Axiomatic structure of k-additive capacities

Details Axiomatic structure of k-additive capacities Axiomatic structure of k-additive capacities

2007-11-15

arxiv.org/abs/0711.2489v1

Mathematical Social Sciences (2005) 153-178

Computer Science

Discrete Mathematics

Scientific paper

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 M\"obius 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.

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