---
title: "Is the conjunction-fallacy failure of quantum-like models a fatal flaw or a scope limit?"
type: "question"
status: "open"
date_raised: "2026-07-09T00:00:00.000Z"
tags: ["quantum-cognition","conjunction-fallacy","scope-limit"]
---


## The question

Boyer-Kassem, Duchêne & Guerci (2016) found quantum-like models fail to predict
the conjunction fallacy under a question-order design
([[claim-quantum-like-models-fail-conjunction-fallacy]]), while the same family
lawfully captures survey order effects
([[claim-question-order-effects-follow-quantum-qq-equality]]). Is this a
**fatal** inconsistency for the program, or a **scope limit** — order-effect
judgments and conjunction judgments simply requiring different quantum operators
(different Hilbert-space structure), rather than one model owing both?

## Why it matters

It decides how much weight the whole quantum-cognition bridge can bear. If the
failure is fatal, the order-effect successes need a non-quantum explanation; if
it's a scope limit, the honest framing is "quantum probability explains
measurement order-dependence, full stop — not all judgment anomalies."

## What I'd need to answer it

- Read Boyer-Kassem et al. (arXiv:1606.03430 / *Theory and Decision* 81:479–510)
  in full, including how they operationalize the three test configurations.
- Find the quantum-cognition camp's reply (Busemeyer/Wang response literature,
  if any) — is there a published rebuttal arguing the operators were
  mis-specified?

## Candidate next moves

- Track down whether Busemeyer & Bruza's framework claims conjunction-fallacy
  coverage explicitly, or only order effects.

## Progress log

- 2026-07-21: Read Boyer-Kassem et al. in full, including the three nested
  hypotheses and the conclusion section
  ([[claim-boyer-kassem-refutation-rejects-non-degenerate-and-degenerate-models]],
  [[claim-conjunction-fallacy-order-effect-account-refuted-generally]],
  [[claim-boyer-kassem-names-scope-retreat-and-povm-fix-as-untested-escape-routes]]).
  Verdict: **partially answered, leaning toward "more than a narrow scope
  limit," short of "fatal to quantum cognition as a whole."** The paper
  rejects the general (degenerate-or-non-degenerate) hypothesis shared by the
  field's own leading authors, and separately argues its order-effect-without-
  conjunction-fallacy tasks rule out *any* order-effect-based account, quantum
  or classical — pushing past a merely quantum-specific technicality. But the
  authors themselves decline to call the whole program dead: a
  scenario-restricted retreat and an untested POVM-based repair are both
  named as live options, not closed doors. A targeted search for a published
  rebuttal or rescue came up empty — the nearest candidate (Lebedev &
  Khrennikov) targets a different question entirely
  ([[claim-no-rebuttal-found-lebedev-khrennikov-targets-different-question]]).
  Left open: whether either named escape route has since been made to work.
  Not closing — the paper's own hedge is the reason this stays a live
  question rather than a settled one.