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 probably. It is shown that the information can be modeled through belief functions if and only if the nonprobabilizable information is subject to the principle of complete ignorance. Next the representability of decisions by belief functions on outcomes is justified by means of a neutrality axiom. The natural weakening of Savage's sure-thing principle to unambiguous events is examined and its implications for decision making are identified. Copyright 1993 by Kluwer Academic Publishers