Quantum-like cognition and decision making in the light of quantum measurement theory
This work addresses the challenge of accurately modeling cognitive phenomena using quantum theory, which is incremental in refining quantum-like approaches for psychology and decision science.
The paper tackles the problem of applying quantum theory to cognition and decision making by identifying a specific class of quantum measurements (sharp repeatable non-projective measurements) that match cognitive effects like question order and response replicability, which cannot be described by standard projective measurements. It shows that quantum-like modeling explores different parts of quantum measurement theory than physics, highlighting noncommutativity of state update maps as a key factor.
We characterize the class of quantum measurements that matches the applications of quantum theory to cognition (and decision making) - quantum-like modeling. 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, cannot be described by projective measurements. We motivate the use of the special class of quantum measurements, namely {\it sharp repeatable non-projective measurements} - ${\cal SR\bar{P}}. $ This class is practically unused in quantum physics. Thus, physics and cognition explore different parts of quantum measurement theory. Quantum-like modeling isn't automatic borrowing of the quantum formalism. Exploring the class ${\cal SR\bar{P}}$ highlights the role of {\it noncommutativity of the state update maps generated by measurement back action.} Thus, ``non-classicality'' in quantum physics as well as quantum-like modeling for cognition is based on two different types of noncommutativity, of operators (observables) and instruments (state update maps): {\it observable-noncommutativity} vs. {\it state update-noncommutativity}. We speculate that distinguishing quantum-like properties of the cognitive effects are the expressions of the latter, or possibly both.