Achievable Hierarchies In Voting Games
AbstractPrevious work by Diffo Lambo and Moulen [Theory and Decision 53, 313â€“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 Shapleyâ€“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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Bibliographic InfoArticle provided by Springer in its journal Theory and Decision.
Volume (Year): 61 (2006)
Issue (Month): 4 (December)
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Web page: http://www.springerlink.com/link.asp?id=100341
desirability relation; ordinal equivalence; power indices; swap robust; voting games;
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- 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.
- 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.
- Josep Freixas & Montserrat Pons, 2010. "Hierarchies achievable in simple games," Theory and Decision, Springer, vol. 68(4), pages 393-404, April.
- 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.
- Pongou, Roland & Tchantcho, Bertrand & Diffo Lambo, Lawrence, 2008.
"Political Influence in Multi-Choice Institutions: Cyclicity, Anonymity and Transitivity,"
18240, University Library of Munich, Germany, revised 20 Oct 2009.
- 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.
- 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.
- Dwight Bean & Jane Friedman & Cameron Parker, 2008. "Simple Majority Achievable Hierarchies," Theory and Decision, Springer, vol. 65(4), pages 285-302, December.
- 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.
- 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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