Mathematical Structure of Quantum Decision Theory

TL;DR

This paper introduces a Quantum Decision Theory based on Hilbert space mathematics to explain human decision-making anomalies like the conjunction fallacy and disjunction effect, unifying various paradoxes under a quantum framework.

Contribution

It develops a novel quantum mathematical framework for decision theory that accounts for complex phenomena such as superposition, entanglement, and interference in human decision making.

Findings

Explains the violation of Savage's sure-thing principle as interference effects.

Provides a unified quantum explanation for classical decision-making paradoxes.

Shows all known anomalies can be modeled with a few quantum archetypes.

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.