4. Quantum structures in the Ellsberg paradox We expose in this section our approach to economic agents decision making based on the mathematical formalism of quantum mechanics. We do not present the technical details of our modeling, but instead we aim to be as intuitive and explicative as possible. The reader interested to the technical aspects of our approach can refer to our papers (Aerts et al., 2014), (Khrennikov & Haven, 2009), (Aerts et al., 2012). The first insight towards the elaboration of a quantum probabilistic framework to model Ellsberg-type situations came from our conceptual and structural investigation of how the approaches generalizing SEUT cope with ambiguity and ambiguity aversion (Gilboa, 1987), (Gilboa & Schmeidler, 1989), (Maccheroni et al., 2006), (Klibanoff et al., 2005). As we know, ambiguity characterizes a situation without a probability model describing it, while risk characterizes a situation where one presupposes that a classical probability model on a σ–algebra of events exists. The generalizations in (i)–(iv), Section 3, consider more general structures than a single classical probability model on a σ–algebra. We are convinced that this is exactly the point: ambiguity, due to its contextual nature, structurally needs a non-classical probability model. To this end we have elaborated a general framework for this type of situations, based on the notion of ‘contextual risk’ and inspired by the probability structure of quantum mechanics. The latter is indeed intrinsically different from a classical probability on a σ–algebra, because the set of events does ‘not’ form a Boolean algebra (see Section 2).
