Introducing Quantum-Like Influence Diagrams for Violations of the Sure Thing Principle

TL;DR

This paper extends quantum-like Bayesian networks into influence diagrams to model decision-making, leveraging quantum interference effects to better explain violations of classical decision principles like the Sure Thing Principle.

Contribution

It introduces quantum-like influence diagrams that incorporate quantum interference into utility-based decision models, enhancing the understanding of decision violations.

Findings

Quantum interference influences decision probabilities.

The model explains violations of the Sure Thing Principle.

It improves decision-making predictions in game theory.

Abstract

It is the focus of this work to extend and study the previously proposed quantum-like Bayesian networks to deal with decision-making scenarios by incorporating the notion of maximum expected utility in influence diagrams. The general idea is to take advantage of the quantum interference terms produced in the quantum-like Bayesian Network to influence the probabilities used to compute the expected utility of some action. This way, we are not proposing a new type of expected utility hypothesis. On the contrary, we are keeping it under its classical definition. We are only incorporating it as an extension of a probabilistic graphical model in a compact graphical representation called an influence diagram in which the utility function depends on the probabilistic influences of the quantum-like Bayesian network. Our findings suggest that the proposed quantum-like influence digram can indeed take advantage of the quantum interference effects of quantum-like Bayesian Networks to maximise the utility of a cooperative behaviour in detriment of a fully rational defect behaviour under the prisoner's dilemma game.