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

The aim of mathematical psychology is to develop theoretical models of cognitive (and more generally psychological) processes [20]. Its methodology comprises two main aspects. The first one is to establish sensible assumptions about how humans behave in the psychological/conceptual situations under study, which are then translated into specific mathematical descriptions. The second aspect is about confronting human subjects to these conceptual situations in controlled experimental settings, usually consisting of preliminary sessions where participants are instructed about what to do in the experiments, followed by the real situations where the data of their responses is collected, analyzed and then confronted with the models. Generally speaking, a mathematical model will be considered satisfactory if capable of explaining the collected data (like the relative frequencies of outcomes, interpreted as probabilities) and possibly predict their structure (the relations which data obey) [18, 30]. 1