DECISION-MAKING WITH BELIEF FUNCTIONS - COMPATIBILITY AND INCOMPATIBILITY WITH THE SURE-THING PRINCIPLE

This article studies situations in which information is ambiguous and only part of it can be probabilized. It is shown that the information can be modeled through belief functions if and only if the nonprobabil izable information is subject to the principles of complete ignorance. Next the representability of decisions by belief functions on outcome s is justified by means of a neutrality axiom. The natural weakening o f Savage's sure-thing principle to unambiguous events is examined and its implications for decision making are identified.