Axiomatic structure of k-additive capacities
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.
|Date of creation:||Mar 2005|
|Publication status:||Published in Mathematical Social Sciences, Elsevier, 2005, 49 (2), pp.153-178. <10.1016/j.mathsocsci.2004.06.001>|
|Note:||View the original document on HAL open archive server: https://hal.archives-ouvertes.fr/hal-00188165|
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