Resolving the so-called “probabilistic paradoxes in legal reasoning” with Bayesian networks

Examples of reasoning problems such as the twins problem and poison paradox have been proposed by legal scholars to demonstrate the limitations of probability theory in legal reasoning. Specifically, such problems are intended to show that use of probability theory results in legal paradoxes. As such, these problems have been a powerful detriment to the use of probability theory – and particularly Bayes theorem – in the law. However, the examples only lead to ‘paradoxes’ under an artificially constrained view of probability theory and the use of the so-called likelihood ratio, in which multiple related hypotheses and pieces of evidence are squeezed into a single hypothesis variable and a single evidence variable. When the distinct relevant hypotheses and evidence are described properly in a causal model (a Bayesian network), the paradoxes vanish. In addition to the twins problem and poison paradox, we demonstrate this for the food tray example, the abuse paradox and the small town murder problem. Moreover, the resulting Bayesian networks provide a powerful framework for legal reasoning.