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A general tension-reduction (GTR) model was recently considered to derivequantum probabilities as (universal) averages over all possible forms ofnon-uniform fluctuations, and explain their considerable success in describingexperimental situations also outside of the domain of physics, for instance inthe ambit of quantum models of cognition and decision. Yet, this result alsohighlighted the possibility of observing violations of the predictions of theBorn rule, in those situations where the averaging would not be large enough,or would be altered because of the combination of multiple measurements. Inthis article we show that this is indeed the case in typical psychologicalmeasurements exhibiting question order effects, by showing that theirstatistics of outcomes are inherently non-Hilbertian, and require the largerframework of the GTR-model to receive an exact mathematical description. Wealso consider another unsolved problem of quantum cognition: responsereplicability. It is has been observed that when question order effects andresponse replicability occur together, the situation cannot be handled anymoreby quantum theory. However, we show that it can be easily and naturallydescribed in the GTR-model. Based on these findings, we motivate the adoptionin cognitive science of a hidden-measurements interpretation of the quantumformalism, and of its GTR-model generalization, as the natural interpretationalframework explaining the data of psychological measurements on conceptualentities.

Beyond-Quantum Modeling of Question Order Effects and Response Replicability in Psychological Measurements