IDEAS home Printed from https://ideas.repec.org/p/ivi/wpasad/2000-02.html
   My bibliography  Save this paper

- 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

    Download full text from publisher

    File URL: http://www.ivie.es/downloads/docs/wpasad/wpasad-2000-02.pdf
    File Function: Fisrt version / Primera version, 2000
    Download Restriction: no

    Other versions of this item:

    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. Robert J. Weber, 1977. "Probabilistic Values for Games," Cowles Foundation Discussion Papers 471R, Cowles Foundation for Research in Economics, Yale University.
    3. 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.
    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. Robert J. Weber, 1979. "Subjectivity in the Valuation of Games," Cowles Foundation Discussion Papers 515, Cowles Foundation for Research in Economics, Yale University.
    6. 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.
    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. Roth, Alvin E., 1977. "Utility functions for simple games," Journal of Economic Theory, Elsevier, vol. 16(2), pages 481-489, December.
    9. E. Calvo & Juan Carlos Santos, 2000. "Weighted weak semivalues," International Journal of Game Theory, Springer;Game Theory Society, vol. 29(1), pages 1-9.
    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
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Kauppi, Heikki & Widgrén, Mika, 2008. "Do Benevolent Aspects Have Room in Explaining EU Budget Receipts?," CEPR Discussion Papers 6778, C.E.P.R. Discussion Papers.
    2. Albizuri Irigoyen, Miren Iosune & Laruelle, Annick, 2011. "An axiomatization of success," IKERLANAK 2011-49, Universidad del País Vasco - Departamento de Fundamentos del Análisis Económico I.
    3. Kauppi, Heikki & Widgrén, Mika, 2005. "Voting Rules and Budget Allocation in an Enlarged EU," CEPR Discussion Papers 5134, C.E.P.R. Discussion Papers.
    4. 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.
    5. Fabien Lange & László Kóczy, 2013. "Power indices expressed in terms of minimal winning coalitions," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 41(2), pages 281-292, July.
    6. Bhattacherjee, Sanjay & Sarkar, Palash, 2017. "Correlation and inequality in weighted majority voting games," MPRA Paper 83168, University Library of Munich, Germany.
    7. 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.
    8. Jean-François Caulier, 2010. "On the measurement of Fragmentation," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-00633613, HAL.
    9. 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.
    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. 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.
    12. 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.
    13. Ori Haimanko, 2017. "Composition Independence In Compound Games: A Characterization Of The Banzhaf Power Index And The Banzhaf Value," Working Papers 1713, Ben-Gurion University of the Negev, Department of Economics.
    14. 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.
    15. Kauppi, Heikki & Widgrén, Mika, 2008. "Do Benevolent Aspects Have Room Explaining EU Bydget Receipts?," Discussion Papers 1161, The Research Institute of the Finnish Economy.
    16. Aleskerov, Fuad, 2009. "Power indices taking into account agents' preferences," The Warwick Economics Research Paper Series (TWERPS) 898, University of Warwick, Department of Economics.
    17. repec:spr:grdene:v:27:y:2018:i:1:d:10.1007_s10726-017-9546-6 is not listed on IDEAS
    18. Jean-François Caulier, 2010. "On the measurement of Fragmentation," Working Papers hal-00633613, HAL.
    19. 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.
    20. 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.
    21. 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.
    22. 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.
    23. 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.
    24. repec:spr:grdene:v:21:y:2012:i:5:d:10.1007_s10726-011-9239-5 is not listed on IDEAS

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:ivi:wpasad:2000-02. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Departamento de Edición) or (Hassan Zaidi). General contact details of provider: http://edirc.repec.org/data/ievages.html .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.