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Kurz, Sascha:
Generalized roll-call model for the Shapley-Shubik index.
Bayreuth
,
2016
. - 18 S.
Volltext
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.
Weitere Angaben
| Publikationsform: | Preprint, Postprint |
|---|---|
| Keywords: | simple games; influence; Shapley-Shubik index; several levels of approval |
| Fachklassifikationen: | Mathematics Subject Classification Code: 91A12 (91A40 91A80) |
| Institutionen der Universität: | Fakultäten > Fakultät für Mathematik, Physik und Informatik Fakultäten > Fakultät für Mathematik, Physik und Informatik > Mathematisches Institut Fakultäten > Fakultät für Mathematik, Physik und Informatik > Mathematisches Institut > Lehrstuhl Wirtschaftsmathematik Profilfelder > Emerging Fields > Governance and Responsibility Fakultäten Profilfelder Profilfelder > Emerging Fields |
| Titel an der UBT entstanden: | Ja |
| Themengebiete aus DDC: | 000 Informatik,Informationswissenschaft, allgemeine Werke > 004 Informatik 500 Naturwissenschaften und Mathematik > 510 Mathematik |
| Eingestellt am: | 20 Feb 2016 22:00 |
| Letzte Änderung: | 14 Aug 2018 08:19 |
| URI: | https://eref.uni-bayreuth.de/id/eprint/31099 |
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