Mathematical Structure of Quantum Decision Theory

Advances in Complex Systems, Vol. 13, pp. 659-698, 2010

40 Pages Posted: 8 Sep 2008 Last revised: 12 Nov 2010

See all articles by Vyacheslav I. Yukalov

Vyacheslav I. Yukalov

Joint Institute for Nuclear Research; D-MTEC, ETH Zurich

Didier Sornette

Risks-X, Southern University of Science and Technology (SUSTech); Swiss Finance Institute; ETH Zürich - Department of Management, Technology, and Economics (D-MTEC); Tokyo Institute of Technology

Date Written: September 5, 2008

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 finding straightforward explanations in the frame of the developed quantum approach.

Keywords: decision theory, quantum theory, Hilbert space, utility theory, emotions, loss aversion, uncertainty aversion, Allais paradox, independence paradox, inversion paradox, Ellsberg paradox, conjunction fallacy, disjunction effect, isolation effect

JEL Classification: D81, C02, A12

Suggested Citation

Yukalov, Vyacheslav I. and Sornette, Didier, Mathematical Structure of Quantum Decision Theory (September 5, 2008). Advances in Complex Systems, Vol. 13, pp. 659-698, 2010, Available at SSRN: https://ssrn.com/abstract=1263853

Vyacheslav I. Yukalov

Joint Institute for Nuclear Research ( email )

Bogolubov Laboratory of Theoretical Physics
Dubna, 141980
Russia

D-MTEC, ETH Zurich ( email )

Zurich
Switzerland

Didier Sornette (Contact Author)

Risks-X, Southern University of Science and Technology (SUSTech) ( email )

1088 Xueyuan Avenue
Shenzhen, Guangdong 518055
China

Swiss Finance Institute ( email )

c/o University of Geneva
40, Bd du Pont-d'Arve
CH-1211 Geneva 4
Switzerland

ETH Zürich - Department of Management, Technology, and Economics (D-MTEC) ( email )

Scheuchzerstrasse 7
Zurich, ZURICH CH-8092
Switzerland
41446328917 (Phone)
41446321914 (Fax)

HOME PAGE: http://www.er.ethz.ch/

Tokyo Institute of Technology ( email )

2-12-1 O-okayama, Meguro-ku
Tokyo 152-8550, 52-8552
Japan

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