A Bayesian Variant of Shafer's Commonalities For Modelling Unforeseen Events

Shafer's theory of belief and the Bayesian theory of probability are two alternative and mutually inconsistent approaches toward modelling uncertainty in artificial in­ telligence. To help reduce the conflict between these two approaches, this paper reexammes expected utility theory from which Bayesian probability theory is derived. Expected utility theory req mres the decision maker to ass1gn a utility to each decision conditioned on every possible event that might occur. But frequently the decision maker cannot foresee all the events that might occur, i.e., one of the possible events is the occurrence of an unforeseen event. So once we acknowledge the existence of unforeseen events, we need to develop some way of assigning utilities to tlecisions conditioned on unforeseen events. The commonsensical solution to this problem is to assign similar utilities to events which are similar. Implementing this commonsensical solution is equivalent to replac­ ing Bayesian subjective probabilities over the space of foreseen and unforeseen events by random set theory probabilities over the space of foreseen events. This leads to an expected utility principle in which normalized variants of Shafer's commonalities play the role of subjective probabilities. lienee allowing for unforeseen events in decision analysis causes Bayesian proba*Operating Sciences Department; General Motors Research JJabs;\Varren,Michigan 48090