Decision-Making with Belief Functions: a Review

TL;DR

This review paper examines various decision-making methods within the belief function framework, comparing their theoretical foundations, practical applications, and highlighting the need for further research into their fundamental and normative aspects.

Contribution

It provides a comprehensive overview of decision-making approaches under belief functions, including their relation to imprecise probabilities and Shafer's constructive decision theory.

Findings

Most methods blend ignorance criteria with expected utility principles.

Distinction between complete preference relations and incomparability due to lack of information.

Highlights the need for deeper investigation of fundamental issues and normative evaluation.

Abstract

Approaches to decision-making under uncertainty in the belief function framework are reviewed. Most methods are shown to blend criteria for decision under ignorance with the maximum expected utility principle of Bayesian decision theory. A distinction is made between methods that construct a complete preference relation among acts, and those that allow incomparability of some acts due to lack of information. Methods developed in the imprecise probability framework are applicable in the Dempster-Shafer context and are also reviewed. Shafer's constructive decision theory, which substitutes the notion of goal for that of utility, is described and contrasted with other approaches. The paper ends by pointing out the need to carry out deeper investigation of fundamental issues related to decision-making with belief functions and to assess the descriptive, normative and prescriptive values of the different approaches.