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Dummy Players and the Quota in Weighted Voting Games: Some Further Results

In: Evaluating Voting Systems with Probability Models

Author

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  • Fabrice Barthélémy

    (Université de Versailles Saint-Quentin en Yvelines, CEMOTEV)

  • Mathieu Martin

    (CY Cergy Paris UniversitHEMA)

Abstract

This chapter is a companion paper of Barthélémy et al. (2019) which studies the role of the quota on the occurrence of “dummy” players in small weighted voting games (i.e., in voting games with 3, 4 or 5 players). We here extend the results obtained in this paper by considering voting games with a larger number of players (up to 15). It is shown that the probability of having a player without voting power is very sensitive to the choice of the quota and the quota values that minimize this probability are derived.

Suggested Citation

  • Fabrice Barthélémy & Mathieu Martin, 2021. "Dummy Players and the Quota in Weighted Voting Games: Some Further Results," Studies in Choice and Welfare, in: Mostapha Diss & Vincent Merlin (ed.), Evaluating Voting Systems with Probability Models, pages 299-315, Springer.
    • Handle: RePEc:spr:stcchp:978-3-030-48598-6_13
    DOI: 10.1007/978-3-030-48598-6_13
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    References listed on IDEAS

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    1. Diss, Mostapha & Louichi, Ahmed & Merlin, Vincent & Smaoui, Hatem, 2012. "An example of probability computations under the IAC assumption: The stability of scoring rules," Mathematical Social Sciences, Elsevier, vol. 64(1), pages 57-66.
    2. Fabrice Barthelemy & Mathieu Martin & Bertrand Tchantcho, 2011. "Some conjectures on the two main power indices," THEMA Working Papers 2011-14, THEMA (THéorie Economique, Modélisation et Applications), Université de Cergy-Pontoise.
    3. Dominique Lepelley & Ahmed Louichi & Hatem Smaoui, 2008. "On Ehrhart polynomials and probability calculations in voting theory," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 30(3), pages 363-383, April.
    4. Lindner, Ines & Machover, Moshe, 2004. "L.S. Penrose's limit theorem: proof of some special cases," Mathematical Social Sciences, Elsevier, vol. 47(1), pages 37-49, January.
    5. Fabrice Barthélémy & Dominique Lepelley & Mathieu Martin, 2013. "On the likelihood of dummy players in weighted majority games," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 41(2), pages 263-279, July.
    6. Dan S. Felsenthal & Moshé Machover, 1998. "The Measurement of Voting Power," Books, Edward Elgar Publishing, number 1489.
    7. William V. Gehrlein & Dominique Lepelley, 2017. "Elections, Voting Rules and Paradoxical Outcomes," Studies in Choice and Welfare, Springer, number 978-3-319-64659-6, December.
    8. Sébastien Courtin & Boniface Mbih & Issofa Moyouwou, 2014. "Are Condorcet procedures so bad according to the reinforcement axiom?," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 42(4), pages 927-940, April.
    9. Chang, Pao-Li & Chua, Vincent C.H. & Machover, Moshe, 2006. "L S Penrose's limit theorem: Tests by simulation," Mathematical Social Sciences, Elsevier, vol. 51(1), pages 90-106, January.
    10. Leech, Dennis, 2002. "Power Indices as an Aid to Institutional Design: The Generalised Apportionment Problem," Economic Research Papers 269461, University of Warwick - Department of Economics.
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    More about this item

    JEL classification:

    • C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory
    • D7 - Microeconomics - - Analysis of Collective Decision-Making

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