In
the Prosecution Fallacy
we saw that the prosecutor wrongly confuses the probability of seeing
some evidence with the probability of innocence.
The example we used was the following:
Suppose a crime has
been committed and that the criminal has left some physical evidence,
such as some of their blood at the scene. Suppose the blood type is
such that only 1 in every 1000 people has the matching type. A suspect,
let's call him Fred
who matches
the blood type is put on trial. The prosecutor claims
that the probability that an innocent person has the matching blood
type is 1 in a 1000 (that's a probability of 0.001). Fred has
the matching blood type and therefore the probability that Fred is
innocent is just 1 in a 1000.
We saw how this was a
fallacy by arguing that out of 10 million adult
males we would actually expect a large
number of people to have the matching blood type (about 10,000).
However, it is also a fallacy of the defence to argue either of the
following:
The probability Fred is innocent
is 99.99% (i.e. 0.9999) because Fred is no more likely to
have committed the crime than any of the other 9999 matching males; or
more generally
That the evidence is irrelevant
because it does not eliminate a large proportion of the population
The first statement is only true if
there is no evidence other than the blood to link Fred to the crime.
But, generally there willbe
other evidence and this evidence may eliminate a significant
proportion of the other 'matching' people. The second statement is
false because, irrespective of other evidence, the matching blood type
is 1000 times more likely if Fred is guilty than if he is innocent (and
using Bayes theorem this increases the prior probability of guilt by a
factor of 1000). This clearly cannot be considered irrelevant.
For more information on
fallacies in legal reasoning read this article:
Fenton NE and Neil M,
''The Jury
Observation Fallacy and the use of Bayesian Networks to present
Probabilistic Legal Arguments'', Mathematics Today ( Bulletin of the
IMA, 36(6)), 180-187, 2000.
