Testing ambiguity and Machina preferences within a quantum-theoretic framework for decision-making

Aerts, Diederik; Geriente, Suzette; Moreira, Catarina; Sozzo, Sandro

doi:10.1016/j.jmateco.2017.12.002

Cited by 18 publications

(35 citation statements)

References 39 publications

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“…We illustrate and analyse here a DM test we performed on the Ellsberg two-urn example which confirms traditional ambiguity aversion patterns and enables a quantum-theoretic modelling [18]. The results and ensuing quantum model have far reaching implications on applications of ambiguity aversion to financial and medical decisions, as we will see in Sect.…”

Section: Expected Utility Theory and Its Descriptive Pitfallsmentioning

confidence: 52%

“…We proved in [16,18] that the state-dependence above can exactly explain the inversion of preferences observed in the Ellsberg and Machina paradox situations. The conclusion is interesting, from our point of view.…”

Section: A Quantum-theoretic Framework For Expected Utilitymentioning

confidence: 75%

“…the Machina paradox [17]. Moreover, we have recently proved that the quantum-theoretic framework enables successful representation of various DM tests performed on the Ellsbeg and Machina paradox situations [18].In the present paper, we focus on the quantum-theoretic modelling of the Ellsberg two-urn experiment, inasmuch this experiment involves a choice between an option with a known probability, or risky option, and…”

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confidence: 99%

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

Sozzo

2019

Int J Theor Phys

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Ellsberg thought experiments and empirical confirmation of Ellsberg preferences pose serious challenges to subjective expected utility theory (SEUT). We have recently elaborated a quantum-theoretic framework for human decisions under uncertainty which satisfactorily copes with the Ellsberg paradox and other puzzles of SEUT. We apply here the quantum-theoretic framework to the Ellsberg two-urn example, showing that the paradox can be explained by assuming a state change of the conceptual entity that is the object of the decision (decision-making, or DM, entity) and representing subjective probabilities by quantum probabilities. We also model the empirical data we collected in a DM test on human participants within the theoretic framework above. The obtained results are relevant, as they provide a line to model real life, e.g., financial and medical, decisions that show the same empirical patterns as the two-urn experiment.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]. 1 An innovative aspect of the Kahneman-Tversky programme of judgement heuristics and individual biases was the use of non-Kolmogorovian structures to represent probabilities. In that regard, the research on the foundations of quantum theory has unveiled both the conceptual and mathematical differences between classical and quantum structures, e.g., context-dependent situations crucially need a non-Kolmogorovian quantum-like model of probability (see, e.g., [7,8,9]). This was the starting point of a successful research that applies the mathematical formalism of quantum theory, detached from any physical interpretation, to model situations in cognition and economics that cannot be modelled by classical structures (see, e.g., [6,7,8,9,10]).Why are classical structures problematical in SEUT? In 1961, Daniel Ellsberg proposed a series of DM experiments whose results do not agree with the predictions of SEUT, as far as concrete decisions are mainly influenced by psychological factors, like ambiguity aversion, rather than by the need of maximizing EU [11]. The consequence is that one cannot represent Ellsberg preferences by maximization of EU with respect to a unique Kolmogorovian probability measure, which generates the famous Ellsberg paradox. Ellsberg preferences have been empirically confirmed several times against the predictions of SEUT and its main extensions, in simple DM tests, but also in more complex real life DM situations (see, e.g., [12]).How does the research on quantum structures relate to the pitfalls of SEUT? The answer comes from a 20-year research on the foundations of quantum physics, the origin of quantum structures and the conceptual and mathematical differences between classical and quantum theories. Indeed, we...

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Section: Expected Utility Theory and Its Descriptive Pitfallsmentioning

confidence: 52%

Section: A Quantum-theoretic Framework For Expected Utilitymentioning

confidence: 75%

mentioning

confidence: 99%

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

Sozzo

2019

Int J Theor Phys

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“…2, such bounded rationality models, though descriptively interesting and easily interpretable intuitively, provide a too fragmented view of decision theory, hence they are not able to provide a unitary and adequate explanatory framework to understand the deep aspects of decision processes. In addition, cumulative prospect theory, as well as other major non-expected utility models, fails to reproduce the empirical results of a recently elaborated variant of the Ellsberg paradox, the Machina paradox [27,37,38].…”

Section: Rational Decision Theory and Its Puzzlesmentioning

confidence: 98%

“…5 a mathematical representation in Hilbert space of the Ellsberg paradox situation and the ambiguity aversion pattern found in empirical literature. We had already presented quantum models of various Ellsberg thought experiments, including two-color and three-color urns [16,17,26,27,28]. The novelty of the mathematical representation developed here consists in the fact that it follows directly from the canonical quantum representation of the realistic-operational terms of state, context, property and outcome probability in Hilbert space, which makes the use of quantum mathematics in this kind of situations more firmly founded and generalizable to other decision situations.…”

Section: Introductionmentioning

confidence: 99%

Explaining versus describing human decisions: Hilbert space structures in decision theory

Sozzo

2019

Soft Comput

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Despite the impressive success of quantum structures to model long-standing human judgement and decision puzzles, the quantum cognition research programme still faces challenges about its explanatory power. Indeed, quantum models introduce new parameters, which may fit empirical data without necessarily explaining them. Also, one wonders whether more general non-classical structures are better equipped to model cognitive phenomena. In this paper, we provide a realistic-operational foundation of decision processes using a known decision-making puzzle, the Ellsberg paradox, as a case study. Then, we elaborate a novel representation of the Ellsberg decision situation applying standard quantum correspondence rules which map realistic-operational entities into quantum mathematical terms. This result opens the way towards an independent, foundational rather than phenomenological, motivation for a general use of quantum Hilbert space structures in human cognition.

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Introducing Quantum-Like Influence Diagrams for Violations of the Sure Thing Principle

Moreira

Wichert

2019

Lecture Notes in Computer Science

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It is the focus of this work to extend and study the previously proposed quantum-like Bayesian networks Wichert, 2014, 2016) to deal with decisionmaking scenarios by incorporating the notion of maximum expected utility in influence diagrams. The general idea is to take advantage of the quantum interference terms produced in the quantum-like Bayesian Network to influence the probabilities used to compute the expected utility of some action. This way, we are not proposing a new type of expected utility hypothesis. On the contrary, we are keeping it under its classical definition. We are only incorporating it as an extension of a probabilistic graphical model in a compact graphical representation called an influence diagram in which the utility function depends on the probabilistic influences of the quantum-like Bayesian network. Our findings suggest that the proposed quantum-like influence digram can indeed take advantage of the quantum interference effects of quantum-like Bayesian Networks to maximise the utility of a cooperative behaviour in detriment of a fully rational defect behaviour under the prisoner's dilemma game.

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Testing ambiguity and Machina preferences within a quantum-theoretic framework for decision-making

Cited by 18 publications

References 39 publications

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

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

Explaining versus describing human decisions: Hilbert space structures in decision theory

Introducing Quantum-Like Influence Diagrams for Violations of the Sure Thing Principle

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