Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
10480445 | Mathematical Social Sciences | 2005 | 26 Pages |
Abstract
In this paper we deal with the problem of axiomatizing the preference relations modeled 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.
Related Topics
Physical Sciences and Engineering
Mathematics
Applied Mathematics
Authors
P. Miranda, M. Grabisch, P. Gil,