Rank Dependent Weighted Average Utility Models for Decision Making under Objective Ambiguity * †

Nicolas Gravel () and Thierry Marchant ()
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Nicolas Gravel: AMU - Aix Marseille Université, AMSE - Aix-Marseille Sciences Economiques - EHESS - École des hautes études en sciences sociales - AMU - Aix Marseille Université - ECM - École Centrale de Marseille - CNRS - Centre National de la Recherche Scientifique
Thierry Marchant: UGent - Universiteit Gent = Ghent University = Université de Gand

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Abstract: This paper axiomatically characterizes a family of rank-dependent weighted average utility criteria for comparing finite sets of objective probability distributions over consequences. These sets are interpreted as objectively ambiguous prospects: the relevant probability distributions are part of the description of the alternative, but no likelihood is assigned to their occurrence. The represented criteria evaluate a prospect by applying a utility function to each of its elements and aggregating the resulting utilities through weights that depend on the rank of each element within the prospect. The main theorem characterizes the subclass of such criteria whose rank-dependent weights are generated by a single weighting function on the unit interval. A second characterization covers the larger family in which weights may vary freely with the number of elements in the prospect. The paper also studies the implications of comparative ambiguity aversion, optimism, and pessimism for the utility function and the rank-dependent weights.

Keywords: Ambiguity; Ambiguity Prospects Sets Axioms Ranks Weights Utility; Utility; Weights; Ranks; Axioms; Sets; Prospects (search for similar items in EconPapers)
Date: 2026-07-01
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