  Expected utility theory (EUT) is widely used in economic theory. However, its
subjective probability formulation, first elaborated by Savage, is linked to
Ellsberg-like paradoxes and ambiguity aversion. This has led various scholars
to work out non-Bayesian extensions of EUT which cope with its paradoxes and
incorporate attitudes toward ambiguity. A variant of the Ellsberg paradox,
recently proposed by Mark Machina and confirmed experimentally, challenges
existing non-Bayesian models of decision-making under uncertainty. Relying on a
decade of research which has successfully applied the formalism of quantum
theory to model cognitive entities and fallacies of human reasoning, we put
forward a non-Bayesian extension of EUT in which subjective probabilities are
represented by quantum probabilities, while the preference relation between
acts depends on the state of the situation that is the object of the decision.
We show that the benefits of using the quantum theoretical framework enables
the modeling of the Ellsberg and Machina paradoxes, as the representation of
ambiguity and behavioral attitudes toward it. The theoretical framework
presented here is a first step toward the development of a `state-dependent
non-Bayesian extension of EUT' and it has potential applications in economic
modeling.
