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The cost of getting local monotonicity

Title data

Freixas, Josep ; Kurz, Sascha:
The cost of getting local monotonicity.
In: European Journal of Operational Research. Vol. 251 (June 2016) Issue 2 . - pp. 600-612.
ISSN 0377-2217
DOI: https://doi.org/10.1016/j.ejor.2015.11.030

Official URL: Volltext

Abstract in another language

In 1982 Manfred Holler introduced the Public Good index. In its unnormalized version, i.e., the raw measure, it counts the number of times that a player belongs to a minimal winning coalition. Unlike the Banzhaf index, it does not count the remaining winning coalitions in which the player is crucial. Holler noticed that his index does not satisfy local monotonicity, a fact that can be seen either as a major drawback or as an advantage.
In this paper we consider a convex combination of the two indices and require the validity of local monotonicity. We prove that the cost of obtaining it is high, i.e., the achievable new indices satisfying local monotonicity are closer to the Banzhaf index than to the Public Good index. All these achievable new indices are more solidary than the Banzhaf index, which makes them as very suitable candidates to divide a public good.
As a generalization we consider convex combinations of either: the Shift index, the Public Good index, and the Banzhaf index, or alternatively: the Shift Deegan-Packel, Deegan-Packel, and Johnston indices.

Further data

Item Type: Article in a journal
Refereed: Yes
Keywords: Public Good Index; local monotonicity; design of power indices; solidarity; fair division
Subject classification: Mathematics Subject Classification Code: 91A12 (91A80 91B12)
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: 29 Jun 2016 08:59
Last Modified: 29 Jun 2016 08:59
URI: https://eref.uni-bayreuth.de/id/eprint/33105