Prosecutor's Fallacy

The prosecutor's fallacy is a fallacy of statistical reasoning made in law. In this fallacy, the context in which the accused has been brought to court is falsely assumed to be irrelevant to judging how confident a jury can be in evidence against them with a statistical measure of doubt. If the defendant was selected from a large group merely because of the evidence under consideration, then this fact should be included in weighing how incriminating that evidence is. Not doing so is a base rate fallacy. This fallacy usually results in assuming that the prior probability that a piece of evidence would implicate a randomly chosen member of the population is equal to the probability that it would implicate the defendant.

One form of the fallacy results from misunderstanding conditional probability and neglecting the prior odds of a defendant being guilty before that evidence was introduced. When a prosecutor has collected some evidence (for instance a DNA match) and has an expert testify that the probability of finding this evidence if the accused were innocent is tiny, the fallacy occurs if it is concluded that the probability of the accused being innocent must be comparably tiny. If the DNA match is used to confirm guilt which is otherwise suspected then it is indeed strong evidence. However if the DNA evidence is the sole evidence against the accused and the accused was picked out of a large database of DNA profiles, the jurors should consider the very likely possibility that the match is just a coincidence and the accused is innocent. The odds in this scenario do not relate to the odds of being guilty, they relate to the odds of being picked at random.

The terms "prosecutor's fallacy" and "defense attorney's fallacy" were originated by William C. Thompson and Edward Schumann in the 1987 article Interpretation of Statistical Evidence in Criminal Trials, subtitled The Prosecutor's Fallacy and the Defense Attorney's Fallacy.