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Prosecutor's fallacy
The prosecutor's fallacy is a fallacy of statistical reasoning, typically used by the prosecution to argue for the guilt of a defendant during a criminal trial. Although it is named after prosecutors it is not specific to them, and some variants of the fallacy can be utilized by defense lawyers arguing for the innocence of their client. At its heart the fallacy involves assuming that the prior probability of a random match is equal to the probability that the defendant is innocent. For instance, if a perpetrator is known to have the same blood type as a defendant and 10% of the population share that blood type, then to argue on that basis alone that the probability of the defendant being guilty is 90% makes the prosecutor's fallacy (in a very simple form).
==Concept==
The terms "prosecutor's fallacy" and "defense attorney's fallacy" were originated by William C. Thompson and Edward Schumann in 1987. 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 may be less unlikely by mere chance.
The basic 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 odds of the match being made at random may be increased, and less damaging to the defendant. The odds in this scenario do not relate to the odds of being guilty, they relate to the odds of being picked at random.
抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』
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