Axiomatic structure of k-additive capacities
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.
|Date of creation:||Mar 2005|
|Date of revision:|
|Publication status:||Published, Mathematical Social Sciences, 2005, 49, 2, 153-178|
|Note:||View the original document on HAL open archive server: http://hal.archives-ouvertes.fr/hal-00188165|
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References listed on IDEAS
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- David Schmeidler, 1989.
"Subjective Probability and Expected Utility without Additivity,"
Levine's Working Paper Archive
7662, David K. Levine.
- Schmeidler, David, 1989. "Subjective Probability and Expected Utility without Additivity," Econometrica, Econometric Society, vol. 57(3), pages 571-87, May.
- Porath Elchanan Ben & Gilboa Itzhak, 1994.
"Linear Measures, the Gini Index, and The Income-Equality Trade-off,"
Journal of Economic Theory,
Elsevier, vol. 64(2), pages 443-467, December.
- 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.
- 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.
- Michel Grabisch & Jacques Duchêne & Frédéric Lino & Patrice Perny, 2002. "Subjective Evaluation of Discomfort in Sitting Position," Post-Print halshs-00273179, HAL.
- WEYMARK, John A., .
"Generalized Gini inequality indices,"
CORE Discussion Papers RP
-453, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
- Christophe Labreuche & Michel Grabisch, 2003. "The Choquet integral for the aggregation of interval scales in multicriteria decision making," Post-Print hal-00272090, HAL.
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