  This paper proposes a decision theory for a symbolic generalization of
probability theory (SP). Darwiche and Ginsberg [2,3] proposed SP to relax the
requirement of using numbers for uncertainty while preserving desirable
patterns of Bayesian reasoning. SP represents uncertainty by symbolic supports
that are ordered partially rather than completely as in the case of standard
probability. We show that a preference relation on acts that satisfies a number
of intuitive postulates is represented by a utility function whose domain is a
set of pairs of supports. We argue that a subjective interpretation is as
useful and appropriate for SP as it is for numerical probability. It is useful
because the subjective interpretation provides a basis for uncertainty
elicitation. It is appropriate because we can provide a decision theory that
explains how preference on acts is based on support comparison.
