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 intelligence. To help reduce the conflict between these two
approaches, this paper reexamines expected utility theory-from which Bayesian
probability theory is derived. Expected utility theory requires the decision
maker to assign 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 decisions 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 replacing 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. Hence allowing for unforeseen events in decision analysis causes
Bayesian probability theory to become much more similar to Shaferian theory.
