Prosecutor’s Fallacy
Confuses the probability of observing the evidence if someone is innocent with the probability of innocence given the evidence.
- •Definition: Confuses the probability of observing the evidence if someone is innocent with the probability of innocence given the evidence.
- •Impact: Prosecutor’s Fallacy distorts reasoning by P(Evidence|Innocent) ≠ P(Innocent|Evidence). Failing to incorporate base rates and alternative causes misstates the true probability.
- •Identify: Look for patterns like Present a low probability of evidence under innocence.
What is the Prosecutor’s Fallacy?
This fallacy swaps conditional probabilities, often in legal contexts. A low chance of seeing the evidence under innocence does not automatically mean a low chance of innocence; base rates matter.
People lean on this pattern because Conditional probabilities are counterintuitive; presenting small numbers sounds persuasive in court or argument.
- 1Present a low probability of evidence under innocence.
- 2Conclude the defendant is almost certainly guilty.
- 3Neglect base rates, alternative explanations, or false positives.
Why the Prosecutor’s Fallacy fallacy matters
This fallacy distorts reasoning by P(Evidence|Innocent) ≠ P(Innocent|Evidence). Failing to incorporate base rates and alternative causes misstates the true probability.. It often shows up in contexts like Legal reasoning, Risk communication, Forensics, where quick takes and ambiguity can hide weak arguments.
Examples of Prosecutor’s Fallacy in Everyday Life
DNA evidence with a 1-in-a-million random match rate is treated as near-certain guilt, ignoring population size and other evidence.
Why it is fallacious
P(Evidence|Innocent) ≠ P(Innocent|Evidence). Failing to incorporate base rates and alternative causes misstates the true probability.
Why people use it
Conditional probabilities are counterintuitive; presenting small numbers sounds persuasive in court or argument.
Recognition
- Conditional probabilities are flipped or treated as identical.
- Base rates and alternative causes are ignored.
- Small probability of evidence is equated to small probability of innocence.
Response
- Clarify the difference between P(E|I) and P(I|E).
- Introduce base rates and alternative explanations into the calculation.
- Use concrete numbers to illustrate how probabilities shift with prevalence.
- “Prosecutor’s Fallacy” style claim: Confuses the probability of observing the evidence if someone is innocent with the probability of innocence given the evidence.
- Watch for phrasing that skips evidence, e.g. "Confuses the probability of observing the evidence if someone is innocent with the probability of innocence given the evidence"
- Pattern hint: Present a low probability of evidence under innocence.
Clarify the difference between P(E|I) and P(I|E).
Prosecutor’s Fallacy is often mistaken for Base Rate Fallacy, but the patterns differ. Compare the steps above to see why this fallacy misleads in its own way.
Close variations that are easy to confuse with Prosecutor’s Fallacy.
Frequently Asked Questions
Prosecutor’s Fallacy signals a weak reasoning pattern. Even if the conclusion is true, the path to it is unreliable and should be rebuilt with sound support.
Prosecutor’s Fallacy follows the pattern listed here, while Base Rate Fallacy fails in a different way. Looking at the pattern helps choose the right diagnosis.
You will find it in everyday debates, opinion columns, marketing claims, and quick social posts—anywhere speed or emotion encourages shortcuts.
It can feel persuasive, but it remains logically weak. A careful version should replace the fallacious step with evidence or valid structure.