On modelling non-probabilistic uncertainty in the likelihood ratio approach to evidential reasoning

Abstract

When the likelihood ratio approach is employed for evidential reasoning in law, it is often necessary to employ subjective probabilities, which are probabilities derived from the opinions and judgement of a human (expert). At least three concerns arise from the use of subjective probabilities in legal applications. Firstly, human beliefs concerning probabilities can be vague, ambiguous and inaccurate. Secondly, the impact of this vagueness, ambiguity and inaccuracy on the outcome of a probabilistic analysis is not necessarily fully understood. Thirdly, the provenance of subjective probabilities and the associated potential sources of vagueness, ambiguity and inaccuracy tend to be poorly understood, making it difficult for the outcome of probabilistic reasoning to be explained and validated, which is crucial in legal applications. The former two concerns have been addressed by a wide body of research in AI. The latter, however, has received little attention. This paper presents a novel approach to employ argumentation to reason about probability distributions in probabilistic models. It introduces a range of argumentation schemes and corresponding sets of critical questions for the construction and validation of argument models that define sets of probability distributions. By means of an extended example, the paper demonstrates how the approach, argumentation schemes and critical questions can be employed for the development of models and their validation in legal applications of the likelihood ratio approach to evidential reasoning.