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Generalized roll-call model for the Shapley-Shubik index

URN to cite this document: urn:nbn:de:bvb:703-epub-2748-5

Title data

Kurz, Sascha:
Generalized roll-call model for the Shapley-Shubik index.
Bayreuth , 2016 . - 18 S.

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Abstract

In 1996 D. Felsenthal and M. Machover considered the following model. An assembly consisting of n voters exercises roll-call. All n! possible orders in which the voters may be called are assumed to be equiprobable. The votes of each voter are independent with expectation 0<p<1 for an individual vote yea{. For a given decision rule v the pivotal voter in a roll-call is the one whose vote finally decides the aggregated outcome. It turned out that the probability to be pivotal is equivalent to the Shapley-Shubik index. Here we give an easy combinatorial proof of this coincidence, further weaken the assumptions of the underlying model, and study generalizations to the case of more than two alternatives.

Further data

Item Type: Preprint, postprint
Keywords: simple games; influence; Shapley-Shubik index; several levels of approval
Subject classification: Mathematics Subject Classification Code: 91A12 (91A40 91A80)
DDC Subjects: 000 Computer Science, information, general works > 004 Computer science
500 Science > 510 Mathematics
Institutions of the University: Faculties > Faculty of Mathematics, Physics und Computer Science
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
Profile Fields
Profile Fields > Emerging Fields
Language: English
Originates at UBT: Yes
URN: urn:nbn:de:bvb:703-epub-2748-5
Date Deposited: 17 Feb 2016 07:15
Last Modified: 14 Mar 2019 14:57
URI: https://epub.uni-bayreuth.de/id/eprint/2748

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