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Kagaku tetsugaku

Rationality in quantum decision theory

Taiki Takahashi

Published Jan 1, 2013• 1 citation
Publisher

Abstract

One of the recent promising theoretical approaches to accounts of the violation of rationality (or generalize the concept of rationality) in human decision making is quantum decision theory. In this expository review article, I introduce 1) problems of rationality in quantum decision theory and 2) relationships between psychophysics, theoretical neuroscience including neuroeconomics, and quantum decision theory.

DOI
10.4216/jpssj.46.17

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One of the recent promising theoretical approaches to accounts of the violation of rationality (or generalize the concept of rationality) in human decision making is quantum decision theory. In this expository review article, I introduce 1) problems of rationality in quantum decision theory and 2) relationships between psychophysics, theoretical neuroscience including neuroeconomics, and quantum decision theory.
Quantum theory has inspired many new ideas for understanding Cognition and decision making. Given the nascent state of this field, many new challenges still remain. What are the strengths and unique contributions of these ideas? What are likely next steps in its development? How can it be applied to practical problems in cognitive science? Is this a rational or an irrational system of reasoning? What, if any, are its connections to neuroscience? Should the hard problem of consciousness be considered? These are questions that we try to address in this chapter, albeit at times in a limited way. We end with a debate with a fictitious skeptic (actually previous reviewers) of these ideas. Let us start by reviewing what we have covered so far. Contributions to cognition and decision We begin by summarizing the conclusions reached in previous chapters regarding the usefulness of quantum theory for modelling phenomena in cognition and decision. Chapter 1 provided some motivation and Chapter 2 provided a theoretical introduction to quantum theory. Chapter 3 presented a quantum model to account for question order effects on survey research. An exact and parameter-free test was derived from the model, which produced surprisingly accurate predictions for results obtained from three different large Gallup poll survey studies. Chapter 4 described a quantum model of probability judgments to account for findings that produce violations of classic probability theory, including conjunction and disjunction fallacies and order effects on inference.
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 that can be considered as a game where the objective is to maximize effective communication. This paper discusses the idea of using quantum theory to decision making. 1 HellemicArmy 14, Kanigos Str., Piraeus 18534, Greece.
The review presents the basics of quantum decision theory, with an emphasis on temporary processes in decision making. The aim is to explain the principal points of the theory. How an operationally-testable, rational choice between alternatives differs 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.
This article presents a general framework that allows irrational decision making to be theoretically investigated and simulated. Rationality in human decision making under uncertainty is normatively prescribed by the axioms of probability theory in order to maximize utility. However, substantial literature from psychology and cognitive science shows that human decisions regularly deviate from these axioms. Bistable probabilities are proposed as a principled and straight forward means for modeling (ir)rational decision making, which occurs when a decision maker is in "two minds". We show that bistable probabilities can be formalized by positive-operator-valued projections in quantum mechanics. We found that (1) irrational decision making necessarily involves a wider spectrum of causal relationships than rational decision making, (2) the accessible information turns out to be greater in irrational decision making when compared to rational decision making, and (3) irrational decision making is quantum-like because it violates the Bell-Wigner polytope.
Of the three faculties of subjectivity, the empirical case for quantum cognition is the strongest. In the past decade a rapidly growing body of scholarship has emerged at the intersection of mathematical psychology and physics that not only models cognition in explicitly quantum terms, but has rigorously tested these models as well. While it remains to be seen how mainstream psychologists will respond, “quantum decision theory” has clearly come of age. Moreover, at the same time an almost completely independent literature has emerged on quantum game theory as well. This work is more in a purely formal vein and thus less well tested against real data, although its predictions about how people should behave in quantum games appear to conform to what experimental game theorists have found. I briefly take up quantum game theory at the end of this chapter, but my main focus will be on its decision-theoretic cousin. Quantum consciousness theory suggests that human beings are literally walking wave functions. Most quantum decision theorists would not go that far, and indeed – perhaps wary of controversy – they generally barely mention quantum consciousness, and then only to emphasize that they are making no claims about what is going on deep inside the brain (much less about consciousness), but are only interested in behavior. Instead, they have motivated their work in two other ways. First, they have highlighted the intuitive fit between quantum theory's indeterminism and the probabilistic character of human behavior. If we were founding the social sciences today and started – without metaphysical prejudice – by looking for useful models in physics, then quantum models would be a much more obvious import than classical ones. Second, quantum decision theorists have argued that their model can explain long-standing anomalies in human behavior under uncertainty. Beyond that they have remained agnostic about quantum consciousness, which makes quantum decision theory a form of what is called “weak” or “generalized” quantum theory, in which the formalism is detached from its physical basis and used simply as a tool to describe phenomena.
Artificial Intelligence is set to encompass additional decision space that has traditionally been the purview of humans. However, this decision space remains contested. Incongruencies between artificial intelligence and human rationalization processes introduce uncertainties in human decision-making, which require new conceptualizations that capture these distinct types of uncertainties. Hence, developing new ways to model human and artificial intelligence interactions are necessary to account for such uncertainties and improve situation awareness and decision-making. In this paper, we outline current conceptualizations of human and machine rationalities. Next, we offer the concept of rational prediction deviations (via quantum probability theory) for capturing uncertainty in situational awareness. Lastly, we propose a human-in-the-loop construct to explicate how applications of quantum probability theory in decision science can ameliorate situation awareness models by providing a novel way to capture distinct dynamics of decision making.