Classical probabilities and belief functions in legal cases

Abstract

Abstract I critically discuss a recent suggestion in Nance (Belief Functions and Burdens of Proof. Law, Probability and Risk, 18:53–76, 2018) concerning the question which ratios of beliefs are appropriate when in criminal or civil cases one works with belief functions instead of classical probabilities. I do not call into question the use of belief functions themselves in this context, and I agree with in Nance (Belief Functions and Burdens of Proof. Law, Probability and Risk, 18:53–76, 2018) that so-called ‘uncommitted support’, possible in the framework of belief functions, should not be taken into account in a decision-theoretic framework. However, I argue against in Nance (Belief Functions and Burdens of Proof. Law, Probability and Risk, 18:53–76, 2018) in that, at least in criminal law, relative sizes of beliefs should not be used for decision-making at all. I will argue that only the individual, absolute beliefs should be considered. Since belief functions generalize classical probabilities, this position seems at first sight to conflict with the fact that odds are abundant when we use classical probabilities in a legal context. I will take the opportunity, then, to point out that also in the classical setting, odds are not our primary concern either. They are convenient since they appear, together with the likelihood ratio, in the odds form of Bayes’ rule. Apart from that, they do not have any individual significance. I also note that in civil law the conclusions might be different.