Quantum cognition beyond Hilbert space II: Applications
This work addresses a specific limitation in quantum cognition models for cognitive psychology, representing an incremental advancement by extending prior theoretical work to practical applications.
The paper tackles the problem of modeling human cognition when Hilbert space quantum theory is insufficient, by applying a non-Hilbertian quantum-like model to reproduce probabilities in question order effects experiments, such as the 'Clinton/Gore' and 'Rose/Jackson' cases, and addressing response replicability and unpacking effects.
The research on human cognition has recently benefited from the use of the mathematical formalism of quantum theory in Hilbert space. However, cognitive situations exist which indicate that the Hilbert space structure, and the associated Born rule, would be insufficient to provide a satisfactory modeling of the collected data, so that one needs to go beyond Hilbert space. In Part I of this paper we follow this direction and present a general tension-reduction (GTR) model, in the ambit of an operational and realistic framework for human cognition. In this Part II we apply this non-Hilbertian quantum-like model to faithfully reproduce the probabilities of the 'Clinton/Gore' and 'Rose/Jackson' experiments on question order effects. We also explain why the GTR-model is needed if one wants to deal, in a fully consistent way, with response replicability and unpacking effects.