Appeals to Reason

AuthorMike Redmayne
Date01 January 2002
Published date01 January 2002
Appeals to Reason
Mike Redmayne*
This article considers how statistical reasoning changes conceptions of evidence
and proof. Beginning with three Court of Appeal judgments in which proof is
quantified, it traces the implications of statistical ways of thinking about proof
through the law of criminal evidence. This leads to the bizarre conclusion that
proof is, by and large, impossible. The argument then takes a more constructive
turn. The way in which the presumption of innocence is conceptualised in
statistical argument is criticised and it is suggested that proof depends on a
precondition of trust in the way suspects are selected by the police. For that trust
to be deserved, police suspects must be chosen in a legitimate manner.
I should .. . members of the jury just sound a note of caution about the statistics. However
compelling you may find those statistics to be, we do not convict people in these courts on
statistics. It would be a terrible day if that were so.1
Statistical reasoning is a powerful tool. It allows us to quantify and compare, to
create new concepts and stabilise them. The probabilistic revolution of the
nineteenth and early twentieth centuries has shaped economics, biology, physics
and politics in profound ways. Nor has law escaped the transformative power of
numbers.2To name just two areas: criminal policy and the regulation of industry
are heavily dependent on concepts – crime rates, court performance, safety levels –
which could not exist without statistics. The fact-finding decisions of the criminal
courts, however, have remained largely immune from the deep transformations
statistical reasoning has visited upon other areas. But some recent appellate
decisions hint at a way in which evidence and proof might be changed profoundly
by probabilistic reasoning. It is DNA evidence which provides the background to
this change. But what makes the shift in reasoning involved so significant is that it
need not be confined to DNA cases. Once we go beyond DNA, it turns out that a
statistical conception of proof provokes fundamental questions about the nature of
evidential processes – about how proof is possible at all.
DNA and the Doheny direction
When DNA evidence began to be used in court, a problem quickly emerged. The
problem was how to present DNA statistics – ‘match probabilities’ – to juries. A
DNA profile with a match probability of 1 in 3 million means that there is a 1 in 3
million chance that a person chosen at random from the population will have that
ßThe Modern Law Review Limited 2002 (MLR 65:1, January). Published by Blackwell Publishers,
108 Cowley Road, Oxford OX4 1JF and 350 Main Street, Malden, MA 02148, USA. 19
*London School of Economics and Political Science. A version of this article was presented to my Law
Department colleagues at a staff seminar. I am grateful to them for listening to and commenting on it.
1RvClark CA 07495 Y3 (2 October 2000), para 128. The words are those of Harrison J, the trial
2 See A. Desrosie`res, The Politics of Large Numbers: A History of Statistical Reasoning (Cambridge,
MA: Harvard University Press, Eng tr Camille Naish, 1998); G. Gigerenzer et al, The Empire of
Chance: How Probability Changed Science and Everyday Life (Cambridge: Cambridge University
Press, 1989). For some of the deep ways in which law has been changed by statistics, see W.T.
Murphy, The Oldest Social Science: Configurations of Law and Modernity (Oxford: Clarendon Press,
1997) esp chs 5 and 6.
same profile.3But, when this statistic is presented, the courts now accept that it
must not be taken to imply that there is a 1 in 3 million chance that the defendant is
innocent.4The reason for this is that in a large enough population one would expect
to find several other people with the same profile. Among the whole population of
the United Kingdom one expects to find 20 such people. But that does not mean
that there is a chance of just 1 in 20 that the defendant is guilty. There may be other
evidence to incriminate him. It may also be inappropriate to consider everyone in
the United Kingdom a possible culprit: the facts of the case may imply that the
offender is one among a much smaller group of suspects. After agonising over
these problems, the Court of Appeal in Doheny hit upon an ingenious solution.
Rather than explaining the subtle but important distinction between the probability
of guilt given the DNA evidence and the probability of the DNA evidence given
guilt in semantic terms, it would provide a simple illustration to convey the key
issues, rather as we have just done in presenting the problem here. Its sample jury
instruction for DNA cases proceeds as follows:
Members of the jury, if you accept the scientific evidence called by the Crown, this indicates
that there are probably only four or five white males in the United Kingdom from whom that
semen could have come. The defendant is one of them. If that is the position, the decision
you have to reach, on all the evidence, is whether you are sure that it was the defendant who
left that stain or whether it is possible that it was one of the other small group of men who
share the same DNA characteristics.5
It is clear that the choice of the United Kingdom as the relevant population here is
merely an illustration. The court acknowledged that it might be appropriate to
choose a more limited ‘suspect population’, such as ‘the Caucasian, sexually active
males in the Manchester area’.6
The Doheny direction goes some way towards ensuring that DNA match
probabilities are presented to juries in manageable terms. The impact of the DNA
evidence is conveyed in terms of its ability to whittle a large group of possible
suspects down to a much smaller group. The jury is then left with a relatively
simple task: deciding whether any other evidence singles the defendant out among
this smaller group. There will, however – and this point is crucial to the next part of
our exposition – be cases where there is no other evidence to implicate the accused.
Often this will be because the defendant has been identified by a DNA database
search rather than through conventional investigative strategies. The novelty of the
database scenario is brought home by a recent news story.7In 1999 a database
3 In this article, such figures are taken at face value. They used to be controversial, because the
assumptions on which they were calculated were contestable. Now, owing to intensive research
efforts, the assumptions behind DNA match probabilities seem fairly robust. Nevertheless,
consideration of the degree to which match probabilities do depend on assumptions can still leave
one with a giddy sense of statistical anti-realism. As a group of experts from the Forensic Science
Service puts it, ‘[a]s more and more loci are employed, so the standard calculation produces numbers
that are further and further beyond the realms that can be investigated by statistical methods. The tiny
numbers, although not necessarily ‘‘wrong’’, are without any real meaning.’ I. W. Evett et al, ‘DNA
Profiling: A Discussion of Issues Relating to the Reporting of Very Small Match Probabilities’ [2000]
Crim LR 341, 347. There are also more mundane concerns: many commentators feel that the
probability that blood samples have been mixed up, or contaminated, overshadows the tiny match
probabilities which are presented in court. See, eg, J.J. Koehler, A. Chia and S. Lindsay, ‘The
Random Match Probability in DNA Evidence: Irrelevant and Prejudicial?’ (1995) 35 Jurimetrics J
4RvDeen,The Times, 10 January 1994. See, generally, M. Redmayne, Expert Evidence and Criminal
Justice (Oxford: Oxford University Press, 2001) ch 4.
5Doheny [1997] 1 Cr App R 369, 375.
6ibid 374.
7 ‘Mismatch Calls DNA Tests into Question’, USA Today, 8 February 2000.
The Modern Law Review [Vol. 65
20 ßThe Modern Law Review Limited 2002

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