Dempster-Shafer vs. Probabilistic Logic

TL;DR

This paper compares Dempster-Shafer theory and probabilistic logic in evidence combination, identifying conditions for their agreement and demonstrating cases of disagreement despite common assumptions.

Contribution

It establishes minimal conditions under which Dempster-Shafer and probabilistic logic agree and provides an example where they diverge despite standard assumptions.

Findings

Conditions for agreement are minimal and necessary.

Disagreement can occur even under conditional independence and uniform prior.

Traditional assumptions do not guarantee identical results.

Abstract

The combination of evidence in Dempster-Shafer theory is compared with the combination of evidence in probabilistic logic. Sufficient conditions are stated for these two methods to agree. It is then shown that these conditions are minimal in the sense that disagreement can occur when any one of them is removed. An example is given in which the traditional assumption of conditional independence of evidence on hypotheses holds and a uniform prior is assumed, but probabilistic logic and Dempster's rule give radically different results for the combination of two evidence events.