Preference under risk in the presence of indistinguishable probabilities

Lorentziadis, Panos L.

doi:10.1007/s12351-013-0132-7

Cited by 3 publications

(4 citation statements)

References 53 publications

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“…There have been many discussions concerning choices between similar alternatives with close utilities or close probabilities, such that the choice becomes hard to make [55]- [58]. We refer to such situations as "irresolute".…”

Section: B Choice Between Two Prospectsmentioning

confidence: 99%

Quantitative Predictions in Quantum Decision Theory

Yukalov

Sornette

2018

IEEE Trans. Syst. Man Cybern, Syst.

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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.

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Section: B Choice Between Two Prospectsmentioning

confidence: 99%

Quantitative Predictions in Quantum Decision Theory

Yukalov

Sornette

2018

IEEE Trans. Syst. Man Cybern, Syst.

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“…In contrast, in our approach, the imposed conditions are introduced according to general theoretical arguments, but not fitted afterwards. Thus, the threshold of one percent follows from the requirement that the distance between two alternatives be invariant with respect to the definition of the distance measure [113][114][115][116]. And the Bernoulli distribution is the usual prior distribution under conditions (25) and (26) in standard inference tasks [117][118][119].…”

Section: Analysis For a Large Recent Set Of Empirical Datamentioning

confidence: 99%

“…More rigorously, the threshold difference, when the difference (22) is smaller than some critical value below which the lotteries can be treated as almost equivalent, can be justified in the following way. In psychology and operation research, to quantify the similarity or closeness of two alternatives f 1 and f 2 with close utilities or close probabilities, one introduces [113][114][115][116] the measure of distance between alternatives as | f 1 − f 2 | m with m > 0. In applications, one employs different values of the exponent m, getting the linear distance for m = 1, quadratic distance for m = 2, and so on.…”

Section: Difficult or Easy Choicementioning

confidence: 99%

Quantum Probabilities as Behavioral Probabilities

Yukalov

Sornette

2017

Entropy

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Abstract: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 do 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.Keywords: quantum probability; quantum decision making; behavioral probability; interference and coherence; irrationality measure; lotteries GoalsQuantum theory is one of the most fascinating and successful constructs in the intellectual history of mankind. It applies to light and matter, from the smallest scales so far explored, up to mesoscopic scales. It is also a necessary ingredient for understanding the evolution of the universe. It has given rise to an impressive number of new technologies. Additionally, in recent years, it has been applied to several branches of science, which have previously been analyzed by classical means, such as quantum information processing and quantum computing [1][2][3] and quantum games [4][5][6][7].Our goal here is to demonstrate that the applicability of quantum theory can be extended in one more direction, to the theory of decision making, thus generalizing classical utility theory. This generalization allows us to characterize the behavior of real decision makers, who, when making decisions, evaluate not only the utility of the given prospects, but also are influenced by their respective attractiveness. We show that behavioral probabilities of human decision makers can be modeled by quantum probabilities.We are perfectly aware that, in the philosophical interpretation of quantum theory, there are yet a number of unsettled problems. These have triggered active discussions that started with Einstein's

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“…Leland [41] noted limited abilities of individuals to discriminate close probabilities. Lorentziadis [42] introduced division of probabilities into ranges to reflect coarsened treatment of probabilities. This approach requires an individual to discriminate very close probabilities located of different sides of the range divides (this does not seem realistic but preserves transitivity).…”

Section: Risks and Benefitsmentioning

confidence: 99%

Intransitivity in Theory and in the Real World

Klimenko

2015

Entropy

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This work considers reasons for and implications of discarding the assumption of transitivity-the fundamental postulate in the utility theory of von Neumann and Morgenstern, the adiabatic accessibility principle of Caratheodory and most other theories related to preferences or competition. The examples of intransitivity are drawn from different fields, such as law, biology and economics. This work is intended as a common platform that allows us to discuss intransitivity in the context of different disciplines. The basic concepts and terms that are needed for consistent treatment of intransitivity in various applications are presented and analysed in a unified manner. The analysis points out conditions that necessitate appearance of intransitivity, such as multiplicity of preference criteria and imperfect (i.e., approximate) discrimination of different cases. The present work observes that with increasing presence and strength of intransitivity, thermodynamics gradually fades away leaving space for more general kinetic considerations. Intransitivity in competitive systems is linked to complex phenomena that would be difficult or impossible to explain on the basis of transitive assumptions. Human preferences that seem irrational from the perspective of the conventional utility theory, become perfectly logical in the intransitive and relativistic framework suggested here. The example of competitive simulations for the risk/benefit dilemma demonstrates the significance of intransitivity in cyclic behaviour and abrupt changes in the system. The evolutionary intransitivity parameter, which is introduced in the Appendix, is a general measure of intransitivity, which is particularly useful in evolving competitive systems.

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Preference under risk in the presence of indistinguishable probabilities

Cited by 3 publications

References 53 publications

Quantitative Predictions in Quantum Decision Theory

Quantitative Predictions in Quantum Decision Theory

Quantum Probabilities as Behavioral Probabilities

Intransitivity in Theory and in the Real World

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