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Characterizations of two power indices for voting games with r alternatives

Author

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  • Edward M. Bolger

    (Department of Mathematics and Statistics, Miami University, 123 Bachelor Hall, Oxford, Ohio, 45056-1641, USA)

Abstract

In the first three sections of this paper we present a set of axioms which provide a characterization of an extension of the Banzhaf index to voting games with r alternatives, such as the United Nations Security Council where a nation can vote "yes", "no", or "abstain". The fourth section presents a set of axioms which characterizes a power index based on winning sets instead of pivot sets.

Suggested Citation

  • Edward M. Bolger, 2002. "Characterizations of two power indices for voting games with r alternatives," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 19(4), pages 709-721.
    • Handle: RePEc:spr:sochwe:v:19:y:2002:i:4:p:709-721
    Note: Received: 4 April 2000/Accepted: 30 April 2001
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    Citations

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    Cited by:

    1. Michel Grabisch & Agnieszka Rusinowska, 2010. "A model of influence with an ordered set of possible actions," Theory and Decision, Springer, vol. 69(4), pages 635-656, October.
    2. Birkmeier Olga & Käufl Andreas & Pukelsheim Friedrich, 2011. "Abstentions in the German Bundesrat and ternary decision rules in weighted voting systems," Statistics & Risk Modeling, De Gruyter, vol. 28(1), pages 1-16, March.
    3. René van den Brink & Agnieszka Rusinowska & Frank Steffen, 2009. "Measuring Power and Satisfaction in Societies with Opinion Leaders: Dictator and Opinion Leader Properties," Tinbergen Institute Discussion Papers 09-052/1, Tinbergen Institute.
    4. Grabisch, Michel & Rusinowska, Agnieszka, 2011. "Influence functions, followers and command games," Games and Economic Behavior, Elsevier, vol. 72(1), pages 123-138, May.
    5. Sébastien Courtin & Zéphirin Nganmeni & Bertrand Tchantcho, 2016. "The Shapley–Shubik power index for dichotomous multi-type games," Theory and Decision, Springer, vol. 81(3), pages 413-426, September.
    6. Tchantcho, Bertrand & Lambo, Lawrence Diffo & Pongou, Roland & Engoulou, Bertrand Mbama, 2008. "Voters' power in voting games with abstention: Influence relation and ordinal equivalence of power theories," Games and Economic Behavior, Elsevier, vol. 64(1), pages 335-350, September.
    7. Michel Grabisch & Agnieszka Rusinowska, 2009. "A model of influence with a continuum of actions," Post-Print halshs-00464460, HAL.
    8. René Brink & Agnieszka Rusinowska & Frank Steffen, 2013. "Measuring power and satisfaction in societies with opinion leaders: an axiomatization," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 41(3), pages 671-683, September.
    9. Grabisch, Michel & Rusinowska, Agnieszka, 2011. "A model of influence with a continuum of actions," Journal of Mathematical Economics, Elsevier, vol. 47(4-5), pages 576-587.
    10. M. Álvarez-Mozos & O. Tejada, 2015. "The Banzhaf value in the presence of externalities," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 44(4), pages 781-805, April.
    11. Josep Freixas & Montserrat Pons, 2021. "An Appropriate Way to Extend the Banzhaf Index for Multiple Levels of Approval," Group Decision and Negotiation, Springer, vol. 30(2), pages 447-462, April.
    12. Josep Freixas, 2005. "Banzhaf Measures for Games with Several Levels of Approval in the Input and Output," Annals of Operations Research, Springer, vol. 137(1), pages 45-66, July.
    13. Sascha Kurz, 2014. "Measuring Voting Power in Convex Policy Spaces," Economies, MDPI, vol. 2(1), pages 1-33, March.
    14. Maria Ekes, 2013. "Application of Generalized Owen Value for Voting Games in Partition Function Form," Collegium of Economic Analysis Annals, Warsaw School of Economics, Collegium of Economic Analysis, issue 32, pages 43-53.

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