Abstract
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.
Highlights
Economic theory crucially rests on the so-called ‘Bayesian paradigm’: any source of uncertainty can be probabilistically quantified and the ensuing probability theory satisfies the axioms of Kolmogorov (Kolmogorov, 1933)
Von Neumann and Morgenstern successfully applied the Bayesian paradigm when elaborating an axiomatic form of the expected utility theory (EUT), which is the predominant model of decision-making under uncertainty
The traditional line of reasoning is that, in the absence of objective probabilities, the decision-maker forms her/his own subjective probabilities, and takes decisions on the basis of these subjective probabilities. This is the basic tenet of subjective EUT: individuals take decisions as if they maximized expected utility with respect to a Kolmogorovian probability measure which is interpreted as their subjective probability
Summary
Economic theory crucially rests on the so-called ‘Bayesian paradigm’: any source of uncertainty can be probabilistically quantified and the ensuing probability theory satisfies the axioms of Kolmogorov (Kolmogorov, 1933). We put forward a non-Bayesian generalization of the Bayesian paradigm, where human decision-making under uncertainty is modeled in the mathematical formalism of quantum theory, quantum states incorporate the uncertainty that is present in situations of ambiguity, and state transformations incorporate people’s attitude towards ambiguity. This quantum-conceptual approach was recently employed with success to model Ellsberg- and Machina-like preferences in the corresponding paradox situations, and to faithfully represent data collected in experimental tests on the ‘three-color Ellsberg urn’ and the ‘Machina reflection example’. It is able to reconstruct, via the quantum state of the DM entity, the subjective probability distributions that are actualized in concrete experiments as a consequence of a particular attitude toward ambiguity
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