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arXiv · 0711.2489

Axiomatic structure of k-additive capacities

Pedro Miranda·Michel Grabisch·Pedro Gil
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Abstract

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.

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Pedro Miranda, Michel Grabisch, Pedro Gil. 2007-11-15. Axiomatic structure of k-additive capacities. https://arxiv.org/abs/0711.2489

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