Quantum cognition and bounded rationality

Abstract

We consider several puzzles of bounded rationality. These include the Allais-and Ellsberg paradox, the disjunction effect, and related puzzles. We argue that the present account of quantum cognition-taking quantum probabilities rather than classical probabilities-can give a more systematic description of these puzzles than the alternate treatments in the traditional frameworks of bounded rationality. Unfortunately, the quantum probabilistic treatment does not always provide a deeper understanding and a true explanation of these puzzles. One reason is that quantum approaches introduce additional parameters which possibly can be fitted to empirical data but which do not necessarily explain them. Hence, the phenomenological research has to be augmented by responding to deeper foundational issues. In this article, we make the general distinction between foundational and phenomenological research programs, explaining the foundational issue of quantum cognition from the perspective of operational realism. This framework is motivated by assuming partial Boolean algebras (describing particular perspectives). They are combined into a uniform system (i.e. orthomodular lattice) via a mechanism preventing the simultaneous realization of perspectives. Gleason's theorem then automatically leads to a distinction between probabilities that are defined by pure states and probabilities arising from the statistical mixture of pure states. This formal distinction relates to the conceptual distinction between risk and ignorance. Another outcome identifies quantum aspects in dynamic B Reinhard Blutner

Quantum approaches to music cognition

“…Cosine similarity is closely related to quantum similarity Trueblood 2015) in the framework of quantum cognition models (Busemeyer and Bruza 2012, Blutner and beim Graben 2016. Therefore, we express the attraction value p(x) through a continuous "wave function" ψ(x) upon the circle of fifths which constitutes the onedimensional "tonal configuration space" of our quantum model.…”

Explaining versus describing human decisions: Hilbert space structures in decision theory

“…Bounded rationality models give good predictions in a variety of circumstances. However, despite their simplicity and intuitive character, these models lack a unitary methodology, as well as deeper explanations, and thus provide a very fragmented picture of cognitive phenomena [9].…”

“…Some authors identify the notion of "state" with the notion of "belief state" of the individual participating in the cognitive experiment, e.g., taking the decision (see, e.g.,[4,9,15]). We instead neatly distinguish states from measurements here.…”

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“…For these reasons, it turns out that quantum probability theory is not only useful in physics, but it also useful for psychology (Pothos & Busemeyer, 2013; Blutner & beim Graben, 2016; Bruza et al, 2015). Note that we are not necessarily proposing that the brain is some kind of quantum computer (see, e.g., Hameroff, 2013 for an example of this interpretation), and instead, we are only using the mathematical principles of quantum theory to account for human behavior.…”