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Axiomatic structure of k-additive capacities

Miranda Menéndez, Pedro and Grabisch, Michel and Gil, Pedro (2005) Axiomatic structure of k-additive capacities. Mathematical Social Sciences, 49 (2). pp. 153-178. ISSN 0165-4896

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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 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.

Item Type:Article
Uncontrolled Keywords:Axiomatic; Capacities; k-Additivity
Subjects:Sciences > Mathematics > Functional analysis and Operator theory
ID Code:17081
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