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The inverse problem for power distributions in committees

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  • Sascha Kurz

    (University of Bayreuth)

Abstract

Several power indices have been introduced in the literature in order to measure the influence of individual committee members on an aggregated decision. Here we ask the inverse question and aim to design voting rules for a committee such that a given desired power distribution is met as closely as possible. We generalize the approach of Alon and Edelman who studied power distributions for the Banzhaf index, where most of the power is concentrated on few coordinates. It turned out that each Banzhaf vector of an n-member committee that is near to such a desired power distribution, also has to be near to the Banzhaf vector of a k-member committee. We show that such Alon-Edelman type results exist for other power indices like e.g. the Public Good index or the Coleman index to prevent actions, while such results are principally impossible to derive for e.g. the Johnston index.

Suggested Citation

  • Sascha Kurz, 2016. "The inverse problem for power distributions in committees," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 47(1), pages 65-88, June.
    • Handle: RePEc:spr:sochwe:v:47:y:2016:i:1:d:10.1007_s00355-015-0946-8
    DOI: 10.1007/s00355-015-0946-8
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    1. Sascha Kurz & Stefan Napel, 2014. "Heuristic and exact solutions to the inverse power index problem for small voting bodies," Annals of Operations Research, Springer, vol. 215(1), pages 137-163, April.
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    Cited by:

    1. Sascha Kurz, 2020. "Are weighted games sufficiently good for binary voting?," Papers 2006.05330, arXiv.org, revised Jul 2021.
    2. N. Maaser, 2017. "Simple vs. Sophisticated Rules for the Allocation of Voting Weights," Homo Oeconomicus: Journal of Behavioral and Institutional Economics, Springer, vol. 34(1), pages 67-78, April.
    3. Sascha Kurz, 2021. "Are Weighted Games Sufficiently Good for Binary Voting?," Homo Oeconomicus: Journal of Behavioral and Institutional Economics, Springer, vol. 38(1), pages 29-36, December.
    4. Kurz, Sascha, 2018. "The power of the largest player," Economics Letters, Elsevier, vol. 168(C), pages 123-126.
    5. Molinero, Xavier & Riquelme, Fabián & Roura, Salvador & Serna, Maria, 2023. "On the generalized dimension and codimension of simple games," European Journal of Operational Research, Elsevier, vol. 306(2), pages 927-940.

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