Prosecutor's Fallacy
Definition
The error of treating the RMP (or its reciprocal) as the probability that the defendant is innocent, or as the probability that the defendant did not leave the sample. Formally, it confuses P(evidence | defendant not the source) with P(defendant not the source | evidence). The two are equal only in the trivial case where the prior probability is 0.5.
- Core error
- Equates P(evidence | innocent) with P(innocent | evidence)
- Identified in
- R v. Doheny and Adams 1996
- Correction method
- Apply Bayes' theorem to incorporate prior probability and case context
Common questions
What is the prosecutor's fallacy in forensic evidence?+
The prosecutor's fallacy is confusing two different probabilities. It treats the random match probability (the chance a random person matches the evidence) as if it were the probability that the defendant is guilty. These are different questions separated by Bayes' theorem.
Why is this error dangerous in court?+
A tiny random match probability sounds incriminating, but it doesn't directly tell you the probability of guilt. You must also consider the prior odds, alternative suspects, and the broader case context. Jumping from a small match probability to guilt skips critical steps in statistical reasoning.
How do you state the DNA evidence correctly?+
Instead of saying a defendant is almost certainly guilty based on a small match probability, properly present the likelihood ratio or explain what the evidence means given innocence. Let the jury weigh that against other facts, rather than collapsing the entire inference into a single number.
Related terms
- Likelihood Ratio (LR)
- The ratio of two conditional probabilities: the probability of the observed evidence given the prosecution's hypothesis (same source), divided by the probability...
- Random Match Probability (RMP)
- The probability that a randomly chosen unrelated person from the relevant population would match the evidence profile by chance. A very small...
- Defence Fallacy
- The converse error of inflating the importance of the RMP by arguing that, because many people in the population share the profile,...
- Evaluative Reporting
- A framework for expressing forensic conclusions in terms of the probability of the evidence given the prosecution hypothesis versus the defence hypothesis...
- Prior Odds
- The ratio of the probability of the prosecution hypothesis to the probability of the defence hypothesis before the forensic evidence in question...
- Product Rule
- The rule that, under independence, the joint probability of a multi-locus genotype equals the product of the individual locus genotype frequencies. Used...
- Theta (FST) Correction
- A correction factor applied to allele frequency estimates to account for population sub-structure (the tendency for allele frequencies to differ between sub-populations)....
- Activity-Level Proposition
- A proposition about what happened. Example: 'The suspect handled the knife' versus 'The suspect never handled the knife.' Activity-level propositions require the...
- Bayes' Theorem
- The mathematical rule that relates prior odds, the likelihood ratio, and posterior odds. In the odds form: O(Hp|E) = O(Hp) x LR....
- Daubert Standard
- The US federal evidentiary standard (Daubert v. Merrell Dow Pharmaceuticals, 1993) requiring that expert testimony be based on scientifically valid methods with...
- Frye Standard
- The US legal test for admissibility of scientific evidence, originating from Frye v. United States (1923), which required that a technique be...
- Hardy-Weinberg Equilibrium (HWE)
- The expected genotype frequency in a large, randomly mating population with no selection, mutation, or migration. Under HWE, the frequency of a...
Explained in these topics
- Admissibility and Ethics: Daubert, Frye, R v. Doheny and ELSIThe error of transposing the random-match probability (the probability that a random person has the profile, given they are innocent) to state that the defenda...
- Bayes Theorem in Evidence EvaluationThe error of treating the probability of the evidence given innocence as if it were the probability of innocence given the evidence. Formally, confusing P(E |...
- DNA Match Probability CalculationThe error of treating the RMP as the probability that the suspect is innocent. An RMP of one in a million means one person per million would match by chance; i...
- Error, Uncertainty and the Statistics of Forensic ScienceThe logical error of treating P(evidence | innocence) as if it equals P(innocence | evidence). A tiny random-match probability does not by itself imply a high...
- History of Statistical Evidence in CourtsThe error of treating P(evidence | innocent) as if it equals P(innocent | evidence). A small random-match probability does not itself establish a high probabil...
- The Likelihood Ratio: Definition and LogicThe logical error of treating the probability of the evidence given innocence as if it were the probability of innocence given the evidence. In symbols, confus...
- How Numbers Enter Forensic ConclusionsThe error of treating the probability of the evidence given innocence as if it were the probability of innocence given the evidence. Conflates P(evidence | inn...
- Probative Value and the Weight of EvidenceThe error of treating the probability of the evidence given innocence (match probability) as if it were the probability of innocence given the evidence. These...
- Allele Frequencies, Random Match Probability and the Likelihood RatioThe incorrect equation of P(evidence | innocent) with P(innocent | evidence). Treats the RMP as if it were the posterior probability of innocence, ignoring the...
- The Concept of Random Match ProbabilityThe error of treating the RMP (or its reciprocal) as the probability that the defendant is innocent, or as the probability that the defendant did not leave the...
- The Role of Statistics in Evidence EvaluationThe logical error of treating P(evidence | innocence) as equivalent to P(innocence | evidence). A very small match probability does not directly equal the prob...
- Serology Evidence in Court: Interpretation and TestimonyTreating the probability of the evidence given innocence (the match probability) as if it were the probability of innocence given the evidence, which conflates...
- The Defence FallacyThe mirror error to the defence fallacy: treating the random match probability as equivalent to the probability the suspect is innocent (i.e., equating P(evide...
- The Prosecutor's FallacyThe erroneous equation of P(evidence | innocence) with P(innocence | evidence). The first is a match frequency or rarity statement; the second is a posterior p...
- Writing Evaluative Statements in Forensic ReportsThe logical error of confusing P(evidence | innocence) with P(innocence | evidence). An expert who states that a one-in-a-million match probability means there...