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TRAP #571 ·VOL V The Toolkit · Logical Fallacies & Structured Reasoning

Bayes’ Theorem

Discovered by Thomas Bayes, 1763

How much should this evidence change your mind? Bayes' theorem gives you the number.
Category: TheoremEvidence: ReplicatedUniversality: HighTier 1Type: Mechanismⓘ what these mean

This is a Lexicon entry: the mechanism, when it shows up, and the countermeasure. The full correction, with real-world cases and the audit prompt, hasn't been written yet.

Definition

The foundational formula of probabilistic reasoning: the probability of a hypothesis given evidence equals the prior probability of the hypothesis times the likelihood of the evidence given the hypothesis, divided by the overall probability of the evidence. In plain language: new evidence should change your belief but by how much depends on your prior probability and the strength of the evidence. A weak prior combined with strong evidence produces a large update; a strong prior combined with weak evidence produces a small one.

When it shows up

When new evidence arrives; when deciding how much to update your beliefs. In any expert field: when understanding your own calibration helps you communicate uncertainty to stakeholders. In research: when hypothesis pre-registration forces you to articulate your prior before seeing data.

Failure mode

Either under-updating (not moving enough when evidence is strong) or over-updating (moving too much when evidence is weak). Both produce poor calibration.

Countermeasure

Make your prior explicit before encountering evidence. Weight new evidence by its likelihood ratio. Ask: "Given what I already knew, how much should this move me?"

Related traps

Also connected in the map4 more, locked

Credit & first seen

DiscoveredBayes, T. (1763).An Essay towards solving a Problem in the Doctrine of Chances.Philosophical Transactions 53, 370-418 source ↗

Also revealed

Want the full correction for Bayes’ Theorem?

This entry has the mechanism and countermeasure. The full write-up - real cases, sources, the audit prompt - comes later.

Entry #571 of 631 in The Lexicon · see the full Lexicon