Abstract
{\it Ellsberg thought experiments} and empirical confirmation of Ellsberg preferences pose serious challenges to {\it subjective expected utility theory} (SEUT). We have recently elaborated a quantum-theoretic framework for human decisions under uncertainty which satisfactorily copes with the Ellsberg paradox and other puzzles of SEUT. We apply here the quantum-theoretic framework to the {\it Ellsberg two-urn example}, showing that the paradox can be explained by assuming a state change of the conceptual entity that is the object of the decision ({\it decision-making}, or {\it DM}, {\it entity}) and representing subjective probabilities by quantum probabilities. We also model the empirical data we collected in a DM test on human participants within the theoretic framework above. The obtained results are relevant, as they provide a line to model real life, e.g., financial and medical, decisions that show the same empirical patterns as the two-urn experiment.
Highlights
Daniel Kahneman was awarded the Nobel Prize in Economic Science in 2002 for his pioneering studies on the identification and estimation of the psychological factors that influence human behaviour under uncertainty, which led to the birth of a new domain called behavioural economics.Cognitive psychologists have assumed for years, often implicitly, that complex cognitive processes, like human judgement and decision-making (DM), have to be modelled by combining set-theoretic structures and should obey to mathematical relations that resemble those typically used in logic, formalized by Boole (Boolean logic), and probability, axiomatized by Kolmogorov (Kolmogorovian probability) [1]
These structures are known in physics as classical structures: they were originally used in classical physics, and later extended to statistics, psychology, economics, finance and computer science
Classical structures are implicitly assumed in the so-called Bayesian approach, according to which any source of uncertainty can be formalized probabilistically, while people update knowledge according to the Bayes law of Kolmogorovian probability
Summary
Daniel Kahneman was awarded the Nobel Prize in Economic Science in 2002 for his pioneering studies on the identification and estimation of the psychological factors that influence human behaviour under uncertainty, which led to the birth of a new domain called behavioural economics. The above realistic and operational description of the DM process as a “constructive (creation) process in which a context-mediated transition occurs from potential to actual” closely resembles a quantum measurement process in which the interaction with the physical measurement context determines an intrinsically probabilistic state change of the measured quantum entity, which suggests that a quantum mechanical representation is appropriate in this case In this regard, we have elaborated a quantum-theoretic framework to represent human DM under uncertainty that enables modelling of the Ellsberg paradox [14, 15, 16] and more general DM situations [14, 16] that are problematical from the point of view of SEUT and its extensions, i.e. the Machina paradox [17].
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