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Representation-compatible power indices

Author

Listed:
  • Serguei Kaniovski

    (Austrian Institute of Economic Research (WIFO))

  • Sascha Kurz

    (University of Bayreuth)

Abstract

This paper studies power indices based on average representations of a weighted game. If restricted to account for the lack of power of null voters, average representations become coherent measures of voting power, with power distributions being proportional to the distribution of weights in the average representation. This makes these indices representation-compatible, a property not fulfilled by classical power indices. In this paper we introduce two computationally cheaper alternatives to the existing representation-compatible power indices, and study the properties of a family that now comprises four measures.

Suggested Citation

  • Serguei Kaniovski & Sascha Kurz, 2018. "Representation-compatible power indices," Annals of Operations Research, Springer, vol. 264(1), pages 235-265, May.
    • Handle: RePEc:spr:annopr:v:264:y:2018:i:1:d:10.1007_s10479-017-2672-3
    DOI: 10.1007/s10479-017-2672-3
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    References listed on IDEAS

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    1. Sascha Kurz, 2012. "On minimum sum representations for weighted voting games," Annals of Operations Research, Springer, vol. 196(1), pages 361-369, July.
    2. Dan Felsenthal & Moshé Machover, 2005. "Voting power measurement: a story of misreinvention," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 25(2), pages 485-506, December.
    3. EINY, Ezra & LEHRER, Ehud, 1989. "Regular simple games," LIDAM Reprints CORE 850, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    4. Houy, Nicolas & Zwicker, William S., 2014. "The geometry of voting power: Weighted voting and hyper-ellipsoids," Games and Economic Behavior, Elsevier, vol. 84(C), pages 7-16.
    5. Carreras, Francesc & Freixas, Josep, 1996. "Complete simple games," Mathematical Social Sciences, Elsevier, vol. 32(2), pages 139-155, October.
    6. Einy, Ezra & Lehrer, Ehud, 1989. "Regular Simple Games," International Journal of Game Theory, Springer;Game Theory Society, vol. 18(2), pages 195-207.
    7. Freixas, Josep & Kurz, Sascha, 2014. "On minimum integer representations of weighted games," Mathematical Social Sciences, Elsevier, vol. 67(C), pages 9-22.
    8. Josep Freixas & Montserrat Pons, 2010. "Hierarchies achievable in simple games," Theory and Decision, Springer, vol. 68(4), pages 393-404, April.
    9. Freixas, Josep & Kaniovski, Serguei, 2014. "The minimum sum representation as an index of voting power," European Journal of Operational Research, Elsevier, vol. 233(3), pages 739-748.
    10. Dan S. Felsenthal & Moshé Machover, 1998. "The Measurement of Voting Power," Books, Edward Elgar Publishing, number 1489.
    11. Pradeep Dubey & Lloyd S. Shapley, 1979. "Mathematical Properties of the Banzhaf Power Index," Mathematics of Operations Research, INFORMS, vol. 4(2), pages 99-131, May.
    12. Kurz, Sascha & Napel, Stefan & Nohn, Andreas, 2014. "The nucleolus of large majority games," Economics Letters, Elsevier, vol. 123(2), pages 139-143.
    13. Josep Freixas & Xavier Molinero, 2009. "On the existence of a minimum integer representation for weighted voting systems," Annals of Operations Research, Springer, vol. 166(1), pages 243-260, February.
    14. J. Bilbao & J. Fernández & A. Losada & J. López, 2000. "Generating functions for computing power indices efficiently," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 8(2), pages 191-213, December.
    15. Dan S. Felsenthal & Moshé Machover, 2004. "A Priori Voting Power: What Is It All About?," Political Studies Review, Political Studies Association, vol. 2(1), pages 1-23, January.
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