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On ordinal equivalence of power measures given by regular semivalues

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  • Carreras, Francesc
  • Freixas, Josep
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    Abstract

    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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    Bibliographic Info

    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

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    Web page: http://www.elsevier.com/locate/inca/505565

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    1. 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.
    2. Carreras, Francesc & Freixas, Josep, 1996. "Complete simple games," Mathematical Social Sciences, Elsevier, vol. 32(2), pages 139-155, October.
    3. Annick Laruelle & Federico Valenciano, 2005. "A critical reappraisal of some voting power paradoxes," Public Choice, Springer, vol. 125(1), pages 17-41, July.
    4. 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.
    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. Taylor Alan & Zwicker William, 1993. "Weighted Voting, Multicameral Representation, and Power," Games and Economic Behavior, Elsevier, vol. 5(1), pages 170-181, January.
    7. van Deemen, Adrian & Rusinowska, Agnieszka, 2003. " Paradoxes of Voting Power in Dutch Politics," Public Choice, Springer, vol. 115(1-2), pages 109-37, April.
    8. Jane Friedman & Lynn Mcgrath & Cameron Parker, 2006. "Achievable Hierarchies In Voting Games," Theory and Decision, Springer, vol. 61(4), pages 305-318, December.
    9. Dreyer, Jacob S & Schotter, Andrew, 1980. "Power Relationships in the International Monetary Fund: The Consequences of Quota Changes," The Review of Economics and Statistics, MIT Press, vol. 62(1), pages 97-106, February.
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    Cited by:
    1. Pongou, Roland & Tchantcho, Bertrand & Diffo Lambo, Lawrence, 2008. "Political Influence in Multi-Choice Institutions: Cyclicity, Anonymity and Transitivity," MPRA Paper 18240, University Library of Munich, Germany, revised 20 Oct 2009.
    2. Freixas, Josep & Marciniak, Dorota & Pons, Montserrat, 2012. "On the ordinal equivalence of the Johnston, Banzhaf and Shapley power indices," European Journal of Operational Research, Elsevier, vol. 216(2), pages 367-375.
    3. Josep Freixas & Dorota Marciniak, 2013. "Egalitarian property for power indices," Social Choice and Welfare, Springer, vol. 40(1), pages 207-227, January.
    4. Cheung, Wai-Shun & Ng, Tuen-Wai, 2014. "A three-dimensional voting system in Hong Kong," European Journal of Operational Research, Elsevier, vol. 236(1), pages 292-297.
    5. Bishnu, Monisankar & Roy, Sonali, 2009. "Hierarchy of Players in Swap Robust Voting Games," Staff General Research Papers 13118, Iowa State University, Department of Economics.
    6. Chameni Nembua, Célestin & Demsou, Themoi, 2013. "Ordinal equivalence of values and Pigou-Dalton transfers in TU-games," MPRA Paper 44895, University Library of Munich, Germany, revised 09 Mar 2013.
    7. Josep Freixas & Montserrat Pons, 2010. "Hierarchies achievable in simple games," Theory and Decision, Springer, vol. 68(4), pages 393-404, April.
    8. Freixas, Josep & Kaniovski, Serguei, 2014. "The minimum sum representation as an index of voting power," European Journal of Operational Research, Elsevier, vol. 233(3), pages 739-748.
    9. Freixas, Josep, 2012. "Probabilistic power indices for voting rules with abstention," Mathematical Social Sciences, Elsevier, vol. 64(1), pages 89-99.
    10. Josep Freixas, 2010. "On ordinal equivalence of the Shapley and Banzhaf values for cooperative games," International Journal of Game Theory, Springer, vol. 39(4), pages 513-527, October.
    11. Roberto Lucchetti & Paola Radrizzani & Emanuele Munarini, 2011. "A new family of regular semivalues and applications," International Journal of Game Theory, Springer, vol. 40(4), pages 655-675, November.
    12. Parker, Cameron, 2012. "The influence relation for ternary voting games," Games and Economic Behavior, Elsevier, vol. 75(2), pages 867-881.

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