Decision Making with Linear Constraints on Probabilities

TL;DR

This paper explores decision-making methods under linear probability constraints, unifying various scenarios like risk, uncertainty, and partial information through convex polyhedra and a generalized Hurwicz criterion.

Contribution

It introduces a unified approach to decision making with linear probability constraints, extending traditional criteria to handle diverse informational scenarios.

Findings

Methods for processing marginal probabilities to enhance decision quality.

A generalized Hurwicz criterion applicable to various types of probability constraints.

Framework unifying decision making under risk, uncertainty, and partial knowledge.

Abstract

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.