On the Likelihood of Dummy players in Weighted Majority Games
AbstractWhen the number of players is small in a weighted majority voting game, it can occur that one of the players has no influence on the result of the vote, in spite of a strictly positive weight. Such a player is called a “dummy” player in game theory. The purpose of this paper is to investigate the conditions that give rise to such a phenomenon and to compute its likelihood. It is shown that the probability of having a dummy player is surprisingly high and some paradoxical results are observed.
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Bibliographic InfoPaper provided by THEMA (THéorie Economique, Modélisation et Applications), Université de Cergy-Pontoise in its series THEMA Working Papers with number 2011-17.
Date of creation: 2011
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Cooperative game theory; weighted voting games; dummy player; likelihood of voting paradoxes.;
Other versions of this item:
- Fabrice Barthélémy & Dominique Lepelley & Mathieu Martin, 2013. "On the likelihood of dummy players in weighted majority games," Social Choice and Welfare, Springer, vol. 41(2), pages 263-279, July.
- C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory
- D7 - Microeconomics - - Analysis of Collective Decision-Making
This paper has been announced in the following NEP Reports:
- NEP-ALL-2012-03-08 (All new papers)
- NEP-CDM-2012-03-08 (Collective Decision-Making)
- NEP-GTH-2012-03-08 (Game Theory)
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.:
- Wilson, Mark C. & Pritchard, Geoffrey, 2007. "Probability calculations under the IAC hypothesis," Mathematical Social Sciences, Elsevier, vol. 54(3), pages 244-256, December.
- Dominique Lepelley & Ahmed Louichi & Hatem Smaoui, 2006.
"On Ehrhart Polynomials and Probability Calculations in Voting Theory,"
Economics Working Paper Archive (University of Rennes 1 & University of Caen)
200610, Center for Research in Economics and Management (CREM), University of Rennes 1, University of Caen and CNRS.
- Dominique Lepelley & Ahmed Louichi & Hatem Smaoui, 2008. "On Ehrhart polynomials and probability calculations in voting theory," Social Choice and Welfare, Springer, vol. 30(3), pages 363-383, April.
- William V. Gehrlein, 2002. "Obtaining representations for probabilities of voting outcomes with effectively unlimited precision integer arithmetic," Social Choice and Welfare, Springer, vol. 19(3), pages 503-512.
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