Do transitive preferences always result in indifferent divisions?

The transitivity of preferences is one of the basic assumptions used in the theory of games and decisions. It is often equated with rationality of choice and is considered useful in building rankings. Intransitive preferences are considered paradoxical and undesirable. This problem is discussed by many social and natural sciences. The paper discusses a simple model of sequential game in which two players in each iteration of the game choose one of the two elements. They make their decisions in different contexts defined by the rules of the game. It appears that the optimal strategy of one of the players can only be intransitive! (the so-called \textsl{relevant intransitive strategies}.) On the other hand, the optimal strategy for the second player can be either transitive or intransitive. A quantum model of the game using pure one-qubit strategies is considered. In this model, an increase in importance of intransitive strategies is observed -- there is a certain course of the game where intransitive strategies are the only optimal strategies for both players. The study of decision-making models using quantum information theory tools may shed some new light on the understanding of mechanisms that drive the formation of types of preferences.Comment: 16 pages, 5 figure

Inconclusive quantum measurements and decisions under uncertainty

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 has been developed in analogy with the theory of quantum measurements, the inconclusive quantum measurements correspond, in Quantum Decision Theory, 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.Comment: Latex file, 16 page

Quantum Probabilities as Behavioral Probabilities

We demonstrate that behavioral probabilities of human decision makers share many common features with quantum probabilities. This does not imply that humans are some quantum objects, but just shows that the mathematics of quantum theory is applicable to the description of human decision making. The applicability of quantum rules for describing decision making is connected with the nontrivial process of making decisions in the case of composite prospects under uncertainty. Such a process involves deliberations of a decision maker when making a choice. In addition to the evaluation of the utilities of considered prospects, real decision makers also appreciate their respective attractiveness. Therefore, human choice is not based solely on the utility of prospects, but includes the necessity of resolving the utility-attraction duality. In order to justify that human consciousness really functions similarly to the rules of quantum theory, we develop an approach defining human behavioral probabilities as the probabilities determined by quantum rules. We show that quantum behavioral probabilities of humans not merely explain qualitatively how human decisions are made, but they predict quantitative values of the behavioral probabilities. Analyzing a large set of empirical data, we find good quantitative agreement between theoretical predictions and observed experimental data.Comment: Latex file, 32 page

Evolutionary Processes in Quantum Decision Theory

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.Comment: Latex file, 39 page

Quantum Economics: A Systematic Literature Review

In the 21st century, various socio-economic crises have revealed that traditional economic science and (neo)classical thinking are unable to explain all the complexity of current economic problems, therefore the application of more complex and non-trivial economic concepts is gaining relevance. In addition to behavioral and evolutionary economic thinking, models of quantum economics have been developed in recent years, which allow solving economic problems, using mainly quantum thinking and the principles of quantum physics, in particular particle-wave dualism, the principle of uncertainty, the absence of a subject-object distinction, superposition and confusion. The article addresses 3 research questions (RQ). According to RQ1, the paper finds that quantum economics research is dominated by the following topics: quantum economics, quantum finance, quantum decision making, and quantum game theory. According to these four thematic descriptors, the article carries out a systematic modern review of scientific works in the period from 1978 to 2022 (if only 50 works were published in 1978-1999, then in 2000-2022 already 3430), with an emphasis on the most cited (Google Scholar) English-language journal articles. The analysis showed that articles on this topic are published mainly in journals of a non-economic profile, that the peaks of publication activity occur at times of powerful socio-economic upheavals (for example, the dot.com bubble, the substandard/financial crisis, the European debt crisis, the coronavirus pandemic, etc.). In accordance with RQ2, the article defines the key characteristics of the quantum economic model: in contrast to neoclassical economics (based on mechanistic classical physics, is rational and deterministic, with the help of the invisible hand of the market it leads to a stable equilibrium), the quantum approach, on the contrary, considers the economy as more complex, empirically oriented, uncertain, probabilistic, superpositional, as an archetypal example of a quantum social system that has its own versions of duality, measurement, and entanglement. According to RQ 3, the article determines to what extent quantum economics can update (neo)classical economics (integration of new ontological premises into economic thinking, more experimental and practical approach, connection between the concept of entanglement and sustainable development, management of financial risks based on the concept of quantum probability, rethinking the concept of randomness by quantum probability, introduction of quantum money, equilibrium using quantum games, etc.)