%0 Journal Article
%A Miranda Menéndez, Pedro
%A Grabisch, Michel
%A Gil Álvarez, Pedro
%T Axiomatic structure of k-additive capacities
%D 2005
%@ 0165-4896
%U https://hdl.handle.net/20.500.14352/50190
%X 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 Mobius 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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