Decision Making with Linear Constraints on Probabilities
  Techniques for decision making with knowledge of linear constraints on
condition probabilities are examined. These constraints arise naturally in many
situations: upper and lower condition probabilities are known; an ordering
among the probabilities is determined; marginal probabilities or bounds on such
probabilities are known, e.g., data are available in the form of a
probabilistic database (Cavallo and Pittarelli, 1987a); etc. Standard
situations of decision making under risk and uncertainty may also be
characterized by linear constraints. Each of these types of information may be
represented by a convex polyhedron of numerically determinate condition
probabilities. A uniform approach to decision making under risk, uncertainty,
and partial uncertainty based on a generalized version of a criterion of
Hurwicz is proposed, Methods for processing marginal probabilities to improve
decision making using any of the criteria discussed are presented.
