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On ordinal equivalence of power measures given by regular semivalues

  • Carreras, Francesc
  • Freixas, Josep
Registered author(s):

    Tomiyama [Tomiyama, Y., 1987. Simple game, voting representation and ordinal power equivalence. International Journal on Policy and Information 11, 67-75] proved that, for every weighted majority game, the preorderings induced by the classical Shapley-Shubik and Penrose-Banzhaf-Coleman indices coincide. He called this property the ordinal equivalence of these indices for weighted majority games. Diffo Lambo and Moulen [Diffo Lambo, L., Moulen, J., 2002. Ordinal equivalence of power notions in voting games. Theory and Decision 53, 313-325] extended Tomiyama's result to all linear (i.e. swap robust) simple games. Here we extend Diffo Lambo and Moulen's result to all the preorderings induced by regular semivalues (which include both classical indices) in a larger class of games that we call weakly linear simple games. We also provide a characterization of weakly linear games and use nonsymmetric transitive games to supplying examples of nonlinear but weakly linear games.

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    File URL: http://www.sciencedirect.com/science/article/B6V88-4PJM9FG-1/1/4d437ea72c0045bc2db13ad8829058f8
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    Article provided by Elsevier in its journal Mathematical Social Sciences.

    Volume (Year): 55 (2008)
    Issue (Month): 2 (March)
    Pages: 221-234

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    Handle: RePEc:eee:matsoc:v:55:y:2008:i:2:p:221-234
    Contact details of provider: Web page: http://www.elsevier.com/locate/inca/505565

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    1. van Deemen, Adrian & Rusinowska, Agnieszka, 2003. " Paradoxes of Voting Power in Dutch Politics," Public Choice, Springer, vol. 115(1-2), pages 109-37, April.
    2. Federico Valenciano & Annick Laruelle, 2000. "- Power Indices And The Veil Of Ignorance," Working Papers. Serie AD 2000-13, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
    3. Federico Valenciano & Annick Laruelle, 2004. "A Critical Reappraisal Of Some Voting Power Paradoxes," Working Papers. Serie AD 2004-04, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
    4. Lawrence Diffo Lambo & Joël Moulen, 2002. "Ordinal equivalence of power notions in voting games," Theory and Decision, Springer, vol. 53(4), pages 313-325, December.
    5. Dreyer, Jacob S. & Schotter, Andrew, 1978. "Power Relationships in the International Monetary Fund: The Consequences of Quota Changes," Working Papers 78-06, C.V. Starr Center for Applied Economics, New York University.
    6. Jane Friedman & Lynn Mcgrath & Cameron Parker, 2006. "Achievable Hierarchies In Voting Games," Theory and Decision, Springer, vol. 61(4), pages 305-318, December.
    7. Robert J. Weber, 1979. "Subjectivity in the Valuation of Games," Cowles Foundation Discussion Papers 515, Cowles Foundation for Research in Economics, Yale University.
    8. Taylor Alan & Zwicker William, 1993. "Weighted Voting, Multicameral Representation, and Power," Games and Economic Behavior, Elsevier, vol. 5(1), pages 170-181, January.
    9. 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.
    10. Carreras, Francesc & Freixas, Josep, 1996. "Complete simple games," Mathematical Social Sciences, Elsevier, vol. 32(2), pages 139-155, October.
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