Modeling agent's conditional preferences under objective ambiguity in Dempster-Shafer theory

We manage decisions under “objective” ambiguity by considering generalized Anscombe-Aumann acts, mapping states of the world to generalized lotteries on a set of consequences. A generalized lottery is modeled through a belief function on consequences, interpreted as a partially specified randomizing device. Preference relations on these acts are given by a decision maker focusing on different scenarios (conditioning events). We provide a system of axioms which are necessary and sufficient for the representability of these “conditional preferences” through a conditional functional parametrized by a unique full conditional probability P on the algebra of events and a cardinal utility function u on consequences. The model is able to manage also “unexpected” (i.e., “null”) conditioning events and distinguishes between a systematically pessimistic or optimistic behavior, either referring to “objective” belief functions or their dual plausibility functions. Finally, an elicitation procedure is provided, reducing to a Quadratically Constrained Linear Program (QCLP).