Belief Functions Meet Quantum Logic: A Mathematical Framework for Coherence-Based Decision Theories

Abstract

Decision theories based on cognitive consistency understand decision-making as the process of constructing a coherent representation of reality, capable of providing a reliable causal map that connects actions to consequences. Rejecting assumptions concerning preferences and utility functions, they single out the quest for a coherent representation of reality as the one single factor driving human behaviour. Decision theories based on constructing coherence are justified by free-energy minimisation and supported by computational network models, but they lack a proper mathematical framework. In this article I combine Evidence Theory with Quantum Logic to offer a scaffolding structure to construct coherent representations. I illustrate this framework with stylised examples drawn from medical diagnoses and the BioTech industry.