Abstract
Empirical evidence has confirmed that quantum effects occur frequently also outside the microscopic domain, while quantum structures satisfactorily model various situations in several areas of science, including biological, cognitive and social processes. In this paper, we elaborate a quantum mechanical model which faithfully describes the Ellsberg paradox in economics, showing that the mathematical formalism of quantum mechanics is capable to represent the ambiguity present in this kind of situations, because of the presence of contextuality. Then, we analyze the data collected in a concrete experiment we performed on the Ellsberg paradox and work out a complete representation of them in complex Hilbert space. We prove that the presence of quantum structure is genuine, that is, interference and superposition in a complex Hilbert space are really necessary to describe the conceptual situation presented by Ellsberg. Moreover, our approach sheds light on ‘ambiguity laden’ decision processes in economics and decision theory, and allows to deal with different Ellsberg-type generalizations, e.g., the Machina paradox.
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Notes
The Sure–Thing principle was stated by Savage by introducing the businessman example, but it can be presented in an equivalent form, the independence axiom, as follows: if persons are indifferent in choosing between simple lotteries L 1 and L 2, they will also be indifferent in choosing between L 1 mixed with an arbitrary simple lottery L 3 with probability p and L 2 mixed with L 3 with the same probability p.
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Aerts, D., Sozzo, S. & Tapia, J. Identifying Quantum Structures in the Ellsberg Paradox. Int J Theor Phys 53, 3666–3682 (2014). https://doi.org/10.1007/s10773-014-2086-9
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DOI: https://doi.org/10.1007/s10773-014-2086-9