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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.