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Classic-Probability Accounts of QQ-Equality

Henrik Singmann, David Kellen

Published Oct 15, 2015• 0 citations
OpenAlex

Abstract

R script for results reported in: Classic-Probability Accounts of Mirrored (Quantum-Like) Order Effects in Human Judgments

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Auditing Question-Order Effects in Large Language Models with the QQ Equality: Mechanism Characterization and a Saturation Caveat

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Question-order effects in human survey data have been reported to approximately satisfy the QQ (quantum question) equality, a parameter-free prediction of the standard projective quantum question-order model. We develop this equality into an audit framework for sequential binary judgments of autoregressive large language models (LLMs). Theoretically, we characterize mechanism families that satisfy QQ robustly, show that classical repetition can reproduce the equality exactly, and combine QQ with the rank-2 Contextuality-by-Default criterion through $|q_{QQ}| \le \mathrm{OSS}$. This separates order sensitivity, QQ imbalance, and residual contextuality rather than treating them as interchangeable signatures. Methodologically, we introduce a committed multi-turn forced-branch protocol that reconstructs order-conditioned joint distributions from next-token log-probabilities under counterbalanced label mappings and pre-specified health gates. A first-signal pilot on an open-weight instruction-tuned model reveals the central measurement problem. Although all pre-specified health gates passed, the binary-conditioned distributions were near-deterministic for 17 of 18 item pairs under the direct-evaluation framing and 7 of 8 under the persona framing. Label assignment materially changed several mapping-specific QQ verdicts, and no item was certified as residually contextual. Thus, under the tested conditions, the observed QQ outcomes did not uniquely identify a response mechanism in the presence of a saturated and label-sensitive measurement interface. The main implication is methodological: next-token probabilities should not be interpreted as survey-response distributions without first establishing adequate dispersion. We therefore argue that saturation screening and label counterbalancing should precede structural interpretation in distribution-level audits of LLM judgments.

cs.CLCross-listedarXiv:2607.17219•Jul 21, 2026•0 citations
The hypothesis that human reasoning obeys the laws of quantum rather than classical probability has been used in recent years to explain a variety of seemingly "irrational" judgment and decision-making findings. This article provides independent evidence for this hypothesis based on an a priori prediction, called the quantum question (QQ) equality, concerning the effect of asking attitude questions successively in different orders. We empirically evaluated the predicted QQ equality using 70 national representative surveys and two laboratory experiments that manipulated question orders. Each national study contained 651-3,006 participants. The results provided strong support for the predicted QQ equality. These findings suggest that quantum probability theory, initially invented to explain noncommutativity of measurements in physics, provides a simple account for a surprising regularity regarding measurement order effects in social and behavioral science.
Question-order effects in human survey data have been reported to approximately satisfy the QQ (quantum question) equality, a parameter-free prediction of the standard projective quantum question-order model. We develop this equality into an audit framework for sequential binary judgments of autoregressive large language models (LLMs). Theoretically, we characterize mechanism families that satisfy QQ robustly, show that classical repetition can reproduce the equality exactly, and combine QQ with the rank-2 Contextuality-by-Default criterion through ∣qQQ∣≤OSS|q_{QQ}| \le \mathrm{OSS}∣qQQ​∣≤OSS. This separates order sensitivity, QQ imbalance, and residual contextuality rather than treating them as interchangeable signatures. Methodologically, we introduce a committed multi-turn forced-branch protocol that reconstructs order-conditioned joint distributions from next-token log-probabilities under counterbalanced label mappings and pre-specified health gates. A first-signal pilot on an open-weight instruction-tuned model reveals the central measurement problem. Although all pre-specified health gates passed, the binary-conditioned distributions were near-deterministic for 17 of 18 item pairs under the direct-evaluation framing and 7 of 8 under the persona framing. Label assignment materially changed several mapping-specific QQ verdicts, and no item was certified as residually contextual. Thus, under the tested conditions, the observed QQ outcomes did not uniquely identify a response mechanism in the presence of a saturated and label-sensitive measurement interface. The main implication is methodological: next-token probabilities should not be interpreted as survey-response distributions without first establishing adequate dispersion. We therefore argue that saturation screening and label counterbalancing should precede structural interpretation in distribution-level audits of LLM judgments.