V. I. Yukalov

T. Kovalenko, S. Vincent, V. I. Yukalov et al.

We present the first calibration of quantum decision theory (QDT) to a dataset of binary risky choice. We quantitatively account for the fraction of choice reversals between two repetitions of the experiment, using a probabilistic choice formulation in the simplest form without model assumption or adjustable parameters. The prediction of choice reversal is then refined by introducing heterogeneity between decision makers through their differentiation into two groups: ``majoritarian'' and ``contrarian'' (in proportion 3:1). This supports the first fundamental tenet of QDT, which models choice as an inherent probabilistic process, where the probability of a prospect can be expressed as the sum of its utility and attraction factors. We propose to parameterise the utility factor with a stochastic version of cumulative prospect theory (logit-CPT), and the attraction factor with a constant absolute risk aversion (CARA) function. For this dataset, and penalising the larger number of QDT parameters via the Wilks test of nested hypotheses, the QDT model is found to perform significantly better than logit-CPT at both the aggregate and individual levels, and for all considered fit criteria for the first experiment iteration and for predictions (second ``out-of-sample'' iteration). The distinctive QDT effect captured by the attraction factor is mostly appreciable (i.e., most relevant and strongest in amplitude) for prospects with big losses. Our quantitative analysis of the experimental results supports the existence of an intrinsic limit of predictability, which is associated with the inherent probabilistic nature of choice. The results of the paper can find applications both in the prediction of choice of human decision makers as well as for organizing the operation of artificial intelligence.

V. I. Yukalov, E. P. Yukalova

The dynamics of affective decision making is considered for an intelligent network composed of agents with different types of memory: long-term and short-term memory. The consideration is based on probabilistic affective decision theory, which takes into account the rational utility of alternatives as well as the emotional alternative attractiveness. The objective of this paper is the comparison of two multistep operational algorithms of the intelligent network: one based on discrete dynamics and the other on continuous dynamics. By means of numerical analysis, it is shown that, depending on the network parameters, the characteristic probabilities for continuous and discrete operations can exhibit either close or drastically different behavior. Thus, depending on which algorithm is employed, either discrete or continuous, theoretical predictions can be rather different, which does not allow for a uniquely defined description of practical problems. This finding is important for understanding which of the algorithms is more appropriate for the correct analysis of decision-making tasks. A discussion is given, revealing that the discrete operation seems to be more realistic for describing intelligent networks as well as affective artificial intelligence.

V. I. Yukalov

The review analyzes 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 compared, 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. 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. 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.

V. I. Yukalov

The procedure of tossing quantum coins and dice is described. This case is an important example of a quantum procedure because it presents a typical framework employed in quantum information processing and quantum computing. The emphasis is on the clarification of the difference between quantum and classical conditional probabilities. These probabilities are designed for characterizing different systems, either quantum or classical, and they, generally, cannot be reduced to each other. Thus the Lüders probability cannot be treated as a generalization of the classical conditional probability. The analogies between quantum theory of measurements and quantum decision theory are elucidated.

V. I. Yukalov

The review presents the basics of quantum decision theory, with the emphasis on temporary processes in decision making. The aim is to explain the principal points of the theory. The difference of an operationally testable rational choice between alternatives 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.

V. I. Yukalov, E. P. Yukalova, D. Sornette

We suggest a model of a multi-agent society of decision makers taking decisions being based on two criteria, one is the utility of the prospects and the other is the attractiveness of the considered prospects. The model is the generalization of quantum decision theory, developed earlier for single decision makers realizing one-step decisions, in two principal aspects. First, several decision makers are considered simultaneously, who interact with each other through information exchange. Second, a multistep procedure is treated, when the agents exchange information many times. Several decision makers exchanging information and forming their judgement, using quantum rules, form a kind of a quantum information network, where collective decisions develop in time as a result of information exchange. In addition to characterizing collective decisions that arise in human societies, such networks can describe dynamical processes occurring in artificial quantum intelligence composed of several parts or in a cluster of quantum computers. The practical usage of the theory is illustrated on the dynamic disjunction effect for which three quantitative predictions are made: (i) the probabilistic behavior of decision makers at the initial stage of the process is described; (ii) the decrease of the difference between the initial prospect probabilities and the related utility factors is proved; (iii) the existence of a common consensus after multiple exchange of information is predicted. The predicted numerical values are in very good agreement with empirical data.