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An Axiomatization of the Shapley-Shubik Index for Interval Decisions

Title data

Kurz, Sascha ; Moyouwou, Issofa ; Touyem, Hilaire:
An Axiomatization of the Shapley-Shubik Index for Interval Decisions.
Bayreuth , 2019 . - 28 p.

Official URL: Volltext

Abstract in another language

The Shapley-Shubik index was designed to evaluate the power distribution in committee systems drawing binary decisions and is one of the most established power indices. It was generalized to decisions with more than two levels of approval in the input and output. In the limit we have a continuum of options. For these games with interval decisions we prove an axiomatization of a power measure and show that the Shapley-Shubik index for simple games, as well as for (j,k) simple games, occurs as a special discretization. This relation and the closeness of the stated axiomatization to the classical case suggests to speak of the Shapley-Shubik index for games with interval decisions, that can also be generalized to a value.

Further data

Item Type: Preprint, postprint
Keywords: simple games; decisions with a continuum of options; aggregation functions; power indices; Shapley-Shubik index
Subject classification: Mathematics Subject Classification Code: 91A40 91A80 91B12
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
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics in Economy > Chair Mathematics in Economy - Univ.-Prof. Dr. Jörg Rambau
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
300 Social sciences > 330 Economics
500 Science > 510 Mathematics
Date Deposited: 06 Jul 2019 21:00
Last Modified: 08 Jul 2019 05:31
URI: https://eref.uni-bayreuth.de/id/eprint/49873