Quantum Decision Theory in Simple Risky Choices

International Journal of Theoretical Physics, 2019

Ellsberg thought experiments and empirical confirmation of Ellsberg preferences pose serious challenges to subjective expected utility theory (SEUT). We have recently elaborated a quantum-theoretic framework for human decisions under uncertainty which satisfactorily copes with the Ellsberg paradox and other puzzles of SEUT. We apply here the quantum-theoretic framework to the Ellsberg two-urn example, showing that the paradox can be explained by assuming a state change of the conceptual entity that is the object of the decision (decision-making, or DM, entity) and representing subjective probabilities by quantum probabilities. We also model the empirical data we collected in a DM test on human participants within the theoretic framework above. The obtained results are relevant, as they provide a line to model real life, e.g., financial and medical, decisions that show the same empirical patterns as the two-urn experiment.

Journal of Economic Psychology, 2021

Using experimental data on choices between pairs of lotteries, we compare a new parameterized Quantum Decision Theory (QDT) with Rank Dependent Utility Theory (RDU) and Cumulative Prospect Theory (CPT). At the aggregate level, CPT-based QDT outperforms. At the individual level, the considerable heterogeneity across subjects is best described by the RDU-based QDT, at odds with the conclusion using the representative agent approach. The quantum attraction factor thus plays a key role in describing subjects' behaviors at both levels. A large fraction of subjects exhibit temporal stability of asset integration attitudes. Another significant fraction of subjects are diagnosed to be using mixtures of mental models, which are elicited selectively depending on the nature of the presented choice alternatives. ✩ The raw data of the studied experiment are accessible via the Open Science Framework, using the following link: DOI 10.17605/OSF.IO/5SEMF.

2018

In this work, we propose another parametrization of Quantum Decision Theory (QDT), based on Rank Dependent Utility Theory (RDU). Using experimental data made of choices between pairs of lotteries, we then compare QDT with "classical" decision theories, RDU and Cumulative Prospect Theory (CPT). At aggregate level, assuming homogeneous preferences across subjects, we find that CPT-based QDT wins by far. At the individual level, we classify decision makers as RDU, CPT or QDT. Our major findings are the following: quantum factor plays a key-role in describing subjects’ behavior; there is a considerable heterogeneity across subjects, so that the classic representative agent approach would be completely wrong for this sample. In light of such results, mixture models are then considered as a possible extension of the present work, in order to take into account potential heterogeneity within a subject himself.

1994

We present a new approach to the old problem of how to incorporate the role of the observer in statistics. We show classical probability theory to be inadequate for this task and take refuge in the epsilon-model, which is the only model known to us capable of handling situations between quantum and classical statistics. An example is worked out and some problems are discussed as to the new viewpoint that emanates from our approach. * Published as: Aerts, D. and Aerts, S., 1995, Application of quantum statistics in psychological studies of decision processes, Foundations of Science, 1, 85 -97, and also (reprinted) as Aerts, D., Aerts, S., 1997, Application of quantum statistics in psychological studies of decision processes, in Topics in the Foundation of Statistics, eds. Van Fraassen B., Kluwer Academic, Dordrecht.

2013

Humans do not always make the most rational decisions. As studies have shown, even when logic and reasoning point in one direction, sometimes humans “walk” to the opposite route, motivated by personal bias or simply "wishful thinking." This paradoxical human behavior has resisted explanation by classical decision theory for over a decade. Scientists have shown that a quantum probability model can provide a simple explanation for human decision-making. In military, decision-making process is considered to be the most neuralgic one. With the recent interest in quantum computing and quantum information theory, there has been an effort to recast classical game theory using quantum probability amplitudes, and hence study the effect of quantum superposition, interference and entanglement on the agents’ optimal strategies. Apart from unsolved problems in quantum information theory, quantum game theory and decision –making, may be useful in studying quantum communication since tha...

Journal of Mathematical Psychology, 2016

Ambiguity and ambiguity aversion have been widely studied in decision theory and economics both at a theoretical and an experimental level. After Ellsberg's seminal studies challenging subjective expected utility theory (SEUT), several (mainly normative) approaches have been put forward to reproduce ambiguity aversion and Ellsberg-type preferences. However, Machina and other authors have pointed out some fundamental difficulties of these generalizations of SEUT to cope with some variants of Ellsberg's thought experiments, which has recently been experimentally confirmed. Starting from our quantum modeling approach to human cognition, we develop here a general probabilistic framework to model human decisions under uncertainty. We show that our quantum theoretical model faithfully represents different sets of data collected on both the Ellsberg and the Machina paradox situations, and is flexible enough to describe different subjective attitudes with respect to ambiguity. Our approach opens the way toward a quantumbased generalization of expected utility theory (QEUT), where subjective probabilities depend on the state of the conceptual entity at play and its interaction with the decision-maker, while preferences between acts are determined by the maximization of this 'state-dependent expected utility'.

SSRN Electronic Journal, 2010

In physics, at the beginning of the twentieth century it was recognized that some experiments could not be explained by the conventional classical mechanics but the same could be explained by the newly discovered quantum theory. It resulted into a new mechanics called quantum mechanics that revolutionized the scientific and technological developments. Again at the beginning of the twenty-first century, it is being recognized that some experiments related with the human decision making processes could not be explained by the conventional classical decision theory but the same could be explained by the models based on quantum mechanics. It is now recognized that we need quantum mechanics in psychology as well as in economics and finance. In this paper we attempt to advance and explain the present understanding of applicability of quantum mechanics to the human decision making processes. Using the postulates analogous to the postulates of quantum mechanics, we show the derivation of the quantum interference equation to illustrate the quantum approach. The explanation of disjunction effect experiments of Tversky and Shafir(1992) has been chosen to demonstrate the necessity of a quantum model. Further to suggest the possibility of application of the quantum theory to the business related decisions, some terms such as price operator, state of mind of the acquiring firm, etc. are introduced and discussed in context of the merger/acquisition of business firms. The possibility of the development in the areas such as quantum finance, quantum management, application of quantum mechanics to the human dynamics related with health care management, etc. is also indicated.

Operations Research, 2013

In physics, at the beginning of the twentieth century it was recognized that some experiments could not be explained by the conventional classical mechanics, but the same could be explained by the newly discovered quantum theory. It resulted in a new mechanics called quantum mechanics that revolutionized scientific and technological developments. Again, at the beginning of the twenty-first century, it is being recognized that some experiments related to the human decision-making processes could not be explained by the conventional classical decision theory but the same could be explained by the models based on quantum mechanics. It is now recognized that we need quantum mechanics in psychology as well as in economics and finance. In this paper we attempt to advance and explain the present understanding of applicability of quantum mechanics to the human decision-making processes. Using the postulates analogous to the postulates of quantum mechanics, we show the derivation of the quan...

Journal of Mathematical Economics, 2018

Because of its mathematical elegance and simplicity, manageability and predictive success, expected utility theory (EUT) provides both the normative and descriptive foundations of decision-making under uncertainty. Following distinction between 'objective uncertainty' (or 'risk') and 'subjective uncertainty' (or 'ambiguity'), von provided for an axiomatic framework which defined EUT using objective probability. and then Anscombe and Aumann (1963) further generalized EUT also in an axiomatic way. Boolean logic , and Bayesian probability theory, axiomatized by , provide for mathematical structures which have been, and currently still are, at the heart of modelling human rational behavior in the presence of uncertainty. Although the economics and finance literature supplies numerous examples where EUT can be seen to work well, the economics profession is well aware of paradoxes such as the paradox and Ellsberg's (1961) 'ambiguity aversion', and the profession is equally aware of the usefulness of non-expected utility theory in resolving some well documented empirical puzzles in finance. and provide extensive reviews of non-expected utility theory, while and Ma (2011) cover non-expected utility theory for its applications in asset pricing theory.

Journal of Mathematical Economics

The Machina thought experiments pose to major non-expected utility models challenges that are similar to those posed by the Ellsberg thought experiments to subjective expected utility theory (SEUT). We test human choices in the 'Ellsberg three-color example', confirming typical ambiguity aversion patterns, and the 'Machina 50/51 and reflection examples', partially confirming the preferences hypothesized by Machina. Then, we show that a quantum-theoretic framework for decision-making under uncertainty recently elaborated by some of us allows faithful modeling of the collected data. In the quantum-theoretic framework subjective probabilities are represented by quantum probabilities, while quantum state transformations enable representations of ambiguity aversion and subjective attitudes toward it.