Foundations of Science 26 (1):103-128 (2020)

We provide here a general mathematical framework to model attitudes towards ambiguity which uses the formalism of quantum theory as a “purely mathematical formalism, detached from any physical interpretation”. We show that the quantum-theoretic framework enables modelling of the Ellsberg paradox, but it also successfully applies to more concrete human decision-making tests involving financial, managerial and medical decisions. In particular, we elaborate a mathematical representation of various empirical studies which reveal that attitudes of managers towards uncertainty shift from ambiguity seeking to ambiguity aversion, and viceversa, thus exhibiting hope effects and fear effects. The present framework provides a promising direction towards the development of a unified theory of decisions in the presence of uncertainty.
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DOI 10.1007/s10699-020-09718-5
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Theory of Games and Economic Behavior.John Von Neumann & Oskar Morgenstern - 1944 - Princeton, NJ, USA: Princeton University Press.
Risk, Uncertainty and Profit.Frank Knight - 1921 - University of Chicago Press.
The Foundations of Statistics.Leonard J. Savage - 1956 - Philosophy of Science 23 (2):166-166.
The Foundations of Statistics.Leonard J. Savage - 1959 - Synthese 11 (1):86-89.

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