Quantum-like cognition and decision-making in the light of quantum measurement theory
Bibliographic record
Abstract
We characterize the class of quantum measurements that matches the applications of quantum theory to cognition (and decision-making)—quantum-like modelling. Projective measurements describe the canonical measurements of the basic observables of quantum physics. However, the combinations of the basic cognitive effects, such as the question order and response replicability effects (RREs), cannot be described by projective measurements. We motivate the use of the special class of quantum measurements, namely, sharp repeatable non-projective measurements — <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mstyle> <mml:mrow> <mml:mstyle displaystyle="false"> <mml:mrow> <mml:mi class="mathcal" mathvariant="script">S</mml:mi> <mml:mi class="mathcal" mathvariant="script">R</mml:mi> <mml:mrow> <mml:mover> <mml:mi class="mathcal" mathvariant="script">P</mml:mi> <mml:mo class="mathcal" mathvariant="script" stretchy="false">¯</mml:mo> </mml:mover> </mml:mrow> </mml:mrow> <mml:mo>.</mml:mo> </mml:mstyle> </mml:mrow> </mml:mstyle> </mml:math> This class is practically unused in quantum physics. Thus, physics and cognition explore different parts of quantum measurement theory. Quantum-like modelling is not the automatic borrowing of the quantum formalism. Exploring the class <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mstyle> <mml:mrow> <mml:mstyle displaystyle="false"> <mml:mrow> <mml:mi class="mathcal" mathvariant="script">S</mml:mi> <mml:mi class="mathcal" mathvariant="script">R</mml:mi> <mml:mrow> <mml:mover> <mml:mi class="mathcal" mathvariant="script">P</mml:mi> <mml:mo class="mathcal" mathvariant="script" stretchy="false">¯</mml:mo> </mml:mover> </mml:mrow> </mml:mrow> </mml:mstyle> </mml:mrow> </mml:mstyle> </mml:math> highlights the role of non-commutativity of the state-update maps generated by measurement back action . Thus, ‘non-classicality’ in quantum physics as well as quantum-like modelling for cognition is based on two different types of non-commutativity, of operators (observables) and instruments (state-update maps): observable non-commutativity versus state-update-non-commutativity . We speculate that distinguishing quantum-like properties of the cognitive effects is the expression of the latter, or possibly both. This article is part of the theme issue ‘Quantum theory and topology in models of decision making (Part 1)’.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".