Quantum-like models cannot account for the conjunction fallacy

Boyer-Kassem, Thomas; Duchêne, Sébastien; Guerci, Éric

doi:10.1007/s11238-016-9549-9

Cited by 33 publications

(31 citation statements)

References 74 publications

(142 reference statements)

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“…Sometimes, one treats the Lüders probability of consecutive measurements as a conditional probability. This, however, is not justified from the theoretical point of view [21,23,30] and also contradicts experimental data [31,32]. But defining the quantum joint probability according to expression (Equation 8) contains no contradictions.…”

Section: Composite Quantum Measurements and Eventsmentioning

confidence: 92%

Inconclusive Quantum Measurements and Decisions under Uncertainty

Yukalov

Sornette

2016

Front. Phys.

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We give a mathematical definition for the notion of inconclusive quantum measurements. In physics, such measurements occur at intermediate stages of a complex measurement procedure, with the final measurement result being operationally testable. Since the mathematical structure of Quantum Decision Theory (QDT) has been developed in analogy with the theory of quantum measurements, the inconclusive quantum measurements correspond, in QDT, to intermediate stages of decision making in the process of taking decisions under uncertainty. The general form of the quantum probability for a composite event is the sum of a utility factor, describing a rational evaluation of the considered prospect, and of an attraction factor, characterizing irrational, subconscious attitudes of the decision maker. Despite the involved irrationality, the probability of prospects can be evaluated. This is equivalent to the possibility of calculating quantum probabilities without specifying hidden variables. We formulate a general way of evaluation, based on the use of non-informative priors. As an example, we suggest the explanation of the decoy effect. Our quantitative predictions are in very good agreement with experimental data.

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Section: Composite Quantum Measurements and Eventsmentioning

confidence: 92%

Inconclusive Quantum Measurements and Decisions under Uncertainty

Yukalov

Sornette

2016

Front. Phys.

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“…And here we have higher expectation of violation of Born's rule than in physics, cf. with the experiment discussed in [4], see also [5], [6] for discussions. In this note we restrict our consideration to Sorkin's 3-equality, but it is easy to generalize our scheme of testing of the probability structure of cognition to the case of arbitrary n.…”

Section: Introductionmentioning

confidence: 80%

“…There is a homogeneous group of people recruited for the experiment. 5 They are informed that during the experiment they will answer to a few questions related to their possible emigration to other countries; for this experiment, three fixed countries; for example, we can select Brazil, Canada, Australia, a = 1, 2, 3.…”

Section: Methodsmentioning

confidence: 99%

“…We consider the finite-dimensional case. Unfortunately, we have to assume that their eigenvalues can be degenerate, because as was found in [2] (see also [5], [6] for detailed analysis), it is impossible to represent some cognitive entities by operators with nondegenerate spectra. 7 Let a i , i = 1, 2, 3, and b j , j = 1, 2, ..., m, be the eigenvalues of a and b. Denote the corresponding projectors by P a i and P b j respectively.…”

Section: Appendix: Derivation Of Sorkin's Equality Of the Third Ordermentioning

confidence: 99%

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Testing Boundaries of Applicability of Quantum Probabilistic Formalism to Modeling of Cognition: Metaphors of Two and Three Slit Experiments

Basieva

Khrennikov

2017

Quantum Interaction

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Recently the mathematical formalism of quantum mechanics, especially methods of quantum probability theory, started to be widely used in a variety of applications outside of physics, e.g., cognition and psychology as well as economy and finances. To distinguish such models from genuine quantum physical models, they often called quantumlike (although often people simply speak about, e.g., "quantum cognition"). These novel applications generate a number of foundational questions. Nowadays we can speak about a new science -foundations of quantum-like modeling. At the first stage this science was mainly about comparison of classical and quantum models, mainly in the probabilistic setting. It was found that statistical data from cognitive psychology violate some basic constraints posed on data by classical probability theory (Kolmogorov, 1933); in particular, the constraints given by the formula of total probability and Bell's type inequalities. Recently another question attracted some attention. In spite of real success in applications, there are no reason to believe that the quantum probability would cover completely all problems of, e.g., cognition. May be more general probability models have to be explored. A similar problem attracted a lot of attention in foundations of quantum physics culminating in a series of experiments to check Sorkin's equality for the triple-slit experiment by Weihs' group. In this note we present a similar test in the cognitive experimental setting. Performance of this test would either give further confirmation of the 1 The idea that quantum and cognitive have something in common is not new. However, before it was presented either in philosophic discussions, e.g., between Jung and Pauli (also Whitehead) or in abstract mathematical models, e.g., [3]. Nowadays numerous research groups work with real experimental data. We also point from very beginning that this activity is devoted to so to say quantum-like modeling cognition, i.e., it has to be sharply distinguished from attempts to model cognition on the basis of genuine quantum physical processes in the brain -in the spirit of, e.g., Penrose.

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“…Recently, the possibility to apply the mathematical formalism of quantum theory outside of physics was actively explored in cognitive science, psychology, economics, finance, social and political sciences, decision making, game theory, and computer science (e.g. quantum-like models for information retrieval), as thoroughly reported in recent monographs [6][7][8][9][10][11][12][13] and representative papers [14][15][16][17][18][19][20][21][22][23]. These are all applications of the quantum-like approach.…”

Section: Introductionmentioning

confidence: 99%

Concept of information laser: from quantum theory to behavioural dynamics

Khrennikov

Toffano

Dubois

2019

Eur. Phys. J. Spec. Top.

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Recently, the methods of quantum theory, especially quantum information, started to be widely applied outside of physics: in cognitive, social sciences, economics, finance, decision making and biology. We propose a quantum-like model: the "information laser". The basic assumption is the discrete structure of state spaces related to the quantization of information. The information field acts in the form of indistinguishable quanta of "social energy" analogue to photons. The massive flow of information acts as a laser pump. In this framework, an information selection process by agents under constant pressure of massive repeated information leads to collective "resonance" effects in analogy with laser cavity and stimulated emission. In order to make operational parallels between physical lasers and the information laser we identify the essential features of laser operation. An application to the analysis of recent disruptive social events (colour revolutions) is discussed. Social analogues to the laser are also considered through the model of Echo Chambers induced by the Internet and Adam Smith's invisible hand.

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Quantum-like models cannot account for the conjunction fallacy

Cited by 33 publications

References 74 publications

Inconclusive Quantum Measurements and Decisions under Uncertainty

Inconclusive Quantum Measurements and Decisions under Uncertainty

Testing Boundaries of Applicability of Quantum Probabilistic Formalism to Modeling of Cognition: Metaphors of Two and Three Slit Experiments

Concept of information laser: from quantum theory to behavioural dynamics

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