Axiomatic structure of k-additive capacities
AbstractIn 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 MÃ¶bius 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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Bibliographic InfoArticle provided by Elsevier in its journal Mathematical Social Sciences.
Volume (Year): 49 (2005)
Issue (Month): 2 (March)
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Web page: http://www.elsevier.com/locate/inca/505565
Other versions of this item:
- Pedro Miranda & Michel Grabisch & Pedro Gil, 2005. "Axiomatic structure of k-additive capacities," UniversitÃ© Paris1 PanthÃ©on-Sorbonne (Post-Print and Working Papers) hal-00188165, HAL.
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
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- Brice Mayag & Michel Grabisch & Christophe Labreuche, 2011. "A characterization of the 2-additive Choquet integral through cardinal information," UniversitÃ© Paris1 PanthÃ©on-Sorbonne (Post-Print and Working Papers) halshs-00625708, HAL.
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