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Cooperative bargaining foundations of the Shapley-Shubik index

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  • Laruelle, Annick
  • Valenciano, Federico

Abstract

In a recent paper, we provide an interpretation of the Shapley-Shubik index as a measure of the 'bargaining power' that a voting rule gives to each member of a committee negotiating in search of consensus. It is assumed that negotiation takes place under the condition that every winning coalition can impose any agreement. In this paper we further investigate the axiomatic foundations of this interpretation of the Shapley-Shubik index. To this end a wider framework admitting random voting rules is considered.

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  • Laruelle, Annick & Valenciano, Federico, 2009. "Cooperative bargaining foundations of the Shapley-Shubik index," Games and Economic Behavior, Elsevier, vol. 65(1), pages 242-255, January.
  • Handle: RePEc:eee:gamebe:v:65:y:2009:i:1:p:242-255
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    References listed on IDEAS

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    1. Kalai, Ehud & Smorodinsky, Meir, 1975. "Other Solutions to Nash's Bargaining Problem," Econometrica, Econometric Society, vol. 43(3), pages 513-518, May.
    2. Myerson, Roger B, 1981. "Utilitarianism, Egalitarianism, and the Timing Effect in Social Choice Problems," Econometrica, Econometric Society, vol. 49(4), pages 883-897, June.
    3. Nash, John, 1950. "The Bargaining Problem," Econometrica, Econometric Society, vol. 18(2), pages 155-162, April.
    4. Laruelle, Annick & Valenciano, Federico, 2007. "Bargaining in committees as an extension of Nash's bargaining theory," Journal of Economic Theory, Elsevier, vol. 132(1), pages 291-305, January.
    5. Hart, Sergiu, 1985. "An Axiomatization of Harsanyi's Nontransferable Utility Solution," Econometrica, Econometric Society, vol. 53(6), pages 1295-1313, November.
    6. Peters, Hans J M, 1986. "Simultaneity of Issues and Additivity in Bargaining," Econometrica, Econometric Society, vol. 54(1), pages 153-169, January.
    7. Roemer, John E., 1988. "Axiomatic bargaining theory on economic environments," Journal of Economic Theory, Elsevier, vol. 45(1), pages 1-31, June.
    8. Aumann, Robert J, 1985. "An Axiomatization of the Non-transferable Utility Value," Econometrica, Econometric Society, vol. 53(3), pages 599-612, May.
    9. Shapley, L. S. & Shubik, Martin, 1954. "A Method for Evaluating the Distribution of Power in a Committee System," American Political Science Review, Cambridge University Press, vol. 48(3), pages 787-792, September.
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    Cited by:

    1. Di Giannatale, Paolo & Passarelli, Francesco, 2013. "Voting chances instead of voting weights," Mathematical Social Sciences, Elsevier, vol. 65(3), pages 164-173.
    2. Martin, Mathieu & Nganmeni, Zephirin & Tchantcho, Bertrand, 2017. "The Owen and Shapley spatial power indices: A comparison and a generalization," Mathematical Social Sciences, Elsevier, vol. 89(C), pages 10-19.
    3. Grabisch, Michel & Rusinowska, Agnieszka, 2011. "Influence functions, followers and command games," Games and Economic Behavior, Elsevier, vol. 72(1), pages 123-138, May.

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