## Title data

Kurz, Sascha:

**Generalized roll-call model for the Shapley-Shubik index.**

Bayreuth
,
2018
. - 19 p.

## Abstract in another language

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) |

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 |

Result of work at the UBT: | Yes |

DDC Subjects: | 000 Computer Science, information, general works > 004 Computer science 500 Science > 510 Mathematics |

Date Deposited: | 18 Aug 2018 21:00 |

Last Modified: | 14 Mar 2019 14:55 |

URI: | https://eref.uni-bayreuth.de/id/eprint/45531 |