Making Decisions with Belief Functions

TL;DR

This paper introduces a probabilistic interpretation for decision-making with belief functions, enabling expected value calculations and extending probabilistic decision analysis methods to belief functions.

Contribution

It provides a formal probabilistic interpretation for belief function decision problems and extends existing probabilistic decision analysis methods to belief functions.

Findings

Expected values with belief functions match probabilistic analysis under the same assumption

A simple assumption disambiguates decision problems in belief functions

Method extends probabilistic decision analysis to belief functions

Abstract

A primary motivation for reasoning under uncertainty is to derive decisions in the face of inconclusive evidence. However, Shafer's theory of belief functions, which explicitly represents the underconstrained nature of many reasoning problems, lacks a formal procedure for making decisions. Clearly, when sufficient information is not available, no theory can prescribe actions without making additional assumptions. Faced with this situation, some assumption must be made if a clearly superior choice is to emerge. In this paper we offer a probabilistic interpretation of a simple assumption that disambiguates decision problems represented with belief functions. We prove that it yields expected values identical to those obtained by a probabilistic analysis that makes the same assumption. In addition, we show how the decision analysis methodology frequently employed in probabilistic reasoning can be extended for use with belief functions.