RT Journal Article
T1 Axiomatic structure of k-additive capacities
A1 Miranda Menéndez, Pedro
A1 Grabisch, Michel
A1 Gil Álvarez, Pedro
AB 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.
PB Elsevier
SN 0165-4896
YR 2005
FD 2005-03
LK https://hdl.handle.net/20.500.14352/50190
UL https://hdl.handle.net/20.500.14352/50190
LA eng
NO Miranda Menéndez, P., Grabisch, M. & Gil Álvarez, P. et al. «Axiomatic Structure of K-Additive Capacities». Mathematical Social Sciences, vol. 49, n.o 2, marzo de 2005, pp. 153-78. DOI.org (Crossref), https://doi.org/10.1016/j.mathsocsci.2004.06.001.
DS Docta Complutense
RD 5 abr 2025