# Prosecutor's fallacy

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The prosecutor's fallacy is a fallacy of statistical reasoning made in law where the context in which the accused has been brought to court is falsely assumed to be irrelevant to judging how confident to be in evidence against them with a statistical measure of doubt. If the defendant was selected from a large group 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.

Typical occurrences of the fallacy are described below:

• 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. The probability of innocence would only be the same small value if the prior odds of guilt were exactly 1:1. If the accused is otherwise totally unconnected to the case, and is only in the courtroom due to that DNA evidence then we should consider a much lower prior probability of guilt, such as the overall rate of offenders in the populace.
• The fallacy can arise from multiple testing, such as when evidence is compared against a large database. The size of the database elevates the likelihood of finding a match by pure chance alone; i.e., DNA evidence is soundest when a match is found after a single directed comparison because the existence of matches against a large database where the test sample is of poor quality (common for recovered evidence) is very likely by mere chance.

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.[1]

## Contents

### Examples of prosecutor's fallacies

1. Conditional probability:

2. Multiple testing. In another scenario, a crime-scene DNA sample is compared against a database of 20,000 men. A match is found, that man is accused and at his trial, it is testified that the probability that two DNA profiles match by chance is only 1 in 10,000. This does not mean the probability that the suspect is innocent is 1 in 10,000. Since 20,000 men were tested, there were 20,000 opportunities to find a match by chance.