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

2015/07/15 by Mikhail Timonin, Timonin, Mikhail
Decision Sciences · Economics, Econometrics and Finance · #Decision-Making and Behavioral Economics #Economic and Environmental Valuation #Multi-Criteria Decision Making

paper · pdf · doi:10.48550/arxiv.1507.04167

Abstract

We prove a representation theorem for the Choquet integral model. The\npreference relation is defined on a two-dimensional heterogeneous product set\nX = X₁ \× X₂ where elements of X₁ and X₂ are not necessarily\ncomparable with each other. However, making such comparisons in a meaningful\nway is necessary for the construction of the Choquet integral (and any\nrank-dependent model). We construct the representation, study its uniqueness\nproperties, and look at applications in multicriteria decision analysis,\nstate-dependent utility theory, and social choice. Previous axiomatizations of\nthis model, developed for decision making under uncertainty, relied heavily on\nthe notion of comonotocity and that of a "constant act". However, that requires\nX to have a special structure, namely, all factors of this set must be\nidentical. Our characterization does not assume commensurateness of criteria a\npriori, so defining comonotonicity becomes impossible.\n

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