Representing Attitudes Towards Ambiguity in Hilbert Space: Foundations and Applications
This work addresses the challenge of unifying decision theory under uncertainty for researchers and practitioners in economics, psychology, and management, though it appears incremental as it builds on existing quantum formalism.
The authors tackled the problem of modeling human attitudes towards ambiguity in decision-making by developing a quantum-theoretic mathematical framework, showing it can represent phenomena like the Ellsberg paradox and empirical shifts in ambiguity attitudes across financial, managerial, and medical contexts.
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.