Conditional decisions under objective and subjective ambiguity in Dempster-Shafer theory

This paper deals with conditional decisions on generalized Anscombe-Aumann acts mapping states of the world to finitely additive probabilities on the set of menus of consequences, the latter conveying a form of “objective” ambiguity. If the decision maker has a systematic pessimistic/optimistic attitude towards “objective” ambiguity, acts reduce to functions mapping states of the world to belief/plausibility functions on consequences. We provide a system of axioms assuring the representability of a family of conditional preference relations on such acts by a conditional functional in which “subjective” uncertainty is modeled through a conditional belief/plausibility function on the states of the world, obeying to a suitable axiomatic definition.