Axiomatic structure of k-additive capacities

Pedro Miranda (), Michel Grabisch and Pedro Gil
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Pedro Miranda: UCM - Universidad Complutense de Madrid = Complutense University of Madrid [Madrid]
Pedro Gil: Universidad de Oviedo = University of Oviedo

Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) from HAL

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.

Keywords: Axiomatic; Capacities; k-Additivity (search for similar items in EconPapers)
Date: 2005-03
Note: View the original document on HAL open archive server: https://hal.science/hal-00188165
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Citations: View citations in EconPapers (12)

Published in Mathematical Social Sciences, 2005, 49 (2), pp.153-178. ⟨10.1016/j.mathsocsci.2004.06.001⟩

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Journal Article: Axiomatic structure of k-additive capacities (2005)
Working Paper: Axiomatic structure of k-additive capacities (2005)
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Persistent link: https://EconPapers.repec.org/RePEc:hal:cesptp:hal-00188165

DOI: 10.1016/j.mathsocsci.2004.06.001

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