Probability reasoning in judicial fact-finding
| Date | 01 January 2020 |
| Author | Ian Hunt,Justice Mostyn |
| Published date | 01 January 2020 |
| DOI | 10.1177/1365712719875753 |
| Subject Matter | Articles |
Article
Probability reasoning
in judicial fact-finding
Ian Hunt
School of Mathematics, Monash University, Australia
The Hon. Mr Justice Mostyn
Royal Courts of Justice, London, UK
Abstract
We argue that the laws of probability promote coherent fact-finding and avoid potentially
unjust logical contradictions. But we do not argue that a probabilistic Bayesian approach is
sufficient or even necessary for good fact-finding. First, we explain the use of probability
reasoning in Re D (A Child) [2014] EWHC 121 (Fam) and Re L (A Child) [2017] EWHC 3707
(Fam). Then we criticise the attack on this probabilistic reasoning found in Re A (Children)
[2018] EWCA Civ 1718, which is the appeal decision on Re L. We conclude that the attack is
unjustified and that the probability statements in the two cases were both valid and useful. We
also use probabilistic reasoning to enlighten legal principles related to inherent probability, the
Binary Method and the blue bus paradox.
Keywords
Fact-finding, Bayes’ formula, laws of probability, inference to the best explanation, relative
plausibility, inherent probability, blue bus paradox, the binary method
In this article, we argue that the laws of probability can promote coherent fact-finding and avoid logical
contradictions. We assume that the laws of pr obability hold, that Bayes’ formula is valid and that
probability is interpreted as subjective degrees of belief. Our argument is essentially that probability
reasoning is therapeutic: an ‘elementary probabilistic model of degrees of belief often contains just the
right balance of accuracy and simplicity to enable us to command a clear view of the issues and see
where we [are or could be] going wrong’ (Horwich, 1993: 62).
An example of therapeutic probabilistic reasoning in fact-finding is as follows. Assume that there are
three mutually exclusive and exhaustive explanations for something that happened and that the judge
reckons that the probability of each explanation being true is less than 0.5. Also assume that on pain of
incoherence the judge ensures that the sum of her subjective probabilities is one. In this case, no legal
facts can be found ‘on the balance of probabilities’; to find otherwise would imply a contradiction in
Corresponding author:
Ian Hunt, School of Mathematics, Monash University, 9 Rainforest Walk, Room 401, Clayton, Victoria 3800, Australia.
E-mails: ihunt@bunhill.co.uk: ian.hunt@monash.edu
The International Journalof
Evidence & Proof
2020, Vol. 24(1) 75–94
ªThe Author(s) 2019
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DOI: 10.1177/1365712719875753
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terms of the laws of probability (in particular that the three probabilities must sum to one) or require a
post-hoc fix to the originally reckoned probabilities. Worse than a mere contradiction or a fix-up of the
odds, a finding of fact for an event with probability less than 0.5 risks serious injustice.
We analyse two real cases in which judges apply similar reasoning. These cases are Re D (A Child)
[2014] EWHC 121 (Fam) and Re L (A Child) [2017] EWHC 3707 (Fam). We also analyse Re A
(Children) [2018] EWCA Civ 1718, which is the appeal decision on Re L. The ruling in Re A admonishes
judges to avoid using the laws of probability in findings of fact, going as far to suggest that referring to
the probability of a past event is pseudo-mathematics. In this article we respectfully respond to the
criticisms launched by Re A. We conclude that the probability references in Re D and Re L were careful,
justified and useful. We acknowledge that there is an element of vindicatorship in these conclusions. But
we carefully quote from the cases concerned, so a reader can make her own mind up about the bones of
contention; and we have made an honest effort to provide reasons for our conclusions.
The rest of this paper is structured as follows. First, we explain the reasoning behind the fact-finding
decisions in Re D and Re L. Secondly, we give a generous inter pretation to the objections to th is
reasoning that were raised in Re A. Thirdly, we criticise the best objections and set out our case for
using subjective probability arguments in judicial fact-finding. Fourthly, we argue that probabilistic
reasoning enlightens, in a therapeutic sense, legal principles related to inherent probability, the Binary
Method and the blue bus paradox.
The first three sections are written in the style of an opinionated ‘case comment’. Our responses to the
judgments are coloured by our respective experiences as an implicated judge and an independent
statistician. The last section is in the context of particular principles related to fact-finding.
1
Here we
take the opportunity to further explicate our theoretical position, which is essentially that Bayesian
reasoning has an important therapeutic, but not defining, role to play in judicial fact-finding. Implicitly,
we also argue that subjective probabilistic reasoning can be well constrained by legal principles; hence,
we conclude that there is little risk in allowing judges to use the laws of probability, especially when it
helps explain their ultimate fact-finding decisions, as it did in Re D and Re L. Our theoretical position
borrows much from the pragmatic philosophical stance of Horwich (1993) and concurs with Friedman
(1997), who concludes on page 291 that ‘[i]t is necessary to keep Bayesian methods in their proper place
with respect to juridical proof. For the most part, they are of analytical assistance only, to those who
think about and craft evidentiary law—but for that purpose they are of very great assistance indeed.’
Illustrative examples
The two examples in this section are real cases in which there are three competing explanations for
something that happened. In both cases, each scenario has a probability reckoned by the judge and the
probabilities aggregate to one, according to the laws of probability.
Example I
The first example is from Re D (A Child) [2014] EWHC 121 (Fam), which Mostyn J tried in January
2014. The factual issue was whether the mother had turned off the oxygen supply to her seriously ill
daughter. The parties in the case agreed that there was a closed class of possible scenarios, namely:
1. The oxygen supply was not in fact turned off, and Nurse G was mistaken in believing that it was;
or
2. The oxygen supply was accidentally turned off by Student Nurse J; or
3. The oxygen supply was deliberately turned off by the mother.
1. We limit our analysis to fact-finding by judges and do not discuss civil jury instructions.
76 The International Journal of Evidence & Proof 24(1)
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