Representing Attitudes Towards Ambiguity in Hilbert Space: Foundations and Applications

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 (DM) 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.