Decision Making with Linear Constraints on Probabilities
This work addresses decision-making problems in fields like economics or AI where probabilistic constraints are common, but it appears incremental as it builds on existing criteria and methods.
The paper tackles decision making under linear constraints on probabilities, such as bounds or orderings, by representing them as convex polyhedra and proposes a generalized Hurwicz criterion for uniform handling across risk, uncertainty, and partial uncertainty, with methods to process marginal probabilities for improved decisions.
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.