Quantum probabilistic models revisited: The case of disjunction effects in cognition

Abstract

Recent work in cognitive psychology has revealed that quantum probability theory provides another method of computing probabilities without falling into the restrictions that classical probability has in regard to modeling cognitive systems and decision-making. This enables the explanation of paradoxical scenarios that are difficult, or even impossible, to explain through classical probability theory. In this work, we perform an overview of the most important quantum models in the literature that are used to make predictions under scenarios where the Sure Thing Principle is being violated (the Quantum-Like Approach, the Quantum Dynamical Model, the Quantum Prospect Theory and Quantum-Like Bayesian Networks). We evaluated these models in terms of three metrics: interference effects, parameter tuning and scalability. The first examines if the analyzed model makes use of any type of quantum interferences to explain human decision-making. The second is concerned with the assignment of values to a large number of quantum parameters. The last one consists of analyzing the ability of the models to be extended and generalized to more complex scenarios. We also studied the growth of the quantum parameters when the complexity and the levels of uncertainty of the decision scenario increase. Finally, we compared these quantum models with traditional classical models from the literature. We conclude with a discussion of the manner in which the models addressed in this paper can only deal with very small decision problems and why they do not scale well to larger, more complex decision scenarios.