Probabilistic models of legal corroboration
| Author | Rafal Urbaniak,Pavel Janda |
| Date | 01 January 2020 |
| DOI | 10.1177/1365712719864608 |
| Published date | 01 January 2020 |
| Subject Matter | Articles |
Article
Probabilistic models
of legal corroboration
Rafal Urbaniak
LoPSE, University of Gdansk, Gdansk, Poland
Pavel Janda
LoPSE, University of Gdansk, Gdansk, Poland
Abstract
The aim is to develop a sensible probabilistic model of legal corroboration in response to an
attack on the probabilistic approach to legal reasoning due to Cohen. One of Cohen’s argu-
ments is that there is no probabilistic measure of evidential support which satisfactorily cap-
tures the situation in which independent witnesses testify to the truth of the same proposition
(or independent pieces of evidence converge on a certain claim)—the phenomenon called
corroboration (or convergence). We investigate the properties of several probabilistic mea-
sures discussed by Cohen, discuss Cohen’s criticism of those measures, and develop our own.
Finally, we offer a probabilistic measure of corroboration that evades the critical points raised
against the ones discussed so far.
Keywords
Legal probabilism, corroboration, probabilistic evidence evaluation, evidence aggregation
Introduction
Corroboration, intuitively speaking, takes place when two independent witnesses testify to the truth of
the same proposition. In his large-scale attack on the probabilistic approach to legal reasoning, Cohen
(1977) devotes Chapter 10 of his book to what he calls the difficulty about corroboration and con-
vergence. In that chapter he argues that the probabilistic model of weight of evidence and legal
decision standards is incapable of adequately capturing the phenomenon. In this paper, we develop
a probabilistic model of corroboration which handles Cohen’s and other objections better than its
predecessors. The model that we will offer follows quite natur ally from general Bayesian considera-
tions, and, following Cohen’s desideratum, it incorporates the fact that witnesses can report multiple
false stories.
Corresponding author:
Rafal Urbaniak, LoPSE, University of Gdansk, Bazynskiego 4, Gdansk, 80-309, Poland.
E-mail: rfl.urbaniak@gmail.com
The International Journalof
Evidence & Proof
2020, Vol. 24(1) 12–34
ªThe Author(s) 2019
Article reuse guidelines:
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DOI: 10.1177/1365712719864608
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Given corroborating testimonies, it seems that the probability of the target claim should increase
significantly.
1
Cohen argues that no known probabilistic measure of confirmation results in a theorem
that would somehow capture this intuition—and that is the main gist of his criticism. Cohen is not the
only one who shares this critical view. As Hailperin (1986: 383) points out,
Although at one time actively pursued, the combination of testimonies (or of evidence) is now no longer a
standard item in the repertoire of probability applications.
This opinion is also confirmed by Zabell (1988):
In the increasingly frequentist environment of the latter 19th century [ ...] the probabilistic analysi s of
testimony was viewed with increasing hostility and suspicion. In the end it became largely discredited, and
today such attempts are often considered mere curiosities: naive, erroneous, or uninformative. [327]
For this reason, Cohen does not have much to go on in his search for probabilistic explications of the
phenomenon in question.
2
He does, however, take the existing approaches for a ride, one by one.
The approaches Cohen discusses and finds lacking are: Boole’s formula (Boole, 1857), Ekelo¨f’s
principle (Ekelo¨f, 1964) and his own theorem about the issue. The latter he finds unsatisfactory, because
it only states that the joint confirmation level will be higher than the separate confirmation levels, but not
that it will be much higher.
The plan is to evaluate Cohen’s criticism of probabilistic measuresof corroboration and then introduce
the improvedmeasure. In the next sectionwe introduce Boole’s formula,propose a modern derivationof it,
discuss Cohen’scriticism, and put forward our own.It turns out that from our perspectiveBoole’s formula
is in a sense correct, but it applies only to very specificscenarios, in which exactly two witnessesanswer a
‘yes’/’‘no’ question as to the truth of a hypothesis with prior probability .5. In the following section we
discuss Ekelo¨f’s measure of corroboration based on the 17th century Hooper’s formula and extend
Cohen’s criticismof this measure. Next, we briefly discuss another probabilisticmeasure of corroboration
due to Lambertthat Cohen didn’t consider inthe chapter and show that the measureis unfit for the task due
to strong assumptions that it makes. Finally, we offer an improved probabilistic corroboration model.
Boole’s formula
Deriving Boole’s formula
Let’s focus on a very simple case in which two witnesses testify regarding the truth of a single simple
statement.Let pbe the probability th at the first witness t ells the truth, and qthe probability thatthe other one
1. If, instead of witnesses’ testimonies, we are faced with two independent pieces of (circumstantial) evidence, the analogous
phenomenon is called ‘circumstantial convergence’. Since as far as it is known there are no major formal differences here, in the
paper we’ll focus on corroboration, with the thought that everything that is said, applies, mutatis mutandis, to circumstantial
convergence.
2. We are aware of recent developments in theory of combining evidence by obtaining likelihood ratios for independent pieces of
evidence and then multiplying the results to get the overall weight of combined evidence (Robertson et al., 2016: 69–71) or
combining various pieces of evidence in a Bayesian Network (Fenton and Neil, 2013: 412–414). We want to, however, fill a gap
in the literature by developing an explicit probabilistic approach to corroboration that answers Cohen’s worries directly and is
more closely connected to his criticism. This being said, our strategy and reply to Cohen’s criticism is in line with these recent
general developments. We can find a related approach to witness testimonies in (Bovens and Hartmann, 2003). Bovens and
Hartmann concentrate on modelling the following Cohen’s thought about surprising information: the lower the prior probability
of the information provided by the witnesses, the higher the posterior probability that the information is true (Bovens and
Hartmann, 2003). They generalize to multiple false stories and multiple witnesses, but they do not consider Cohen’s
requirement that the jump be significant and that the element of surprise should contribute to this significance. We come to a
similar result from a slightly different angle, mostly focusing on Cohen’s worry about the significance of the jump caused by a
surprising agreement of unreliable witnesses. We do not focus on how unbelievable the story itself is, although its prior
probability is a factor also in our analysis.
Urbaniak and Janda 13
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