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arXiv:2006.16763 · Entropy

Evolutionary Processes in Quantum Decision Theory

Vyacheslav I. Yukalov

Published Jun 18, 2020• 34 citations
arXivHTMLPDF

Abstract

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.

DOI
10.3390/e22060681

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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.
An approach is presented treating decision theory as a probabilistic theory based on quantum techniques. Accurate definitions are given and thorough analysis is accomplished for the quantum probabilities describing the choice between separate alternatives, sequential alternatives characterizing conditional quantum probabilities, and behavioral quantum probabilities taking into account rational-irrational duality of decision making. The comparison between quantum and classical probabilities is explained. The analysis demonstrates that quantum probabilities serve as an essentially more powerful tool of characterizing various decision-making situations including the influence of psychological behavioral effects.
In cognitive psychology, some experiments of games were reported [1, 2, 3, 4], and these demonstrated that real players did not use the "rational strategy" provided by classical game theory. To discuss probabilities of such "irrational choice", recently, we proposed a decision-making model which is based on the formalism of quantum mechanics [5, 6, 7, 8]. In this paper, we briefly explain the above model and calculate the probability of irrational choice in several prisoner's dilemma (PD) games.
Abstract The review analyses the fundamental principles which Artificial Intelligence should be based on in order to imitate the realistic process of taking decisions by humans experiencing emotions. Two approaches are considered, one based on quantum theory and the other employing classical terms. Both these approaches have a number of similarities, being principally probabilistic. The analogies between quantum measurements under intrinsic noise and affective decision making are elucidated. It is shown that cognitive processes have many features that are formally similar to quantum measurements. This, however, in no way means that for the imitation of human decision making Affective Artificial Intelligence has necessarily to rely on the functioning of quantum systems. The analogies between human decision making and quantum measurements merely demonstrate formal common properties in their functioning. It is in this sense that one has to understand quantum operation of Artificial Intelligence. Appreciating the common features between quantum measurements and decision making helps for the formulation of an axiomatic approach employing only classical notions. Artificial Intelligence, following this approach, operates similarly to humans, by taking into account the utility of the considered alternatives as well as their emotional attractiveness. Affective Artificial Intelligence, whose operation takes account of the cognition-emotion duality, avoids numerous behavioural paradoxes of traditional decision making. A society of intelligent agents, interacting through the repeated multistep exchange of information, forms a network accomplishing dynamic decision making based on the evaluation of utility and affected by the emotional attractiveness of alternatives. The considered intelligent networks can characterize the operation of either a human society of affective decision makers, or the brain composed of neurons, or a typical probabilistic network of an artificial intelligence.
Organizational decision making is often explored with theories from the heuristics and biases research program, which have demonstrated great value as descriptions of how people in organizations make decisions. Nevertheless, rational analysis and classical probability theory are still seen by many as the best accounts of how decisions should be made and classical probability theory is the preferred framework for cognitive modelling for many researchers. The focus of this work is quantum probability theory, an alternative probabilistic framework. Results in decision making, which appear paradoxical from a perspective of classical probability theory, may make perfect sense if one adopts quantum probability theory. We review some cognitive models of decision making based on quantum probability theory. Each of these models is based on a challenge to prescription from classical probability theory. The transition from labeling a particular behavior as irrational, by classical probability standards, to (potentially) rational (or, at any rate, not fallacious), raises interesting possibilities, including that of characterizing certain heuristics in formal, probabilistic terms.
Quantum decision theory, advanced earlier by the authors, and illustrated for lotteries with gains, is generalized to the games containing lotteries with gains as well as losses. The mathematical structure of the approach is based on the theory of quantum measurements, which makes this approach relevant both for the description of decision making of humans and the creation of artificial quantum intelligence. General rules are formulated allowing for the explicit calculation of quantum probabilities representing the fraction of decision makers preferring the considered prospects. This provides a method to quantitatively predict decision-maker choices, including the cases of games with high uncertainty for which the classical expected utility theory fails. The approach is applied to experimental results obtained on a set of lottery gambles with gains and losses. Our predictions, involving no fitting parameters, are in very good agreement with experimental data. The use of quantum decision making in game theory is described. A principal scheme of creating quantum artificial intelligence is suggested.