Quantum cognition goes beyond-quantum: modeling the collective participant in psychological measurements

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 beyond-quantum - non-Bornian - probabilistic models, when sequential measurements at the individual level are considered, and this though a pure quantum description remains valid for single measurement situations.