Naked statistical evidence and incentives for lawful conduct
| Published date | 01 April 2020 |
| Date | 01 April 2020 |
| DOI | http://doi.org/10.1177/1365712720913333 |
| Subject Matter | Articles |
Article
Naked statistical evidence
and incentives for lawful conduct
Christian Dahlman
1
Lund University, Lund, Sweden
Abstract
The problem of ‘naked statistical evidence’ is one of the most debated issues in evidence
theory. Most evidence scholars agree that it is deeply problematic to base a verdict on naked
statistical evidence, but they disagree on why it is problematic, and point to different char-
acteristics of naked statistical evidence as the root of the problem. In this article, the author
discusses the merits of different solutions to the problem of naked statistical evidence, and
argues for the incentive-solution: verdicts based on naked statistical evidence are unacceptable as
they do not contribute in a positive way to the incentive structure for lawful behaviour.
Keywords
blue bus, gatecrasher, incentive, proof paradox, statistical evidence
1. Introduction
‘punishment ought not to be inflicted where it cannot act to prevent the mischief’
Jeremy Bentham
The problem of ‘naked statistical evidence’ is one of the most debated issues in evidence theory. Most
evidence scholars agree that it is deeply problematic to base a verdict on naked statistical evidence, but
they disagree on why it is problematic, and point to different characteristics of naked statistical evidence
as the root of the problem. Naked statistical evidence is a special kind of statistical evidence, tradition-
ally captured by three famous examples: the Gatecrasher Case,thePrison Riot Case and the Blue Bus
Case. These examples are to some extent inspired by actual cases, but it should be stressed that they are
imaginary cases, designed to fit the purpose of a theoretical analysis. I will refer to them as ‘cases’, but
this should not be interpreted to imply that they are real, or even realistic.
Corresponding author:
Christian Dahlman, Lund University, Lund, Sweden.
E-mail: christian.dahlman@jur.lu.se
1. Thanks to Ron Allen, Marvin Backes, Charles Berger, Marcello Di Bello, Edward Imwinkelried, Anne Ruth Mackor, Dale
Nance, Dave Lagnado, Henry Prakken, Amit Pundik, Ellika Sevelin, Martin Smith, Alex Stein, Lena Wahlberg and an
anonymous reviewer for helpful discussions and suggestions.
The International Journalof
Evidence & Proof
2020, Vol. 24(2) 162–179
ªThe Author(s) 2020
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DOI: 10.1177/1365712720913333
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The Gatecrasher Case was introduced by Laurence Jonathan Cohen (1977) and has been debated in
the literature with some minor variations. For the purpose of this investigation, I will use the following
version.
1000 people attend a rodeo. Some of them paid admittance, but a substantial majority ‘crashed the gate’ (did
not pay admittance). We do not know who is a gatecrasher and who is a paying spectator, but we know for
certain that the defendant is one of the people who attended the rodeo. According to the defendant’s own
account of the events, he is one of the spectators who paid admittance. Nevertheless, the organizer of the
rodeo sues for the admission fee. The organizer argues that he has a legally valid claim against the defendant,
since the probability that the defendant did not pay admittance is higher than 50%, given that he claims that he
did pay but a substantial majority of the spectators were gatecrashers, and the standard of proof in civil cases
(‘preponderance of the evidence’) only requires that the plaintiff makes his case more probable than the
defendant’s case. (If so meone would object that the defe ndant’s testimony that he d id pay admittance
substantially decreases the probability of the plaintiff’s case, the percentage of gatecrashers can always be
set sufficiently high to push the probability of the plaintiff’s case above 50%all things considered. Since we
are dealing with an imaginary case, we could assume that 900 or 990 crashed the gate, if this is what it takes to
push the probability above 50%.)
Cohen says that it would be wrong for a court to judge in favour of the plaintiff on this naked
statistical evidence. If the plaintiff would be entitled to claim admittance from this spectator, he would
also be entitled to claim admittance from every other spectator, based on the same naked statistics, and
this means that he we would be legally entitled to force all the spectators who did not crash the gate to
pay twice. In Cohen’s words: ‘The absurd injustice of this suffices to show that there is something wrong
somewhere’ (Cohen, 1977: 75).
The Prison Riot Case was introduced by Charles Nesson (1979). Just like the Gatecrasher Case it has
been discussed with minor variations. I will use the following version.
100 prison inmates participate in a riot and escape from the prison. During the riot, 99 of them assault and kill
a guard on duty. One prisoner is caught, and is prosecuted for participating in the killing of the guard. It is
absolutely certain that he is one of the 100 prisoners that participated in the riot, and it is absolutely certain
that 99 of them participated in the killing of the guard. There is no further evidence (no witnesses, no CCTV
images) that makes it possible to identify the prisoners who participated in the killing, and individuate the
prisoner who did not participate. According to the prosecutor, the evidence that the defendant is one of the
prisoners who participated in the riot is sufficient for the standard of proof in criminal cases, since it
establishes that there is a 99%probability that the defendant participated in the killing of the guard. (If
someone would object that the standard of proof in criminal cases corresponds to a probability higher than
99%, say 99.5%, the circumstances of the case can always be altered to satisfy this number, for example by
making it 1000 prisoners where 999 participated in the killing of the guard.)
According to Nesson, the defendant should not be convicted on such evidence. There is nothing in the
evidence that ‘differentiates the defendant from the other prisoners’ (Nesson, 1979: 1193). A guilty
verdict is therefore unacceptable. And this goes for all cases of naked statistical evidence (Nesson, 1985:
1378).
The Blue Bus Case was introduced to the debate on n aked statistical evidence by Judith Jarv is
Thomson (1986). It has also been discussed in various versions. I will use the following version.
On a rainy night a pedestrian is hit by a bus and injured. It is certain that the vehicle was a bus, and there is no
doubt that the driver was negligent. Several buses were in traffic on the night in question, and it cannot be
established which of them hit the pedestrian. Two bus companies—the Blue Bus Company and the Green Bus
Company—operate in the area, so the bus that hit the pedestrian belongs to one of these companies. Both
companies say that they don’t know if the accident was caused by one of their buses, or by the other company.
The Blue Bus Company has the major market share. 80%of the buses who could have hit the pedestrian
Dahlman 163
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