Defendant’s Fallacy
The defendant’s fallacy can be illustrated from the example used for the
prosecutor’s fallacy. There it was concluded that taking the evidence of a
match on its own, there is only a one in five (20%) chance of guilt. It is,
however, a fallacy to use this figure of 20% when there is other circumstantial
evidence
pointing to the guilt of the defendant. To state the obvious, each
piece of circumstantial evidence for the defendant’s guilt increases the
probability of guilt.
Sally Clark Case
In the United Kingdom there was a famous conviction, of Sally Clark, based
on the prosecutor’s fallacy. In 1998 Sally Clark was accused of killing her first
child, Christopher, at 11 weeks of age and then conceiving a second child,
Harry, and killing him at 8 weeks. For the defence it was argued that both
deaths were cases of sudden infant death syndrome (SIDS). An expert witness
testified that the chance of two deaths in the same family from SIDS was
about 1 in 73 million. Sally Clark was convicted of murder of these two
children in 1999.
Following her conviction the Royal Statistical Society issued a press release
pointing out two errors of reasoning.
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First, they criticised the figure of 1 in
73 million for the frequency of two cases of SIDS in such a family. The
Society said: "This approach is, in general, statistically invalid. It would only
be valid if SIDS cases arose independently within families, an assumption that
would need to be justified empirically. Not only was no such empirical
justification provided in the case, but there are very strong a priori reasons for
supposing that the assumption will be false. There may well be unknown
genetic or environmental factors that predispose families to SIDS, so that a
second case within the family becomes much more likely”.
Second, they pointed out that “figures such as the 1 in
73 million are very
easily misinterpreted. Some press reports at the time stated that this was the
chance that the deaths of Sally Clark's two children were accidental. This (mis-
) interpretation is a serious error of logic known as the Prosecutor's Fallacy.
The jury needs to weigh up two competing explanations for the babies' deaths:
SIDS or murder. Two deaths by SIDS or two murders are each quite unlikely,
but one has apparently happened in this case. What matters is the relative
likelihood of the deaths under each explanation, not just how unlikely they are
under one explanation (in this case SIDS, according to the evidence as
presented)”.
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Royal Statistical Society “News Release” 23 October 2001 -
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