A Barrister's Blog

The so‑called ‘prosecutor’s fallacy’ describes the risk that the fact finding tribunal will reason that evidence of the match probability or the likelihood ratio expresses the probability that an incriminating DNA sample was the DNA of the accused (Wark v WA [2023] WASCA 66). If you want a more succinct definition (from Xie v R [2021] NSWCCA 1) it’s “a fallacious mode of reasoning that transposes the conditional in a likelihood ratio“.

Lies and statistics

Why am I writing about this? Like many ideas for this blog over the years, I came across a case about the prosecutor’s fallacy (which I hadn’t ever heard of) when I was researching something else. I am having flashbacks to studying second year statistics in the early 1980’s when I actually knew something about Baye’s Theorem. In case you’re wondering, Baye’s Theorem is a means of refining probability calculations when more information comes to hand.

Prosecutor’s fallacy – examples

Statistics aside, the best way to describe the prosecutor’s fallacy is with a few examples. In R v Galli [2001] NSWCCA 504, the answer to the question: “What was the probability of the accused having the … DNA of the father compared to a person taken at random?” was 2.4 million to one.

However, the question for the jury was: “What was the probability of the accused being the father?”. Speigleman CJ noted that:

84 One means of committing the Prosecutor’s Fallacy is a reasoning process which treats the answer to the first question as if it was an answer to the second question, i.e. that the probability that he was the father was 2.4 million to one. That is not a permissible form of reasoning.

85 Given the size of the male population in Australia, on the basis of a probability of 2.4 million to one, there would be three or four males in Australia who share the DNA profile of the father of the foetus. A statement in the form that the “odds are 2.4 million to 1 that the accused is the offender” or that the “odds are 1 in 2.4 million that the accused is innocent”, overlooks the number of people who could have committed the offence.

Another example from the English case of R v Adams where the treatment of the evidence was that  ‘[o]nly one person in a million will have a DNA profile which matches that of the crime stain” as demonstrating that “there is a million to one probability that the defendant left the crime stain and is guilty of the crime‘. His Lordship observed that the fallacious nature of that statement becomes clear when it is appreciated that the statement that one person in a million has the DNA profile which matches that obtained from the crime scene means that the suspect will be 1 of perhaps 26 men in the United Kingdom who share that characteristic (presumably assuming a population of 52 million with an equal division in gender). Hence, based on those figures alone, the odds of its being the accused are not a million to one. The prosecutor’s fallacy has a defence counterpart which ignores the statistical significance of the other evidence connecting the accused to the crime.

In case you are still awake and want to follow this further you could have a look at:  An introduction to statistical ‘evidence’ — (2003) 23 Aust Bar Rev 239.

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