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Axiomatic structure of k-additive capacities

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  • Miranda, P.
  • Grabisch, M.
  • Gil, P.

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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Bibliographic Info

Article provided by Elsevier in its journal Mathematical Social Sciences.

Volume (Year): 49 (2005)
Issue (Month): 2 (March)
Pages: 153-178

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Handle: RePEc:eee:matsoc:v:49:y:2005:i:2:p:153-178

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Web page: http://www.elsevier.com/locate/inca/505565

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  1. WEYMARK, John A., . "Generalized Gini inequality indices," CORE Discussion Papers RP -453, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  2. Christophe Labreuche & Michel Grabisch, 2003. "The Choquet integral for the aggregation of interval scales in multicriteria decision making," Post-Print hal-00272090, HAL.
  3. Michel Grabisch & Jacques Duchêne & Frédéric Lino & Patrice Perny, 2002. "Subjective Evaluation of Discomfort in Sitting Positions," Post-Print halshs-00273179, HAL.
  4. Elchanan Ben Porath & Itzhak Gilboa, 1991. "Linear Measures, the Gini Index and the Income-Equality Tradeoff," Discussion Papers 944, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  5. Gajdos, Thibault, 2002. "Measuring Inequalities without Linearity in Envy: Choquet Integrals for Symmetric Capacities," Journal of Economic Theory, Elsevier, vol. 106(1), pages 190-200, September.
  6. David Schmeidler, 1989. "Subjective Probability and Expected Utility without Additivity," Levine's Working Paper Archive 7662, David K. Levine.
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Cited by:
  1. Brice Mayag & Michel Grabisch & Christophe Labreuche, 2011. "A representation of preferences by the Choquet integral with respect to a 2-additive capacity," Theory and Decision, Springer, vol. 71(3), pages 297-324, September.
  2. Alessio Bonetti & Silvia Bortot & Mario Fedrizzi & Silvio Giove & Ricardo Alberto Marques Pereira & Andrea Molinari, 2011. "Modelling group processes and effort estimation in Project Management using the Choquet integral: an MCDM approach," DISA Working Papers 2011/12, Department of Computer and Management Sciences, University of Trento, Italy, revised Sep 2011.
  3. Casta, Jean-François & Stolowy, Hervé & Paugam, Luc, 2011. "Non-additivity in accounting valuation: Internally generated goodwill as an aggregation of interacting assets," Economics Papers from University Paris Dauphine 123456789/5769, Paris Dauphine University.
  4. Miranda, Pedro & Grabisch, Michel & Gil, Pedro, 2006. "Dominance of capacities by k-additive belief functions," European Journal of Operational Research, Elsevier, vol. 175(2), pages 912-930, December.
  5. repec:hal:journl:halshs-00186905 is not listed on IDEAS
  6. Brice Mayag & Michel Grabisch & Christophe Labreuche, 2011. "A characterization of the 2-additive Choquet integral through cardinal information," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00625708, HAL.
  7. Paugam, Luc, 2011. "Valorisation et reporting du goodwill : enjeux théoriques et empiriques," Economics Thesis from University Paris Dauphine, Paris Dauphine University, number 123456789/8007 edited by Casta, Jean-François, September.
  8. Silvia Bortot & Ricardo Alberto Marques Pereira, 2011. "Inconsistency and non-additive Choquet integration in the Analytic Hierarchy Process," DISA Working Papers 2011/06, Department of Computer and Management Sciences, University of Trento, Italy, revised 29 Jul 2011.
  9. repec:hal:journl:halshs-00625708 is not listed on IDEAS

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