Representation of subjective preferences under ambiguity

Abstract The objective of this paper is to show how potentially incomplete preferences of a decision maker (DM) on acts can be modelled formally in a subjective ambiguity perspective. We identify acts as functions from a state space Ω to bounded support (finitely additive) probabilities over a set X of prizes. Then, we characterize preferences over equibounded acts a which have a numerical representation by the family of functionals { J π ( a ) = ∫ Ω [ ∫ X u ( x ) a ( ω ) ( dx ) ] π ( d ω ) ; π ∈ Π } , where u is a cardinal utility on X (representing the risk attitude of the DM) and Π is a unique pointwise closed convex set of probabilities on all events in Ω (representing the ambiguity perceived by the DM). To this end, in addition to the usual independence and continuity assumptions, we add completeness and dominance for preferences restricted to constant acts; moreover, we consider two other properties (subjective monotonicity and coherence) related with the preferences of a DM who is not able, owing to his partial knowledge, to evaluate any event in Ω .

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