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The inverse problem for power distributions in committees

Title data

Kurz, Sascha:
The inverse problem for power distributions in committees.
In: Social Choice and Welfare. Vol. 47 (2016) Issue 1 . - pp. 65-88.
ISSN 1432-217X
DOI: https://doi.org/10.1007/s00355-015-0946-8

Abstract in another language

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 vect
or 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.

Further data

Item Type: Article in a journal
Refereed: Yes
Keywords: simple games; weighted majority games; power indices
Subject classification: Mathematics Subject Classification Code: 91B12 (94C10)
Institutions of the University: Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics in Economy
Profile Fields > Emerging Fields > Governance and Responsibility
Faculties
Faculties > Faculty of Mathematics, Physics und Computer Science
Profile Fields
Profile Fields > Emerging Fields
Result of work at the UBT: Yes
DDC Subjects: 000 Computer Science, information, general works > 004 Computer science
300 Social sciences > 320 Political science
500 Science > 510 Mathematics
Date Deposited: 28 Jun 2016 06:13
Last Modified: 28 Jun 2016 06:13
URI: https://eref.uni-bayreuth.de/id/eprint/33080