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Quantum Reports
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The Close Connection between Economics and Quantum Theory: A Topological...
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The Close Connection between Economics and Quantum Theory: A Topological Exploration

A special issue of Quantum Reports (ISSN 2624-960X).

Deadline for manuscript submissions: closed (31 July 2021) | Viewed by 23173

Special Issue Editors

Prof. Dr. Graciela Chichilnisky

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Guest Editor
Department of Economics, School of Arts and Sciences, Columbia University, 420 West 118th Street, New York, NY 10027, USA
Interests: quantum axioms; topology; mathematical economics; international trade and development; social choice; environmental economics
Prof. Dr. Peter M. Eisenberger

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Guest Editor
Department of Earth and Environmental Sciences, Columbia University, 116th and Broadway, New York, NY 10027, USA
Interests: quantum entanglement; global environmental issues; direct air capture of CO2; material physics; X-ray observations
Prof. Dr. Emmanuel Haven

E-Mail Website
Guest Editor
Faculty of Business Administration, Memorial University of Newfoundland, St. John’s, NL A1C 5S7, Canada
Interests: quantum models in social sciences; pilot-wave theory; expected utility theory; financial non-arbitrage theorem; wavelet method; option pricing
Prof. Dr. Andrei Khrennikov

E-Mail Website
Guest Editor
International Center for Mathematical Modeling in Physics and Cognitive Sciences, Linnaeus University, SE-351 95 Växjö, Sweden
Interests: quantum foundations; information; probability; contextuality; applications of the mathematical formalism of quantum theory outside of physics: cognition, psychology, decision making, economics, finances, and social and political sciences; p-adic numbers; p-adic and ultrametric analysis; dynamical systems; p-adic theoretical physics; utrametric models of cognition and psychological behavior; p-adic models in geophysics and petroleum research
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

What is the key tenet that rationalizes why quantum formalism in social science and especially in social choice and decision-making can be used? This is a central question that has not been previously answered. In classic physics, events, when seen as sets in a sigma-algebra, are described by one sample space with a single basis of coordinates (one framework) as in classical probability. The concept of ‘unicity’ essentially indicates that a single framework can describe all observed events. However, in decision-making, there is no reason to believe there is only one framework, which can capture all events.

This Special Issue will collect research that is being performed around applying elements of the formalism of quantum mechanics to the social sciences. There will be a particular focus on the key tenet(s) that rationalize(s) why the quantum formalism can be used in economics (in social choice and decision-making). As a central objective, this Special Issue will rigorously explore the foundational connections between economics and quantum theory.

Prof. Dr. Graciela Chichilnisky
Prof. Dr. Peter Eisenberger
Prof. Dr. Emmanuel Haven
Prof. Dr. Andrei Khrennikov
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Quantum Reports is an international peer-reviewed open access quarterly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 1400 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • decision making
  • social choice
  • sigma-algebra
  • classical probability
  • quantum probability
  • unicity

Published Papers (7 papers)

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20 pages, 1108 KiB  
Article
The Topology of Quantum Theory and Social Choice
by Graciela Chichilnisky
Quantum Rep. 2022, 4(2), 201-220; https://0-doi-org.brum.beds.ac.uk/10.3390/quantum4020014 - 16 Jun 2022
Viewed by 2655
Abstract
Based on the axioms of quantum theory, we identify a class of topological singularities that encode a fundamental difference between classic and quantum probability, and explain quantum theory’s puzzles and phenomena in simple mathematical terms so they are no longer ‘quantum paradoxes’. The [...] Read more.
Based on the axioms of quantum theory, we identify a class of topological singularities that encode a fundamental difference between classic and quantum probability, and explain quantum theory’s puzzles and phenomena in simple mathematical terms so they are no longer ‘quantum paradoxes’. The singularities provide also new experimental insights and predictions that are presented in this article and establish a surprising new connection between the physical and social sciences. The key is the topology of spaces of quantum events and of the frameworks postulated by these axioms. These are quite different from their counterparts in classic probability and explain mathematically the interference between quantum experiments and the existence of several frameworks or ‘violation of unicity’ that characterizes quantum physics. They also explain entanglement, the Heisenberg uncertainty principle, order dependence of observations, the conjunction fallacy and geometric phenomena such as Pancharatnam–Berry phases. Somewhat surprisingly, we find that the same topological singularities explain the impossibility of selecting a social preference among different individual preferences: which is Arrow’s social choice paradox: the foundations of social choice and of quantum theory are therefore mathematically equivalent. We identify necessary and sufficient conditions on how to restrict experiments to avoid these singularities and recover unicity, avoiding possible interference between experiments and also quantum paradoxes; the same topological restriction is shown to provide a resolution to the social choice impossibility theorem of Chichilnisky. Full article
(This article belongs to the Special Issue The Close Connection between Economics and Quantum Theory: A Topological Exploration)
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8 pages, 254 KiB  
Article
Application of Quantum Cognition to Judgments for Medical Decisions
by Sheng Yi, Meijuan Lu and Jerome Busemeyer
Quantum Rep. 2022, 4(2), 193-200; https://0-doi-org.brum.beds.ac.uk/10.3390/quantum4020013 - 19 Apr 2022
Viewed by 2396
Abstract
The psychology of judgment and decision making can provide useful guidance to the task of medical decision making. More specifically, we describe how a new approach to judgment and decisions, based on quantum probability theory, can shed new light on seemingly irrational judgments, [...] Read more.
The psychology of judgment and decision making can provide useful guidance to the task of medical decision making. More specifically, we describe how a new approach to judgment and decisions, based on quantum probability theory, can shed new light on seemingly irrational judgments, as well as indicate ways to ameliorate these judgment errors. Five different types of probability judgment errors that occur in medical decisions are reviewed. For each one, we provide a simple account using theory from quantum cognition. We conclude by drawing the implications of quantum cognition for ameliorating these common medical probability judgment errors. Full article
(This article belongs to the Special Issue The Close Connection between Economics and Quantum Theory: A Topological Exploration)
8 pages, 272 KiB  
Article
Socio-Economic Sciences: Beyond Quantum Math-like Formalisms
by Vikram Athalye and Emmanuel Haven
Quantum Rep. 2021, 3(4), 656-663; https://0-doi-org.brum.beds.ac.uk/10.3390/quantum3040041 - 07 Oct 2021
Cited by 2 | Viewed by 3770
Abstract
Since the beginning of the 21st century, a new interdisciplinary research movement has started, which aims at developing quantum math-like (or simply quantum-like) models to provide an explanation for a variety of socio-economic processes and human behaviour. By making use of [...] Read more.
Since the beginning of the 21st century, a new interdisciplinary research movement has started, which aims at developing quantum math-like (or simply quantum-like) models to provide an explanation for a variety of socio-economic processes and human behaviour. By making use of mainly the probabilistic aspects of quantum theory, this research movement has led to many important results in the areas of decision-making and finance. In this article, we introduce a novel and more exhaustive approach, to analyze the socio-economic processes and activities, than the pure quantum math-like modelling approach, by taking into account the physical foundations of quantum theory. We also provide a plausibility argument for its exhaustiveness in terms of what we can expect from such an approach, when it is applied to, for example, a generic socio-economic decision process. Full article
(This article belongs to the Special Issue The Close Connection between Economics and Quantum Theory: A Topological Exploration)
13 pages, 390 KiB  
Article
An Application of Quantum Logic to Experimental Behavioral Science
by Louis Narens
Quantum Rep. 2021, 3(4), 643-655; https://0-doi-org.brum.beds.ac.uk/10.3390/quantum3040040 - 07 Oct 2021
Viewed by 2266
Abstract
In 1933, Kolmogorov synthesized the basic concepts of probability that were in general use at the time into concepts and deductions from a simple set of axioms that said probability was a σ-additive function from a boolean algebra of events into [0, [...] Read more.
In 1933, Kolmogorov synthesized the basic concepts of probability that were in general use at the time into concepts and deductions from a simple set of axioms that said probability was a σ-additive function from a boolean algebra of events into [0, 1]. In 1932, von Neumann realized that the use of probability in quantum mechanics required a different concept that he formulated as a σ-additive function from the closed subspaces of a Hilbert space onto [0,1]. In 1935, Birkhoff & von Neumann replaced Hilbert space with an algebraic generalization. Today, a slight modification of the Birkhoff-von Neumann generalization is called “quantum logic”. A central problem in the philosophy of probability is the justification of the definition of probability used in a given application. This is usually done by arguing for the rationality of that approach to the situation under consideration. A version of the Dutch book argument given by de Finetti in 1972 is often used to justify the Kolmogorov theory, especially in scientific applications. As von Neumann in 1955 noted, and his criticisms still hold, there is no acceptable foundation for quantum logic. While it is not argued here that a rational approach has been carried out for quantum physics, it is argued that (1) for many important situations found in behavioral science that quantum probability theory is a reasonable choice, and (2) that it has an arguably rational foundation to certain areas of behavioral science, for example, the behavioral paradigm of Between Subjects experiments. Full article
(This article belongs to the Special Issue The Close Connection between Economics and Quantum Theory: A Topological Exploration)
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23 pages, 401 KiB  
Article
Contextuality in Neurobehavioural and Collective Intelligence Systems
by William Sulis
Quantum Rep. 2021, 3(4), 592-614; https://0-doi-org.brum.beds.ac.uk/10.3390/quantum3040038 - 25 Sep 2021
Cited by 6 | Viewed by 2973
Abstract
Contextuality is often described as a unique feature of the quantum realm, which distinguishes it fundamentally from the classical realm. This is not strictly true, and stems from decades of the misapplication of Kolmogorov probability. Contextuality appears in Kolmogorov theory (observed in the [...] Read more.
Contextuality is often described as a unique feature of the quantum realm, which distinguishes it fundamentally from the classical realm. This is not strictly true, and stems from decades of the misapplication of Kolmogorov probability. Contextuality appears in Kolmogorov theory (observed in the inability to form joint distributions) and in non-Kolmogorov theory (observed in the violation of inequalities of correlations). Both forms of contextuality have been observed in psychological experiments, although the first form has been known for decades but mostly ignored. The complex dynamics of neural systems (neurobehavioural regulatory systems) and of collective intelligence systems (social insect colonies) are described. These systems are contextual in the first sense and possibly in the second as well. Process algebra, based on the Process Theory of Whitehead, describes systems that are generated, transient, open, interactive, and primarily information-driven, and seems ideally suited to modeling these systems. It is argued that these dynamical characteristics give rise to contextuality and non-Kolmogorov probability in spite of these being entirely classical systems. Full article
(This article belongs to the Special Issue The Close Connection between Economics and Quantum Theory: A Topological Exploration)
8 pages, 259 KiB  
Article
The Color of Money: Threshold Effects in Quantum Economics
by David Orrell
Quantum Rep. 2021, 3(2), 325-332; https://0-doi-org.brum.beds.ac.uk/10.3390/quantum3020020 - 14 May 2021
Cited by 5 | Viewed by 2948
Abstract
Many cognitive phenomena of the sort studied by behavioral psychologists show evidence of a threshold effect, where a certain minimum impulse is required in order to produce a change. An example is the phenomenon of preference reversal, where a change in context affects [...] Read more.
Many cognitive phenomena of the sort studied by behavioral psychologists show evidence of a threshold effect, where a certain minimum impulse is required in order to produce a change. An example is the phenomenon of preference reversal, where a change in context affects a decision, but only if the effect on perceived utility is sufficiently large. Similar threshold effects play a role in the endowment effect, where the change of context from owning to buying something induces a step change in its perceived value, or the ultimatum game, where people demand a certain minimum threshold amount before a deal can be accepted. The situation is similar to the photoelectric experiment in physics, where a minimum threshold of energy from a photon is required in order to dislodge an electron from an atom. In physics, this quantum of energy is written as the product of Planck’s constant and frequency. This paper uses the concept of entropic force to derive a similar expression for quantum economics. The theory is applied to a range of cognitive and economic phenomena exhibiting a threshold effect. Full article
(This article belongs to the Special Issue The Close Connection between Economics and Quantum Theory: A Topological Exploration)
11 pages, 497 KiB  
Article
What Is Rational and Irrational in Human Decision Making
by Emmanuel M. Pothos, Oliver J. Waddup, Prince Kouassi and James M. Yearsley
Quantum Rep. 2021, 3(1), 242-252; https://0-doi-org.brum.beds.ac.uk/10.3390/quantum3010014 - 19 Mar 2021
Cited by 3 | Viewed by 4450
Abstract
There has been a growing trend to develop cognitive models based on the mathematics of quantum theory. A common theme in the motivation of such models has been findings which apparently challenge the applicability of classical formalisms, specifically ones based on classical probability [...] Read more.
There has been a growing trend to develop cognitive models based on the mathematics of quantum theory. A common theme in the motivation of such models has been findings which apparently challenge the applicability of classical formalisms, specifically ones based on classical probability theory. Classical probability theory has had a singularly important place in cognitive theory, because of its (in general) descriptive success but, more importantly, because in decision situations with low, equivalent stakes it offers a multiply justified normative standard. Quantum cognitive models have had a degree of descriptive success and proponents of such models have argued that they reveal new intuitions or insights regarding decisions in uncertain situations. However, can quantum cognitive models further benefit from normative justifications analogous to those for classical probability models? If the answer is yes, how can we determine the rational status of a decision, which may be consistent with quantum theory, but inconsistent with classical probability theory? In this paper, we review the proposal from Pothos, Busemeyer, Shiffrin, and Yearsley (2017), that quantum decision models benefit from normative justification based on the Dutch Book Theorem, in exactly the same way as models based on classical probability theory. Full article
(This article belongs to the Special Issue The Close Connection between Economics and Quantum Theory: A Topological Exploration)
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