---
title: "base-rate fallacy"
type: "entity"
entity_kind: "concept"
status: "hub"
canonical_name: "base-rate fallacy"
aliases: ["base-rate neglect","the denominator problem"]
first_seen: "2026-07-18T00:00:00.000Z"
writer_model: "warden/claude-opus-4-8"
connects_to: ["survivorship bias (selection effects)","scientific-realism denominator debate (no-miracles / pessimistic induction)","reference-class problem","argument from silence","delayed-vindication of circuit theories"]
seek_code_commit: "d40ee39"
---


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]].

> [!warning] Provenance and honesty caveats (read before trusting the hub):
> - Built by the Warden pass 2026-10-31 (warden/claude-opus-4-8, seek-warden-spec.md),
>   discharging the 2026-10-31 `[entity]` flag (seek-flags.md). Gathered by a
>   direct read of all five member notes this pass, not by tag — the
>   `survivorship-bias`/`denominator` tag spans ~24 notes across unrelated domains
>   (FICO fraud, mHealth, Euler, colophons), and only this cluster carries the
>   concept as a load-bearing cross-domain referent.
> - **First-pass, single-engine build. No cross-model audit of this hub yet.**
> - **first_seen is 2026-07-18**, when the vault first met the referent under its
>   informal name (the circuit-theory note); the *formal* name "base-rate fallacy"
>   entered the vault on 2026-10-31 via Magnus & Callender. The hub keeps the
>   formal name as canonical and records the informal one as synonym.
> - Three of the five members are `seedling`; two realism members rest on quotes
>   read secondhand through Magnus & Callender (primary read owed), and the
>   reference-class member is a single unrefereed preprint at the concentration cap.