The prosecutor’s fallacy and the defense fallacy are misinterpretations of conditional probabilities.

Dr. R.E. Gaensslen, Univ. of Illinois (emeritus)

## Prosecutor and Defense Fallacies

Two common fallacies might arise in connection with statistical evidence: the prosecutor’s fallacy and the defense fallacy.

The **prosecutor’s fallacy** is when *the context in which the accused has been brought to court* is falsely assumed to be irrelevant when weighing the evidence. For example, an analyst may testify that “There’s only a 1/X chance that someone other than the suspect left the sample.” This statement ignores other crime scene evidence and overemphasizes the weight of the evidence under discussion.

In the **defense fallacy**, a defense attorney infers that if the probability of a suspect is 1/Y, then X/Y people could have committed the crime. For example, perhaps a suspect in a town of 1,000,000 people has a Random Match Probability (RMP) of 1/10,000. The defense attorney may imply that this suggests that any one of 100 people in the city may be the culprit. This fallacy underemphasizes the weight of DNA evidence and, like the prosecutor’s fallacy, causes jurors to ignore other evidence by focusing on what they perceive to be an important figure.

It is important for attorneys to distinguish the RMP from a source probability, since in the final analysis the litigation is usually interested in the source probability rather than the random match probability. Learn more about random match probability in the video, at right.

These fallacies are not solely related to DNA, as in the above examples. They are statistical fallacies that may arise in any statistical context.

## Addressing Fallacies

The prosecutor’s fallacy and the defense fallacy are two distinct, opposing hypotheses. How will the jury weigh them?

An analyst can address the situation statistically, testing one hypothesis mathematically against the other. There are several calculations that aim at making this comparison, but the most common is the likelihood ratio, also known as the Bayesian theorem.

The Bayesian theorem is often used to compute the probability of paternity, or paternity index. These fairly complicated computations work well in a case when comparing single-source specimens, from unrelated people.

The likelihood ratio is more broadly used in Europe, but given the increasing emphasis on statistics, it may become more popular in the United States.