Theory, Springer;Game Theory Society, vol. 29(1), pages 1-9.
    8. repec:cup:apsrev:v:63:y:1969:i:01:p:40-56_26 is not listed on IDEAS
    9. Pradeep Dubey & Robert J. Weber, 1977. "Probabilistic Values for Games," Cowles Foundation Discussion Papers 471, Cowles Foundation for Research in Economics, Yale University.
    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).
    11. repec:cup:apsrev:v:48:y:1954:i:03:p:787-792_00 is not listed on IDEAS
    12. Feltkamp, Vincent, 1995. "Alternative Axiomatic Characterizations of the Shapley and Banzhaf Values," International Journal of Game Theory, Springer;Game Theory Society, vol. 24(2), pages 179-186.
    Full references (including those not matched with items on IDEAS)

    Citations

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    Cited by:

    1. Berghammer, Rudolf & Bolus, Stefan & Rusinowska, Agnieszka & de Swart, Harrie, 2011. "A relation-algebraic approach to simple games," European Journal of Operational Research, Elsevier, vol. 210(1), pages 68-80, April.
    2. 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.
    3. Fuad Aleskerov, 2006. "Power Indices Taking into Account Agents’ Preferences," Studies in Choice and Welfare, in: Bruno Simeone & Friedrich Pukelsheim (ed.), Mathematics and Democracy, pages 1-18, Springer.
    4. 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.
    5. Carreras, Francesc & Freixas, Josep & Puente, Maria Albina, 2003. "Semivalues as power indices," European Journal of Operational Research, Elsevier, vol. 149(3), pages 676-687, September.
    6. Barua, Rana & Chakravarty, Satya R. & Sarkar, Palash, 2009. "Minimal-axiom characterizations of the Coleman and Banzhaf indices of voting power," Mathematical Social Sciences, Elsevier, vol. 58(3), pages 367-375, November.
    7. 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;The Society for Social Choice and Welfare, vol. 37(3), pages 511-541, September.
    8. Widgren, Mika & Kauppi, Heikki, 2008. "Do Benevolent Aspects Have Room in Explaining EU Budget Receipts?," CEPR Discussion Papers 6778, Centre for Economic Policy Research.
    9. 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.
    10. 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.
    11. Kauppi, Heikki & Widgrén, Mika, 2008. "Do Benevolent Aspects Have Room Explaining EU Bydget Receipts?," Discussion Papers 1161, The Research Institute of the Finnish Economy.
    12. Dubey, Pradeep & Einy, Ezra & Haimanko, Ori, 2005. "Compound voting and the Banzhaf index," Games and Economic Behavior, Elsevier, vol. 51(1), pages 20-30, April.
    13. Jean-François Caulier, 2010. "On the measurement of Fragmentation," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-00633613, HAL.
    14. Pradeep Dubey & Ezra Einy & Ori Haimanko, 2003. "Compound Voting and the Banzhaf Power Index," Discussion Paper Series dp333, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem.
    15. Yan-An Hwang & Yu-Hsien Liao, 2010. "Consistency and dynamic approach of indexes," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 34(4), pages 679-694, April.
    16. Jean-François Caulier, 2010. "On the measurement of Fragmentation," Working Papers hal-00633613, HAL.
    17. 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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