A General Structure for Legal Arguments Using Bayesian Networks

A Bayesian network (BN) is a graphical model of uncertainty that is especially well-suited to legal arguments. It enables us to visualise and model dependencies between different hypotheses and pieces of evidence and to calculate the revised probability beliefs about all uncertain factors when any piece of new evidence is presented. Although BNs have been widely discussed and recently used in the context of legal arguments there is no systematic, repeatable method for modelling legal arguments as BNs. Hence, where BNs have been used in the legal context, they are presented as completed pieces of work, with no insights into the reasoning and working that must have gone into their construction. This means the process of building BNs for legal arguments is ad-hoc, with little possibility for learning and process improvement. This paper directly addresses this problem by describing a method for building useful legal arguments in a consistent and repeatable way. The method complements and extends recent work by Hepler, Dawid and Leucari on objected-oriented BNs for complex legal arguments and is based on the recognition that such arguments can be built up from a small number of basic causal structures (referred to as idioms). We present a number of examples that demonstrate the practicality and usefulness of the method. The method also enables us to handle an apparent paradox observed in previous empirical studies, whereby it has been observed that people may reason about evidence in a 'non-normative' way, meaning that their conclusions conflict with the results of the associated causal BN. In particular, subjects exhibited such non-normative behaviour by asserting different probability beliefs when evidence was presented in a different order (whereas in a BN calculation the impact of evidence is not affected by the order in which the evidence is presented). By using the method presented in this paper we are able to show that the subjects were not necessarily reasoning irrationally. Rather, we are able to show that the order in which evidence is presented may require an alternative causal BN structure. Executable version of all of the BN models described in the paper are freely available for inspection and use (web link provided in paper).