Quantum cognition beyond Hilbert space II: Applications

TL;DR

This paper extends quantum cognition models beyond traditional Hilbert space to better explain complex cognitive phenomena, demonstrating the GTR model's effectiveness in replicating experimental data and addressing response effects.

Contribution

It introduces the GTR model as a non-Hilbertian quantum-like framework for human cognition, improving modeling of question order and response effects.

Findings

Successfully reproduces probabilities in question order experiments

Explains response replicability and unpacking effects more consistently

Demonstrates advantages over traditional Hilbert space models

Abstract

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.