Representation of subjective preferences under ambiguity

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 Omega 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 a family of integral functionals defined by means of a cardinal utility u on X (representing the risk attitude of the DM) and a unique pointwise closed convex set P of probabilities on all events in Omega (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.