The “Jury Observation Fallacy” and the use of Bayesian Networks to present Probabilistic Legal Arguments

Probability theory, especially Bayesian probability, is widely misunderstood by the general public. Lawyers are no different from ordinary members of the public in falling victim to arguments that have been known to mathematicians for decades to be fallacies. The so-called prosecutor’s fallacy and the defendant’s fallacy are two well-known examples that arise from a basic misunderstanding of conditional probability and Bayes’ Theorem. In this paper we introduce what we believe is a previously unreported fallacy, which we refer to as the jury observation fallacy. In this fallacy there is a basic misunderstanding about the belief in probability of guilt when a prior similar conviction by a defendant is revealed after the jury returns a not guilty verdict. Specifically, it is widely believed that the information about the prior conviction might suggest to external observers that the jury verdict was wrong (the belief is that probability of guilt increases). In fact, using very reasonable (and indeed conservative) assumptions it can be shown, using Bayesian reasoning, that such a response is irrational in many situations. To explain the Bayesian argument without exposing readers to any of the mathematical details we use Bayesian Networks (BNs) and a tool (AgenaRisk) to execute them. Hence, a secondary objective of this paper is to show that there is a way of making all of the implications of Bayesian reasoning clear to lay people, without them having to understand any of the underlying mathematics. The implications of this in the legal profession are profound. Courts could eventually accept Bayesian arguments just as they accept forensic evidence without having to resort to explanations from first principles. Additionally, the results presented suggest that there may be reason for disquiet about the use of previous convictions as a basis for selecting suspects as is common Police practice. Jury Fallacy, 31 July 2007 2/17