Paper short abstract:

This paper will confront two aspects of the use of probabilities in court, namely the use of Bayesian reasoning in the assessment of the weight of forensic evidence, and the ‘reasonable doubt’ standard of proof, which can prima facie be interpreted as referring to a probabilistic threshold.

Paper long abstract:

Interdisciplinary efforts are deployed in the UK to promote Bayesian reasoning in the assessment and communication of the weight of forensic evidence (against some judges' attempts at ruling out statistics from the court), and to make tools for analysing arguments (eg Bayesian networks, Fenton et al. 2012, 2013a) accessible to judges and juries. Indeed, simply appealing to probabilities is not sufficient to avoid miscarriages of justice. As Fenton et al. (2013b) show, likelihood ratios can be used to assess the probative value of evidence under certain circumstances only — namely, that the prosecution and defence hypotheses be exhaustive and mutually exclusive, and at the offence level, rather than at the source or activity levels (Cook et al. 1998).

I will draw on this proposal, adopting the perspective of the jurors, who are instructed to estimate whether guilt was proven 'beyond a reasonable doubt'. This may prima facie indicate that the evidence presented in court should support the hypothesis of guilt to a certain degree — that a certain probabilistic threshold has to be met — for the defendant to be convicted. However, depending on how the defence and prosecution hypotheses are formulated and argued for (scenarios do not reduce to "he is guilty" / "he is not guilty"), and on their logical relationships, the evaluation of the probability of guilt — and of its robustness and resilience to potentially different structurations of the hypotheses space — may vary. This, I will argue, should be taken into account in any effort to clarify the 'reasonable doubt' standard.