base-rate fallacy

The established statistical error of judging how probable something is from the conspicuous cases while ignoring the base rate — the denominator, the full pool the conspicuous cases were drawn from. In this vault it is the formal name for a structure the notes kept reaching by hand under the informal label survivorship bias: a sample built only from the outcomes that got retold (vindicated theories, successful sciences, the observers who exist to ask) cannot license a claim about the rate, because membership in the sample already presupposes the property being measured. The concept is load-bearing across three otherwise unconnected strands, and the vault's interest is less the error itself than that the same error wears a different name in each room it appears in.

Base-rate fallacy vs. survivorship bias. They are the same structural mistake described from two directions. Survivorship bias names the sampling act — you only counted the survivors. Base-rate fallacy / base-rate neglect names the inferential consequence — you reasoned as if that sample fixed the denominator. Magnus & Callender (2004) make the identity explicit, calling their Bayesian version "the realist would thus avoid base rate neglect, but at the cost of sample selection bias" — the two errors are a pair you cannot escape by swapping one for the other. This hub keeps the formal name and treats survivorship bias as the vault's informal synonym, not a separate referent.

References

The scientific-realism denominator debate — the error worked out in Bayesian notation for the whole history of science:

• claim-magnus-callender-2004-base-rate-fallacy-is-the-denominator-problem-generalized — the no-miracles argument and the pessimistic induction both commit it; the pool of candidate theories cannot be enumerated, and restricting it to adopted theories only swaps base-rate neglect for sample selection bias. (Tier 1, capture-verified.)
• claim-lewis-2001-no-full-denominator-survey-of-past-theories-ever-attempted — the census of past theories, true and false alike, that would settle convergent realism has never been attempted. (Tier 2, read secondhand through Magnus & Callender; primary owed at question-read-lewis-2001-and-laudan-1981-realism-primaries.)
• claim-laudan-1981-list-challenged-as-unrepresentative-since-the-1980s — the most influential partial denominator (built from the failure side) was challenged for representativeness within a few years; that fight is still live. (Tier 2.)

Delayed vindication / survivorship (the vault's originating case) — where the vault first met the structure under its own informal name:

• claim-circuit-theory-vindication-lacks-denominator-survivorship-not-ruled-out — four cases of circuit theory preceding its anatomy cannot be distinguished from survivorship bias, because no survey counts all proposed circuit theories. Magnus & Callender identify this note's informal reasoning as "the formal, probabilistic twin" of base-rate fallacy. (Observation; the four positive instances are Tier 1–2, the absence held unverified.)

Reference-class / anthropic reasoning — the neighbouring diagnosis that the trouble lives in how a denominator is drawn:

• claim-reference-class-problem-dissolves-with-proportions-not-population-counts — Brewer, Lewis & Goodman (2026) argue the reference-class problem is an artifact of writing likelihoods in population counts rather than proportions; the dependence is a denominator-coordinate choice. (Tier 1 preprint, at the single-source cap; offered as demonstration, not theorem.)

• Related MOC: moc-argument-from-silence — all three strands sit beside it ("a search that returns only successes is not evidence that failures are rare").

• Sibling cognitive-bias / statistical-error hubs: entity-conjunction-fallacy · entity-ecological-fallacy · entity-reference-class-problem.