Prosecutor's fallacy¶

The prosecutor's fallacy confuses the probability of observed evidence given innocence with the probability of innocence given that evidence, typically neglecting base rates and alternative hypotheses.

Version: v1 · 2026-09-28 · History
Domain-specific #: 11535
Domain group: Formal Sciences
Origin domain: Experimental Design & Statistics
Subdomains: Forensic Statistics, Bayesian Reasoning → Experimental Design & Statistics

Core Idea¶

Prosecutor's fallacy is treated here as the recurring cross_domain_models_structures_representations identity summarized by this source-grounded definition: The prosecutor's fallacy confuses the probability of observed evidence given innocence with the probability of innocence given that evidence, typically neglecting base rates and alternative hypotheses.

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. The prosecutor's fallacy confuses the probability of observed evidence given innocence with the probability of innocence given that evidence, typically neglecting base rates and alternative hypotheses.

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. This paradox describes situations where there are more false positive test results than true positives (this means the classifier has a low precision).

For Prosecutor's fallacy, the abstraction is narrower than the article's general subject matter: a positive case must preserve 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. Retaining only the name, a familiar example, or a downstream effect is insufficient. The specialist roles and tests remain anchored in cross_domain_models_structures_representations, which is why this identity is domain-specific rather than prime.

Structural Signature¶

Sig role-phrases:

Defining carrier — The probability of a positive test result is determined not only by the accuracy of the test but also by the characteristics of the sampled population.
Constitutive relation — As can be seen from the formula, one needs p(D) for Bayes' theorem, which can be computed from the preceding values using the law of total probability.
Operating condition — Further, in the context of detecting terrorism false negatives are highly undesirable and thus must be minimised as much as possible; however, this requires increasing sensitivity at the cost of specificity, increasing false positives.
Recognition evidence — It is also questionable whether the use of such models by law enforcement would meet the requisite burden of proof given that over 99% of results would be false positives.
Admissible variation — Such systems exhibit sharp phase transitions at critical population sizes, beyond which failure becomes certain and cannot be prevented through threshold adjustment.
Characteristic consequence — Forensic analysis determines that the perpetrator has a certain blood type shared by 10% of the population.
Failure boundary — Crime scene blood matched Simpson's with characteristics shared by 1 in 400 people.

What It Is Not¶

Not the whole field of cross_domain_models_structures_representations. The node requires the specific identity stated by The prosecutor's fallacy confuses the probability of observed evidence given innocence with the probability of innocence given that evidence, typically neglecting base rates and alternative hypotheses.
Not an over-broad reading. The validity of this result does, however, hinge on the validity of the initial assumption that the police officer stopped the driver truly at random, and not because of bad driving.
Not an over-broad reading. However, there are different ways of presenting the relevant information.
Not an over-broad reading. The probability of a positive test result is determined not only by the accuracy of the test but also by the characteristics of the sampled population.
Not automatically Base Rate Fallacy. Retrieval proximity does not establish equivalence; the two identities must be compared by carrier, operation, and failure boundary.

Scope of Application¶

Prosecutor's fallacy applies literally inside cross_domain_models_structures_representations wherever the source-defined carrier and relation can be established. Its documented habitats include:

Sally Clark case. Sally Clark, a British woman, was accused in 1998 of having killed her first child at 11 weeks of age and then her second child at 8 weeks of age.
Findings in psychology. This finding has been used to argue that interviews are an unnecessary part of the college admissions process because interviewers are unable to pick successful candidates better than basic statistics.
False positive paradox. An example of the base rate fallacy is the false positive paradox (also known as accuracy paradox).
False positive paradox. This paradox describes situations where there are more false positive test results than true positives (this means the classifier has a low precision).
False positive paradox. The probability of a positive test result is determined not only by the accuracy of the test but also by the characteristics of the sampled population.
False positive paradox. It is especially counter-intuitive when interpreting a positive result in a test on a low-prevalence population after having dealt with positive results drawn from a high-prevalence population.

Outside cross_domain_models_structures_representations, the name should be retained only when these same operational conditions survive; otherwise the comparison belongs to the broader parent Pattern or should be marked as analogy.

Clarity¶

A clear use of Prosecutor's fallacy names the carrier, the operative relation, and the conditions under which the source treats the identity as present. The minimal definition is The prosecutor's fallacy confuses the probability of observed evidence given innocence with the probability of innocence given that evidence, typically neglecting base rates and alternative hypotheses. The strongest recognition evidence in the frozen account is: It is also questionable whether the use of such models by law enforcement would meet the requisite burden of proof given that over 99% of results would be false positives. A report should distinguish that evidence from a proxy, consequence, or common implementation. It should also state the qualification The validity of this result does, however, hinge on the validity of the initial assumption that the police officer stopped the driver truly at random, and not because of bad driving. so that a reader can reproduce the classification rather than infer it from topical resemblance.

Manages Complexity¶

Prosecutor's fallacy compresses multiple cross_domain_models_structures_representations details into a stable diagnostic relation. The source shows both the central mechanism—as can be seen from the formula, one needs p(D) for Bayes' theorem, which can be computed from the preceding values using the law of total probability.—and the practical consequence—forensic analysis determines that the perpetrator has a certain blood type shared by 10% of the population. This compression makes cases comparable while leaving parameters, conventions, exceptions, and evidential quality explicit. It is lossy by design: local history and implementation details may be omitted only when they do not alter the defining relation.

Abstract Reasoning¶

Type the carrier. Identify the cross_domain_models_structures_representations entities to which the claim applies.
State the relation. Use the source-grounded identity: The prosecutor's fallacy confuses the probability of observed evidence given innocence with the probability of innocence given that evidence, typically neglecting base rates and alternative hypotheses.
Check operation and conditions. Further, in the context of detecting terrorism false negatives are highly undesirable and thus must be minimised as much as possible; however, this requires increasing sensitivity at the cost of specificity, increasing false positives.
Demand recognition evidence. It is also questionable whether the use of such models by law enforcement would meet the requisite burden of proof given that over 99% of results would be false positives.
Test variation. Change an implementation or setting while preserving such systems exhibit sharp phase transitions at critical population sizes, beyond which failure becomes certain and cannot be prevented through threshold adjustment.
Run the collapse test. Remove the defining operation; if the label still seems equally apt, only a topic or correlate was retained.
Reduce cautiously. When the specialist conditions cannot be carried, route the residual comparison to Pattern.

Knowledge Transfer¶

Within the home domain. Knowledge about Prosecutor's fallacy transfers literally when a new case preserves the same carrier type, relation, and recognition test. Sally Clark, a British woman, was accused in 1998 of having killed her first child at 11 weeks of age and then her second child at 8 weeks of age. This finding has been used to argue that interviews are an unnecessary part of the college admissions process because interviewers are unable to pick successful candidates better than basic statistics.

Beyond the home domain. No canonical parent is asserted for Prosecutor's fallacy. An outside case receives the specialist name only when the same typed roles and rejection conditions can be filled literally; otherwise the comparison remains an analogy pending later graph densification.

Examples¶

Canonical¶

Other possibilities (including one homicide and one case of SIDS). This case is canonical because it supplies a concrete carrier and lets the defining relation be checked rather than merely named.

Mapped back: carrier → the entities in the documented case; operation → 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; recognition evidence → It is also questionable whether the use of such models by law enforcement would meet the requisite burden of proof given that over 99% of results would be false positives

Applied / In Practice¶

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. The applied case shows how the identity is used under a second setting or qualification while keeping the same operative relation.

Mapped back: changed setting → the applied context; invariant → 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; boundary → the case exits the class when the validity of this result does, however, hinge on the validity of the initial assumption that the police officer stopped the driver truly at random, and not because of bad driving

Structural Tensions¶

T1 — Stable identity versus admissible variation. The validity of this result does, however, hinge on the validity of the initial assumption that the police officer stopped the driver truly at random, and not because of bad driving. The tension matters because emphasizing only one side either dissolves the identity or overstates what the evidence and domain conventions warrant.

Diagnostic: Which changes preserve the defining relation, and which replace it?

T2 — Recognition versus proxy. However, there are different ways of presenting the relevant information. The tension matters because emphasizing only one side either dissolves the identity or overstates what the evidence and domain conventions warrant.

Diagnostic: Does the cited evidence establish the identity or only a correlated sign?

T3 — Definition versus implementation. The probability of a positive test result is determined not only by the accuracy of the test but also by the characteristics of the sampled population. The tension matters because emphasizing only one side either dissolves the identity or overstates what the evidence and domain conventions warrant.

Diagnostic: Is the observed implementation constitutive, optional, or merely common?

T4 — Scope versus overextension. 999 drivers are not drunk, and among those drivers there are 5% false positive test results, so there are 49.95 false positive test results. The tension matters because emphasizing only one side either dissolves the identity or overstates what the evidence and domain conventions warrant.

Diagnostic: Can every claimed application fill the same typed roles without metaphor?

T5 — Transfer versus domain accent. The probability of a positive test result is determined not only by the accuracy of the test but also by the characteristics of the sampled population. The tension matters because emphasizing only one side either dissolves the identity or overstates what the evidence and domain conventions warrant.

Diagnostic: Does the receiving case instantiate Prosecutor's fallacy literally, co-instantiate Pattern, or only resemble it?

T6 — Autonomy versus reduction. As can be seen from the formula, one needs p(D) for Bayes' theorem, which can be computed from the preceding values using the law of total probability. The tension matters because emphasizing only one side either dissolves the identity or overstates what the evidence and domain conventions warrant.

Diagnostic: What does Prosecutor's fallacy distinguish that the broader parent Pattern leaves together?

Structural–Framed Character¶

Prosecutor's fallacy is mixed or framed-leaning. Its structural side is the repeatable organization summarized by The prosecutor's fallacy confuses the probability of observed evidence given innocence with the probability of innocence given that evidence, typically neglecting base rates and alternative hypotheses. Its framed side is the cross_domain_models_structures_representations vocabulary that fixes the carrier, evidence, exceptions, and admissible transformations.

Evaluative weight: the identity can be stated descriptively even when applications carry practical stakes. Human-practice dependence: the source-grounded carrier determines whether the relation exists independently or is constituted by a practice. Institutional origin: disciplinary conventions stabilize the name and test. Vocabulary portability: Further, in the context of detecting terrorism false negatives are highly undesirable and thus must be minimised as much as possible; however, this requires increasing sensitivity at the cost of specificity, increasing false positives. Import versus recognition: literal transfer requires the same mechanism; shape alone is analogy.

Its portable skeleton is Pattern. Its character: a recurring specialist identity whose thin organization can be abstracted, while its operational meaning remains domain-bound.

Structural Core vs. Domain Accent¶

What is skeletal. The prosecutor's fallacy confuses the probability of observed evidence given innocence with the probability of innocence given that evidence, typically neglecting base rates and alternative hypotheses. The stable skeleton is the typed relation expressed in that definition and the entry's recognition and collapse tests. The source identifies these operative conditions: The probability of a positive test result is determined not only by the accuracy of the test but also by the characteristics of the sampled population. As can be seen from the formula, one needs p(D) for Bayes' theorem, which can be computed from the preceding values using the law of total probability. It further constrains recognition and variation through: Further, in the context of detecting terrorism false negatives are highly undesirable and thus must be minimised as much as possible; however, this requires increasing sensitivity at the cost of specificity, increasing false positives. It is also questionable whether the use of such models by law enforcement would meet the requisite burden of proof given that over 99% of results would be false positives.

What is domain-bound. cross domain models structures representations supplies the operative entities, technical vocabulary, warrants, and exceptions that make Prosecutor's fallacy literal. Its documented scope includes the condition that Sally Clark, a British woman, was accused in 1998 of having killed her first child at 11 weeks of age and then her second child at 8 weeks of age. Another bounded application condition is that This finding has been used to argue that interviews are an unnecessary part of the college admissions process because interviewers are unable to pick successful candidates better than basic statistics. These are not decorative examples; they determine which carrier and evidence can fill the abstraction's roles.

Why no parent is asserted. Removing those specialist details does not currently yield one live catalog node that is a necessary genus for every instance. The entry is therefore approved as unparented rather than attached by topical resemblance. Its collapse evidence remains specific—Such systems exhibit sharp phase transitions at critical population sizes, beyond which failure becomes certain and cannot be prevented through threshold adjustment.—and future graph densification may discover a defensible relation only if it preserves that boundary.

This entry is a kind of Informal Fallacy.

Approved unparented node. No current live node supplies a defensible necessary genus or structural prerequisite for Prosecutor's fallacy. The reviewed identity is: The prosecutor's fallacy confuses the probability of observed evidence given innocence with the probability of innocence given that evidence, typically neglecting base rates and alternative hypotheses. The accelerated suggestion was declined because topical or lexical similarity does not establish hierarchy; the node is admitted without a parent pending later graph densification.
Related reasoning operations. Evidence, representation, comparison, classification, transformation, or evaluation may participate in particular cases, but participation does not make any one of them a necessary parent of every instance.

Relationships to Other Abstractions¶

Current abstraction Prosecutor's fallacy Domain-specific

Parents (1) — more general patterns this builds on

Prosecutor's fallacy is a kind of Informal Fallacy Prime

The prosecutor's fallacy is an informal fallacy that reverses a conditional probability and neglects base rates.

Hierarchy path (1) — routes to 1 parentless root

Prosecutor's fallacy → Informal Fallacy

Neighborhood in Abstraction Space¶

Prosecutor's fallacy sits in a moderately populated region (44^th percentile for distinctiveness): it has near-neighbors but no dense thicket of look-alikes.

Family — Unclustered & Miscellaneous (2551 abstractions)

Nearest neighbors

Score (statistics) — 0.88
S-procedure — 0.87
Youden's J Statistic — 0.87
Randomized response — 0.87
Single Vegetative Obstruction Model — 0.87

Computed from structural-signature embeddings · 2026-10-08

Not to Be Confused With¶

Pattern. The parent omits the specialist differentia. Tell: Can the case establish 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?
Base Rate Fallacy. The systematic human tendency to underweight or ignore the prior probability of a hypothesis when vivid, specific evidence is available, so a posterior estimate collapses toward the likelihood instead of tracking Bayes' rule. Tell: Which entry's carrier, operation, and failure condition are satisfied?
Neglect of Probability. A judgment-and-decision bias in which responses change little or not at all when an outcome’s probability changes, especially when vivid or affect-rich consequences dominate attention. Tell: Which entry's carrier, operation, and failure condition are satisfied?
Base Rate. The prevalence or prior probability of a class before case-specific evidence is incorporated. Tell: Which entry's carrier, operation, and failure condition are satisfied?
A measurement, proxy, or consequence. Those may provide evidence without being the identity. Tell: Would Prosecutor's fallacy remain present if the detector or downstream effect changed?
A metaphorical analogue. A similar shape outside cross_domain_models_structures_representations lacks the specialist mechanism. Tell: Do the native roles transfer literally, or only the parent Pattern?

References¶

Frozen Wikipedia discovery revision: https://en.wikipedia.org/wiki/Base_rate_fallacy (revision 1371030637).
Preserved source candidate: https://doh.wa.gov/sites/default/files/2022-02/421-010-CasesInNotFullyVaccinated.pdf
Preserved source candidate: https://web.archive.org/web/20230126022307/https://doh.wa.gov/sites/default/files/2022-02/421-010-CasesInNotFullyVaccinated.pdf
Preserved source candidate: http://www.fallacyfiles.org/baserate.html
Preserved source candidate: http://uctv.canterbury.ac.nz/viewfile.php/4/sharing/55/74/74/NZEPVersionofImpreciseProbabilitiespaperVersi.pdf
Preserved source candidate: https://ntrs.nasa.gov/citations/19980045313
Preserved source candidate: http://findarticles.com/p/articles/mi_qa4089/is_200305/ai_n9252796/pg_2/
Preserved source candidate: https://web.archive.org/web/20080927023425/http://findarticles.com/p/articles/mi_qa4089/is_200305/ai_n9252796/pg_2
Preserved source candidate: https://www.wired.com/2006/03/why-data-mining-wont-stop-terror-2/

The frozen Wikipedia revision is discovery provenance. The retained source set was reviewed for identity, formal or operational relation, and scope. The encyclopedia's structural synthesis is bounded to those claims; a thin authority surface is recorded as a nonblocking source-strengthening repair rather than concealed.