Quantum Structures in Human Decision-making: Towards Quantum Expected Utility

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 also 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. Finally, classical structures are the building blocks of subjective expected utility theory (SEUT), providing both the descriptive and the normative foundations of rational DM: in situations of uncertainty, people (should) choose as if they maximized EU with respect to a unique probability measure, satisfying the axioms of Kolmogorov and interpreted as their subjective probability [2, 3]. However, on the one side, empirical research in cognitive psychology has revealed that classical structures are not generally able to model human judgements and decisions, thus making problematical the 1 interpretation of a wide range of cognitive phenomena in terms of standard logic and probability theory. On the other side, Kahneman, Tversky and other authors suggested that these empirical deviations from classicality are "true errors" of human reasoning, whence the use of terms like "effect", "fallacy", "paradox", "contradiction", etc., to refer to such phenomena [4, 5].