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Achievable Hierarchies In Voting Games

Author

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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

Suggested Citation

  • Jane Friedman & Lynn Mcgrath & Cameron Parker, 2006. "Achievable Hierarchies In Voting Games," Theory and Decision, Springer, vol. 61(4), pages 305-318, December.
  • Handle: RePEc:kap:theord:v:61:y:2006:i:4:p:305-318
    DOI: 10.1007/s11238-006-9003-5
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    File URL: http://hdl.handle.net/10.1007/s11238-006-9003-5
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    References listed on IDEAS

    as
    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. repec:cup:apsrev:v:48:y:1954:i:03:p:787-792_00 is not listed on IDEAS
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    Citations

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    Cited by:

    1. Josep Freixas, 2010. "On ordinal equivalence of the Shapley and Banzhaf values for cooperative games," International Journal of Game Theory, Springer;Game Theory Society, vol. 39(4), pages 513-527, October.
    2. Dwight Bean & Jane Friedman & Cameron Parker, 2008. "Simple Majority Achievable Hierarchies," Theory and Decision, Springer, vol. 65(4), pages 285-302, December.
    3. 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.
    4. Josep Freixas & Montserrat Pons, 2010. "Hierarchies achievable in simple games," Theory and Decision, Springer, vol. 68(4), pages 393-404, April.
    5. 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.
    6. 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.
    7. Dwight Bean, 2012. "Proportional quota weighted voting system hierarchies II," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 39(4), pages 907-918, October.
    8. repec:kap:theord:v:82:y:2017:i:4:d:10.1007_s11238-016-9576-6 is not listed on IDEAS
    9. Dwight Bean & Jane Friedman & Cameron Parker, 2010. "Proportional quota weighted voting system hierarchies," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 34(3), pages 397-410, March.
    10. Parker, Cameron, 2012. "The influence relation for ternary voting games," Games and Economic Behavior, Elsevier, vol. 75(2), pages 867-881.
    11. 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.
    12. repec:kap:theord:v:83:y:2017:i:4:d:10.1007_s11238-017-9606-z is not listed on IDEAS
    13. 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.

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