# Quantum Models for Psychological Measurements: An Unsolved Problem

arXiv: https://arxiv.org/abs/1403.3654 · HTML: https://mlsanity.com/paper/1403.3654/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 12 Mar 2014.

## Built on by (most cited first, 5 of 5)

- [Coupling quantum-like cognition with the neuronal networks within generalized probability theory](https://mlsanity.com/paper/2411.00036/) (2024)
- [Quantum-like cognition and decision making in the light of quantum measurement theory](https://mlsanity.com/paper/2503.05859/) (2025)
- [Order Effects in Bayesian Updates](https://mlsanity.com/paper/2105.07354/) (2021)
- [More Causes Less Effect: Destructive Interference in Decision Making](https://mlsanity.com/paper/2106.13320/) (2021)
- [Yes, Prime Minister, question order does matter -- and it's certainly not classical! But is it quantum?](https://mlsanity.com/paper/2409.08930/) (2024)

## Abstract (arXiv)

There has been a strong recent interest in applying quantum mechanics (QM) outside physics, including in cognitive science. We analyze the applicability of QM to two basic properties in opinion polling. The first property (response replicability) is that, for a large class of questions, a response to a given question is expected to be repeated if the question is posed again, irrespective of whether another question is asked and answered in between. The second property (question order effect) is that the response probabilities frequently depend on the order in which the questions are asked. Whenever these two properties occur together, it poses a problem for QM. The conventional QM with Hermitian operators can handle response replicability, but only in the way incompatible with the question order effect. In the generalization of QM known as theory of positive-operator-valued measures (POVMs), in order to account for response replicability, the POVMs involved must be conventional operators. Although these problems are not unique to QM and also challenge conventional cognitive theories, they stand out as important unresolved problems for the application of QM to cognition . Either some new principles are needed to determine the bounds of applicability of QM to cognition, or quantum formalisms more general than POVMs are needed.