# Representing Attitudes Towards Ambiguity in Hilbert Space: Foundations and Applications

## TL;DR

This paper introduces a quantum-theoretic framework to model human attitudes towards ambiguity, successfully explaining phenomena like the Ellsberg paradox and various decision-making behaviors across different fields.

## Contribution

It develops a novel mathematical formalism based on quantum theory to unify the modeling of ambiguity attitudes in decision-making.

## Key findings

- Quantum framework models the Ellsberg paradox effectively.
- Attitudes towards ambiguity can shift from seeking to avoiding.
- Framework applies to financial, managerial, and medical decision tests.

## 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 (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.