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A proposal to extend expected utility in a quantum probabilistic framework

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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 enable 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.

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Notes

  1. We prefer using the term ‘ambiguity’ when referring to situations involving unknown probabilities, as done in many textbooks and papers on the topic.

  2. As mentioned in Sect. 5, the choice of \({\mathbb {C}}^{3}\) depends on the fact that there are three mutually exclusive and exhaustive events in the three-color example—the generalization to the Ellsberg n-color example is straightforward.

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Correspondence to Sandro Sozzo.

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Aerts, D., Haven, E. & Sozzo, S. A proposal to extend expected utility in a quantum probabilistic framework. Econ Theory 65, 1079–1109 (2018). https://doi.org/10.1007/s00199-017-1051-2

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