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Achievable Hierarchies In Voting Games

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  • Jane Friedman
  • Lynn Mcgrath
  • Cameron Parker

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    Abstract

    Previous work by Diffo Lambo and Moulen [Theory and Decision 53, 313–325 (2002)] and Felsenthal and Machover [The Measurement of Voting Power, Edward Elgar Publishing Limited (1998)], shows that all swap preserving measures of voting power are ordinally equivalent on any swap robust simple voting game. Swap preserving measures include the Banzhaf, the Shapley–Shubik and other commonly used measures of a priori voting power. In this paper, we completely characterize the achievable hierarchies for any such measure on a swap robust simple voting game. Each possible hierarchy can be induced by a weighted voting game and we provide a constructive proof of this result. In particular, the strict hierarchy is always achievable as long as there are at least five players. Copyright Springer 2006

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    File URL: http://hdl.handle.net/10.1007/s11238-006-9003-5
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    Bibliographic Info

    Article provided by Springer in its journal Theory and Decision.

    Volume (Year): 61 (2006)
    Issue (Month): 4 (December)
    Pages: 305-318

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    Handle: RePEc:kap:theord:v:61:y:2006:i:4:p:305-318

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    Web page: http://www.springerlink.com/link.asp?id=100341

    Related research

    Keywords: desirability relation; ordinal equivalence; power indices; swap robust; voting games;

    References

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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.
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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 & Tchantcho, Bertrand & Tedjeugang, Narcisse, 2014. "Achievable hierarchies in voting games with abstention," European Journal of Operational Research, Elsevier, vol. 236(1), pages 254-260.
    3. Dwight Bean, 2012. "Proportional quota weighted voting system hierarchies II," Social Choice and Welfare, Springer, vol. 39(4), pages 907-918, October.
    4. 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.
    5. Dwight Bean & Jane Friedman & Cameron Parker, 2010. "Proportional quota weighted voting system hierarchies," Social Choice and Welfare, Springer, vol. 34(3), pages 397-410, March.
    6. 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.
    7. Carreras, Francesc & Freixas, Josep, 2008. "On ordinal equivalence of power measures given by regular semivalues," Mathematical Social Sciences, Elsevier, vol. 55(2), pages 221-234, March.
    8. Josep Freixas & Montserrat Pons, 2010. "Hierarchies achievable in simple games," Theory and Decision, Springer, vol. 68(4), pages 393-404, April.
    9. Dwight Bean & Jane Friedman & Cameron Parker, 2008. "Simple Majority Achievable Hierarchies," Theory and Decision, Springer, vol. 65(4), pages 285-302, December.
    10. 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.
    11. 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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