In psychological measurements, two levels should be distinguished: the individual level, relative to the different participants in a given cognitive situation, and the collective level, relative to the overall statistics of their outcomes, which we propose to associate with a notion of collective participant. When the distinction between these two levels is properly formalized, it reveals why the modeling of the collective participant generally requires not only non-classical (non-Kolmogorovian) probabilistic models, but also non-quantum (non-Bornian) probabilistic models, when sequential measurements at the individual level are considered, and this though a classical or pure quantum description might remain valid for single measurement situations.

Aerts, D., Sassoli de Bianchi, M., Sozzo, S. & Veloz, T. (2019). Quantum cognition goes beyond-quantum: modeling the collective participant in psychological measurements. In: Probing the Meaning of Quantum Mechanics. Information, Contextuality, Relationalism and Entanglement. D. Aerts, M.L. Dalla Chiara, C. de Ronde & D. Krause (eds.) World Scientific, pp. 355-382. Doi: 10.1142/9789813276895_0017.