Statistics and the Prosecutors Fallacy

Despite the persuasiveness of such figures, it is quite possible to misuse DNA evidence to incorrectly argue that an innocent suspect must be the perpetrator of the crime, or that a guilty suspect should go free. Both defense and prosecution attorneys can—accidentially or otherwise—misinterpret data to make a highly likely event seem improbable, or a highly unlikely event seem probable. Jurors can be confused because DNA testing reveals the probability that an innocent person's DNA profile matches the sample at the scene of the crime. Jurors must decide, however, what the probability is that a person is innocent, if his DNA matches that sample. The prosecutor's fallacy occurs when investigators focus on the existence of the match, rather than the possibility that the match could be a coincidence.

Let's assume the DNA profile found at the crime scene—and the matching DNA of the suspect—is expected to occur once in every million people. The correct statement of probability arising from these facts is, "If the suspect is innocent, there is a one-in-one-million chance of obtaining this DNA match." The fallacy is to reverse these clauses, and state, "If the DNA matches, there is a one in one million chance that the suspect is innocent." To understand the logical fallacy, imagine the statement, "If it's Tuesday, it must be a school day." The reverse is not true—there are other school days besides Tuesday.

Similarly, there are other ways of misusing statistics in DNA profiling. Let's assume the suspect in the above case is actually guilty. If the suspect hails from a city with a population of ten million, there are ten people in the city whose DNA matches the DNA at the crime scene. Therefore, his defense lawyers could argue there is a 90 percent chance that the suspect is innocent, because he is 1 out of 10 individuals with that same DNA profile. If the defense can convince the jury to ignore other incriminating evidence, such as the suspect's bloody glove left behind at the scene, then the attorney may introduce reasonable doubt. Only by considering DNA typing within the context of other evidence can the probability of a DNA match improve the integrity of the justice system.

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