Conjunction fallacy

The conjunction fallacy is an informal error of reasoning in which one assumes that more specific conditions are more likely than more general ones. It generally occurs because people believe that additional detail makes a statement more believable, while less detail makes a statement more vague and thus less believable.

In probability, the conjunction rule states that the probability of two events A and B occurring cannot be greater than the probability of either A or B occurring. To believe otherwise represents the conjunction fallacy.

The conjunction fallacy is sometimes referred to as the "Linda problem", based on a famous example of the fallacy in action. Given the information that a woman, Linda, is 31 years old, married with three children, and active in the local Republican party, respondents are asked which scenario is more probable:

1) Linda works at a bank.
2) Linda works at a bank and is a Christian.

Most respondents select scenario 2, but this is an error. The probability that Linda works at a bank (less than 100%) must be multiplied by the probability that she is a Christian (also less than 100%) to arrive at the probability of her being both Christian and a bank employee. This will always be less than the probability of her being simply a bank employee with her religion unspecified.

The conjunction fallacy can have significant implications in criminal justice. Given the fact in a criminal case that the defendant has prior convictions for smuggling antiquities, studies have shown that potential jurors are more likely to agree with the statement "the defendant committed murder to prevent an accomplice from talking to the police" than the statement "the defendant committed murder", in the absence of any other evidence. This is because of the bias to favor more specific statements as more probable than less specific statements. Thus an eloquent prosecutor or defense attorney can make an unsupported hypothesis more appealing by adding details even when logically this should make the hypothesis less likely.