The Ellsberg Paradox: A Challenge to Quantum Decision Theory?

al‐Nowaihi, Ali; Dhami, Sanjit

doi:10.2139/ssrn.2844472

Cited by 5 publications

(11 citation statements)

References 44 publications

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“…Indeed, this quantum mathematics in Hilbert spaces has some advantages in modelling the information uncertainty that is induced by a non-controllable context, like a cognitive one (Aerts et al 2014(Aerts et al , 2018aSozzo 2019Sozzo , 2020. It must be noted, in this regard, that the present theoretical framework also accords with other attempts to represent human decisions in Hilbert space (see, e.g., La Mura 2009;Yukalov and Sornette 2010;Gyntelberg and Hansen 2012;al-Nowaihi and Dhami 2017;Basieva et al 2018;Danilov et al 2018;Eichberger and Pirner 2018).…”

Section: Introductionmentioning

confidence: 70%

“…3, 4 and 5 are "ad hoc", in the sense that they require introduction of new parameters, which would describe empirical data, without necessarily explaining them. In particular, one may wonder why we have chosen to use a Hilbert space over complex numbers, whereas a Hilbert space over real numbers would have been sufficient to reproduce ambiguity seeking and ambiguity aversion attitudes, which has already been proved (see, e.g., La Mura 2009;al-Nowaihi and Dhami 2017).…”

Section: Discussionmentioning

confidence: 99%

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Representing Attitudes Towards Ambiguity in Hilbert Space: Foundations and Applications

Sozzo

2020

Found Sci

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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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Section: Introductionmentioning

confidence: 70%

Section: Discussionmentioning

confidence: 99%

Representing Attitudes Towards Ambiguity in Hilbert Space: Foundations and Applications

Sozzo

2020

Found Sci

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“…The most successful approach is probably that of source dependence (Abdellaoui, Baillon, Placido, & Wakker, 2011; Dimmock, Kouwenberg, & Wakker, 2015; Kothiyal, Spinu, & Wakker, 2014). 1 1 See section 3 of al-Nowaihi and Dhami (2017) or sections 3–7 of al-Nowaihi et al (2018) for reviews of classical (non-quantum) approaches to ambiguity. In this paper we investigate the potential of quantum decision theory (QDT) to provide an alternative explanation. We concentrate on the canonical example of ambiguity, namely, the Ellsberg paradox (Ellsberg, 1961, 2001; Keynes, 1921).…”

Section: Introductionmentioning

confidence: 99%

“…A simple quantum model of the Ellsberg paradox was introduced by al-Nowaihi and Dhami (2017). Their derivation of quantum probabilities is parameter-free.…”

Section: Introductionmentioning

confidence: 99%

“…A number of quantum models of the Ellsberg paradox have been developed. 6 6 See the Introduction of al-Nowaihi and Dhami (2017) or subsection 8.1 of al-Nowaihi et al (2018) for reviews of earlier quantum approaches to the Ellsberg paradox. Some of these models do explain the Ellsberg paradox but at the cost of introducing a considerable degree of flexibility. However, when non-quantum models are granted the same degree of flexibility, they too can explain the Ellsberg paradox.…”

Section: Introductionmentioning

confidence: 99%

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Quantum Decision Theory, Bounded Rationality and the Ellsberg Paradox

Wei

al‐Nowaihi

Dhami

2019

Studies in Microeconomics

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We test a simple quantum decision model of the Ellsberg paradox. We find that the theoretical predictions of the model are in conformity with our experimental results. The predictions of our quantum model are not statistically significantly different from those of the source dependent model. The source dependent model requires the specification of probability weighting functions in order to fit the evidence. On the other hand, our quantum model makes no recourse to probability weighting functions. This suggests that much of what is normally attributed to probability weighting may actually be due to quantum probability. When we replace quantum probability by Kolmogorov probability in our model, then the Ellsberg paradox reemerges. Hence, we make essential use of quantum probability theory. All our development uses no more than standard linear algebra and real numbers, which are very familiar to economists. This makes our paper accessible to a wider audience than the quantum community. JEL Classification: D01, D81, D91

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The triple-store experiment: a first simultaneous test of classical and quantum probabilities in choice over menus

et al. 2021

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Recently quantum probability theory started to be actively used in studies of human decision-making, in particular for the resolution of paradoxes (such as the Allais, Ellsberg, and Machina paradoxes). Previous studies were based on a cognitive metaphor of the quantum double-slit experiment -the basic quantum interference experiment. In this paper, we report on an economics experiment based on a three-slit experiment design, where the slits are menus of alternatives from which one can choose. The test of nonclassicality is based on the Sorkin equality (which was only recently tested in quantum physics). Each alternative is a voucher to buy products in one or more stores. The alternatives are obtained from all disjunctions including one, two or three stores. The participants have to reveal the amount for which they are willing to sell the chosen voucher. Interference terms are computed by comparing the willingness to sell a voucher built as a disjunction of stores and the willingness

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The Ellsberg Paradox: A Challenge to Quantum Decision Theory?

Cited by 5 publications

References 44 publications

Representing Attitudes Towards Ambiguity in Hilbert Space: Foundations and Applications

Representing Attitudes Towards Ambiguity in Hilbert Space: Foundations and Applications

Quantum Decision Theory, Bounded Rationality and the Ellsberg Paradox

The triple-store experiment: a first simultaneous test of classical and quantum probabilities in choice over menus

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