Beyond-quantum modeling of question order effects and response replicability in psychological measurements

A general tension-reduction (GTR) model was recently considered (Aerts and Sassoli de Bianchi 2015a, 2015b) to derive quantum probabilities as (universal) averages over all possible forms of non-uniform fluctuations and explain their considerable success in describing experimental situations also outside of the domain of physics, for instance in quantum models of cognition and decision. This result also highlighted the possibility of observing violations of the predictions of the Born rule in those situations where the averaging would not be large enough, or would be altered because of the combination of multiple measurements. We show that this is indeed the case in typical psychological measurements exhibiting question order effects, as the data require the larger (non-Hilbertian) framework of the GTR-model to receive an exact mathematical description. We also consider an unsolved problem of quantum cognition: response replicability. It has been noted that if question order effects and response replicability would occur together, the situation could not be handled anymore by quantum theory. Yet, we show that it can be easily and naturally described in the GTR-model. Based on these findings, we motivate the adoption in cognitive science of a hidden-measurements interpretation of the quantum formalism, and of its GTR-model generalization, as a natural interpretational framework explaining the data of psychological measurements on conceptual entities.