MATHEMATICAL STRUCTURE OF QUANTUM DECISION THEORY

Vyacheslav I. Yukalov and Didier Sornette
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Vyacheslav I. Yukalov: Department of Management, Technology and Economics, ETH Zürich, Zürich CH-8032, Switzerland; Bogolubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research, Dubna 141980, Russia
Didier Sornette: Department of Management, Technology and Economics, ETH Zürich, Zürich CH-8032, Switzerland; Swiss Finance Institute, c/o University of Geneva, CH 1211 Geneva 4, Switzerland

Advances in Complex Systems (ACS), 2010, vol. 13, issue 05, pages 659-698

Abstract: One of the most complex systems is the human brain whose formalized functioning is characterized by decision theory. We present a "Quantum Decision Theory" of decision-making, based on the mathematical theory of separable Hilbert spaces. This mathematical structure captures the effect of superposition of composite prospects, including many incorporated intentions, which allows us to explain a variety of interesting fallacies and anomalies that have been reported to particularize the decision-making of real human beings. The theory describes entangled decision-making, non-commutativity of subsequent decisions, and intention interference of composite prospects. We demonstrate how the violation of the Savage's sure-thing principle (disjunction effect) can be explained as a result of the interference of intentions, when making decisions under uncertainty. The conjunction fallacy is also explained by the presence of the interference terms. We demonstrate that all known anomalies and paradoxes, documented in the context of classical decision theory, are reducible to just a few mathematical archetypes, all of which allow the finding of straightforward explanations in the frame of the developed quantum approach.

Keywords: Decision theory; utility theory; paradoxes in decision-making; action interference and entanglement; action prospects; D03; D81; D83; D84 (search for similar items in EconPapers)
Date: 2010
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