scholarly journals MATHEMATICAL STRUCTURE OF QUANTUM DECISION THEORY

2010 ◽  
Vol 13 (05) ◽  
pp. 659-698 ◽  
Author(s):  
VYACHESLAV I. YUKALOV ◽  
DIDIER SORNETTE
Keyword(s):  
Decision Making ◽  
Decision Theory ◽  
Hilbert Spaces ◽  
Mathematical Structure ◽  
Conjunction Fallacy ◽  
Human Beings ◽  
Quantum Approach ◽  
Sure Thing Principle ◽  
Classical Decision ◽  
Quantum Decision Theory

One of the most complex systems is the human brain whose formalized functioning is characterized by decision theory. We present a "Quantum Decision Theory" of decision-making, based on the mathematical theory of separable Hilbert spaces. This mathematical structure captures the effect of superposition of composite prospects, including many incorporated intentions, which allows us to explain a variety of interesting fallacies and anomalies that have been reported to particularize the decision-making of real human beings. The theory describes entangled decision-making, non-commutativity of subsequent decisions, and intention interference of composite prospects. We demonstrate how the violation of the Savage's sure-thing principle (disjunction effect) can be explained as a result of the interference of intentions, when making decisions under uncertainty. The conjunction fallacy is also explained by the presence of the interference terms. We demonstrate that all known anomalies and paradoxes, documented in the context of classical decision theory, are reducible to just a few mathematical archetypes, all of which allow the finding of straightforward explanations in the frame of the developed quantum approach.

scholarly journals Evolutionary Processes in Quantum Decision Theory

Entropy ◽  
2020 ◽  
Vol 22 (6) ◽  
pp. 681 ◽  
Author(s):  
Vyacheslav I. Yukalov
Keyword(s):  
Decision Making ◽  
Decision Theory ◽  
Rational Choice ◽  
Evolutionary Processes ◽  
Classical Correspondence ◽  
Principal Points ◽  
Quantum Decision Theory

The review presents the basics of quantum decision theory, with an emphasis on temporary processes in decision making. The aim is to explain the principal points of the theory. How an operationally-testable, rational choice between alternatives differs from a choice decorated by irrational feelings is elucidated. Quantum-classical correspondence is emphasized. A model of quantum intelligence network is described. Dynamic inconsistencies are shown to be resolved in the frame of the quantum decision theory.

scholarly journals Role of Information in Decision Making of Social Agents

2015 ◽  
Vol 14 (05) ◽  
pp. 1129-1166 ◽  
Author(s):  
Vyacheslav I. Yukalov ◽  
Didier Sornette
Keyword(s):  
Decision Making ◽  
Decision Theory ◽  
Utility Theory ◽  
Decision Makers ◽  
Mathematical Framework ◽  
Social Agents ◽  
Additional Information ◽  
Probabilistic Version ◽  
Classical Decision

The influence of additional information on the decision making of agents, who are the interacting members of a society, is analyzed within the mathematical framework based on the use of quantum probabilities. The introduction of social interactions, which influence the decisions of individual agents, leads to a generalization of the quantum decision theory (QDT) developed earlier by the authors for separate individuals. The generalized approach is free of the standard paradoxes of classical decision theory. This approach also explains the error-attenuation effects observed for the paradoxes occurring when decision makers, who are members of a society, consult with each other, increasing in this way the available mutual information. A precise correspondence between QDT and classical utility theory is formulated via the introduction of an intermediate probabilistic version of utility theory of a novel form, which obeys the requirement that zero-utility prospects should have zero probability weights.

scholarly journals Zasada ostrożności a klasyczne reguły decyzyjne

2020 ◽  
pp. 83-102
Author(s):  
Grzegorz M. Malinowski
Keyword(s):  
Decision Making ◽  
Decision Theory ◽  
Precautionary Principle ◽  
Decision Rules ◽  
Decision Making Under Risk ◽  
Classical Decision ◽  
Decision Making Criteria

Zasada ostrożności (ZO) traktowana jest w literaturze przedmiotu jako reguła decyzyjna, która powinna być stosowana w sytuacjach charakteryzujących się niepewnością. Jednakże w ramach teorii decyzji już znacznie wcześniej wypracowano algorytmy postępowania w warunkach niepewności. Celem niniejszego artykułu jest porównanie klasycznych reguł decyzyjnych z zasadą ostrożności i odpowiedź na pytanie: czy zasadę ostrożności można zredukować do którejś z klasycznych reguł. Okazuje się, że taka redukcja nie jest możliwa. Precautionary Principle vs Formal Decision: Making Criteria Precautionary principle (PP) is commonly understood as a criterion that should be used in decision-making under risk and/or uncertainty. Yet, long before the approval of PP in the literature – a set of concrete, formal criterions existed in the field of decision theory. Therefore the main goal of this paper is to compare these classical decision – rules with PP. This very comparison will bring us to answer the question: if PP may be reduced to any of the classical criterions? It will tur out that such a reduction cannot be done. Therefore PP has got its own specificity.

scholarly journals A quantum probability explanation for violations of ‘rational’ decision theory

2009 ◽  
Vol 276 (1665) ◽  
pp. 2171-2178 ◽  
Author(s):  
Emmanuel M. Pothos ◽  
Jerome R. Busemeyer
Keyword(s):  
Decision Theory ◽  
Probability Model ◽  
Quantum Probability ◽  
Space Representation ◽  
Quantum Model ◽  
Rational Decision ◽  
Game Show ◽  
Human Decision ◽  
Sure Thing Principle ◽  
Classical Decision

Two experimental tasks in psychology, the two-stage gambling game and the Prisoner's Dilemma game, show that people violate the sure thing principle of decision theory. These paradoxical findings have resisted explanation by classical decision theory for over a decade. A quantum probability model, based on a Hilbert space representation and Schrödinger's equation, provides a simple and elegant explanation for this behaviour. The quantum model is compared with an equivalent Markov model and it is shown that the latter is unable to account for violations of the sure thing principle. Accordingly, it is argued that quantum probability provides a better framework for modelling human decision-making.

Are addictions “biases and errors” in the rational decision process?

2008 ◽  
Vol 31 (4) ◽  
pp. 449-450
Author(s):  
Elias L. Khalil
Keyword(s):  
Decision Making ◽  
Decision Theory ◽  
Decision Process ◽  
Conjunction Fallacy ◽  
The Other ◽  
Rational Decision ◽  
Access Points ◽  
Decision Making Framework ◽  
The One

AbstractRedish et al. view addictions as errors arising from the weak access points of the system of decision-making. They do not analytically distinguish between addictions, on the one hand, and errors highlighted by behavioural decision theory, such as over-confidence, representativeness heuristics, conjunction fallacy, and so on, on the other. Redish et al.'s decision-making framework may not be comprehensive enough to capture addictions.

scholarly journals Quantum probability and quantum decision-making

2016 ◽  
Vol 374 (2058) ◽  
pp. 20150100 ◽  
Author(s):  
V. I. Yukalov ◽  
D. Sornette
Keyword(s):  
Decision Making ◽  
Decision Theory ◽  
Quantum Probability ◽  
Quantum Measurements ◽  
General Definition ◽  
Classical Counterpart ◽  
Composite Events ◽  
Definition Of ◽  
Quantum Decision Theory

A rigorous general definition of quantum probability is given, which is valid not only for elementary events but also for composite events, for operationally testable measurements as well as for inconclusive measurements, and also for non-commuting observables in addition to commutative observables. Our proposed definition of quantum probability makes it possible to describe quantum measurements and quantum decision-making on the same common mathematical footing. Conditions are formulated for the case when quantum decision theory reduces to its classical counterpart and for the situation where the use of quantum decision theory is necessary.

Research and analysis of business management processes implemented under conditions of incomplete certainty

2020 ◽  
Author(s):  
Igor Klimenko ◽  
A. Ivlev
Keyword(s):  
Decision Making ◽  
A Priori ◽  
Business Management ◽  
Statistical Uncertainty ◽  
Management Processes ◽  
Classical Decision ◽  
Decision Making Criteria

The study carried out in this work made it possible to expand the rank scale for a priori assessment of the chosen strategy in terms of increasing the sensitivity of assessing the caution / negligence ratio using risky, as well as classical decision-making criteria under conditions of statistical uncertainty.

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