science & techanalysisWikipedia
Prosecutor's fallacy
The base rate fallacy is the habit of judging the likelihood of something from a specific case while ignoring how common it is in general. The prosecutor's fallacy is its courtroom form: if a DNA match has a one-in-a-million chance of occurring at random, it is wrong to conclude that the defendant is almost certainly innocent or guilty without considering how many people could have left the sample. Consider a city of millions: a rare match can still point to many people, so the chance of a false match somewhere in the database can be large even when any single match is improbable. William C. Thompson and Edward Schumann introduced these terms in 1987 to describe such reasoning errors in law. Bayes' theorem shows how the prior probability of guilt should be combined with the evidence.
Bayes' theorem combines the prior, or base rate, with the strength of the evidence to give the updated probability. If a condition affects one in a million people, a test with a one-in-a-million false positive rate applied to a large population will still produce false positives. The answer depends on the size of the population being searched, not only on the match probability.
Juries and lawyers mix up the probability of evidence given innocence with the probability of innocence given evidence, which can lead to wrongful convictions. Understanding base rates is essential for reading medical tests, DNA evidence and security screening.
background
The base rate fallacy, also called base rate neglect or base rate bias, is a type of fallacy in which people tend to ignore the base rate (e.g., general prevalence) in favor of the information pertaining only to a specific case. Base rate neglect is a specific form of the more general extension neglect.
It is also called the prosecutor's fallacy or defense attorney's fallacy when applied to the results of statistical tests (such as DNA tests) in the context of law proceedings. These terms were introduced by William C. Thompson and Edward Schumann in 1987, although it has been argued that their definition of the prosecutor's fallacy extends to many additional invalid imputations of guilt or liability that are not analyzable as errors in base rates or Bayes's theorem.
From Wikipedia: Base rate fallacy (CC BY-SA 4.0) ↗From Wikipedia, the free encyclopedia · text CC BY-SA 4.0
Illustrative photo · Sh.arasti, CC BY-SA 4.0, via Wikimedia Commons
