Representing Attitudes Towards Ambiguity in Hilbert Space: Foundations and Applications

Abstract

We provide here a general mathematical framework to model attitudes towards ambiguity which uses the formalism of quantum theory as a “purely mathematical formalism, detached from any physical interpretation”. We show that the quantum-theoretic framework enables modelling of the Ellsberg paradox, but it also successfully applies to more concrete human decision-making tests involving financial, managerial and medical decisions. In particular, we elaborate a mathematical representation of various empirical studies which reveal that attitudes of managers towards uncertainty shift from ambiguity seeking to ambiguity aversion, and viceversa, thus exhibiting hope effects and fear effects. The present framework provides a promising direction towards the development of a unified theory of decisions in the presence of uncertainty.

Quantum Core Affect. Process-Semantic Theory of Emotions

“…Practice-oriented research therefore inclines to use quantum theory as "purely mathematical formalism, detached from any physical interpretation" -a sort of theoretical black box, producing correct probabilities for particular behavioral cases in rather mysterious way, cf. Blutner and beim Graben (2016); Pothos and Busemeyer (2013); Sozzo (2021). As a result, working models are often found by blind search with a lot of inefficient effort.…”