During the O.J. Simpson trial, the prosecution made much of the fact that Simpson had a record of violence towards his wife. In response, Simpson’s legal team argued that, of all women subjected to spousal abuse, only one in 2,500 was subsequently killed by the abusive husband. It was hence implied that, since the ratio of abusers to killers was so high, any evidence about the accused’s prior violent behaviour was insignificant.
This sounds plausible. However, there is another way to consider the statistics. According to the German academic Gerd Gigerenzer, we are not trying to predict whether a husband will murder his wife: Simpson’s wife inarguably had been murdered, so instead, we should ask the question backwards: given that a battered wife has been murdered, what are the odds that the husband did it? Gigerenzer calculates that ‘the chances that a batterer actually murdered his partner, given that she has been first abused and then killed, is about eight in nine’.
This is a case where a statistical sleight of hand normally called ‘the prosecutor’s fallacy’ worked for the defence. What is interesting is not merely that we are confused but the degree of our confusion: the presentation of the data affects our judgment by factor of thousands: from 0.04 per cent to 90 per cent. We need to be alert to this kind of error, particularly since computers and ‘big data’ make it easy to generate spurious but plausible statistics on almost any subject.
High-profile criminal cases seem plagued by peculiar mental biases. In particular, they seem to cause people to polarise around only two opposing theories of ‘what happened’.
I felt slightly vindicated when I finally heard that the British police were investigating the possibility that the disappearance of Madeleine McCann was the result of a burglary attempt gone wrong.
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