Axiomatization of the Choquet integral for 2-dimensional heterogeneous product sets

Mikhail Timonin

Papers from arXiv.org

Abstract: We prove a representation theorem for the Choquet integral model. The preference relation is defined on a two-dimensional heterogeneous product set $X = X_1 \times X_2$ where elements of $X_1$ and $X_2$ are not necessarily comparable with each other. However, making such comparisons in a meaningful way is necessary for the construction of the Choquet integral (and any rank-dependent model). We construct the representation, study its uniqueness properties, and look at applications in multicriteria decision analysis, state-dependent utility theory, and social choice. Previous axiomatizations of this model, developed for decision making under uncertainty, relied heavily on the notion of comonotocity and that of a "constant act". However, that requires $X$ to have a special structure, namely, all factors of this set must be identical. Our characterization does not assume commensurateness of criteria a priori, so defining comonotonicity becomes impossible.

Date: 2015-07, Revised 2016-03
New Economics Papers: this item is included in nep-mic and nep-upt
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://arxiv.org/pdf/1507.04167 Latest version (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:arx:papers:1507.04167

Access Statistics for this paper

More papers in Papers from arXiv.org
Bibliographic data for series maintained by arXiv administrators ().