Social Choice and Welfare

, Volume 47, Issue 1, pp 65–88 | Cite as

The inverse problem for power distributions in committees

Original Paper

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.

Mathematics Subject Classification

91B12 94C10 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.Department of Mathematics, Physics, and Computer ScienceUniversity of BayreuthBayreuthGermany

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