Axiomatic structure of k-additive capacities
| dc.creator | Miranda, Pedro | |
| dc.creator | Grabisch, Michel | |
| dc.creator | Gil, Pedro | |
| dc.date | 2007-11-15 | |
| dc.date.accessioned | 2026-07-07T08:43:10Z | |
| dc.date.available | 2026-07-07T08:43:10Z | |
| dc.description | In this paper we deal with the problem of axiomatizing the preference relations modelled through Choquet integral with respect to a $k$-additive capacity, i.e. whose Möbius transform vanishes for subsets of more than $k$ elements. Thus, $k$-additive capacities range from probability measures ($k=1$) to general capacities ($k=n$). The axiomatization is done in several steps, starting from symmetric 2-additive capacities, a case related to the Gini index, and finishing with general $k$-additive capacities. We put an emphasis on 2-additive capacities. Our axiomatization is done in the framework of social welfare, and complete previous results of Weymark, Gilboa and Ben Porath, and Gajdos. | |
| dc.identifier | https://arxiv.org/abs/0711.2489 | |
| dc.identifier | http://arxiv.org/abs/0711.2489 | |
| dc.identifier | Mathematical Social Sciences (2005) 153-178 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/142220 | |
| dc.subject | Discrete Mathematics | |
| dc.title | Axiomatic structure of k-additive capacities | |
| dc.type | text |