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Axiomatic structure of k-additive capacities

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

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URL Oficial: http://www.sciencedirect.com/science/article/pii/S0165489604000575


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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.


Tipo de documento:Artículo
Palabras clave:Axiomatic; Capacities; k-Additivity
Materias:Ciencias > Matemáticas > Análisis funcional y teoría de operadores
Código ID:17081
Depositado:13 Nov 2012 10:08
Última Modificación:07 Feb 2014 09:41

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