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
Date of revision:
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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, 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.:
- 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), Center for Research in Economics and Management (CREM), University of Rennes 1, University of Caen and CNRS
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, Springer, vol. 30(3), pages 363-383, April.
- Wilson, Mark C. & Pritchard, Geoffrey, 2007. "Probability calculations under the IAC hypothesis," Mathematical Social Sciences, Elsevier, Elsevier, vol. 54(3), pages 244-256, December.
- William V. Gehrlein, 2002. "Obtaining representations for probabilities of voting outcomes with effectively unlimited precision integer arithmetic," Social Choice and Welfare, Springer, Springer, vol. 19(3), pages 503-512.
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