A quantum probability explanation for violations of ‘rational’ decision theory

TLDR

Two experimental tasks, the two‑stage gambling game and the Prisoner’s Dilemma, reveal violations of the sure‑thing principle that have defied classical decision theory for over a decade. The authors propose a quantum probability model, grounded in Hilbert space and Schrödinger dynamics, to explain these violations. The model is compared to an equivalent Markov model, demonstrating that the latter cannot account for the observed sure‑thing principle violations. Thus, quantum probability offers a superior framework for modeling human decision‑making.

Abstract

Two experimental tasks in psychology, the two-stage gambling game and the Prisoner's Dilemma game, show that people violate the sure thing principle of decision theory. These paradoxical findings have resisted explanation by classical decision theory for over a decade. A quantum probability model, based on a Hilbert space representation and Schrödinger's equation, provides a simple and elegant explanation for this behaviour. The quantum model is compared with an equivalent Markov model and it is shown that the latter is unable to account for violations of the sure thing principle. Accordingly, it is argued that quantum probability provides a better framework for modelling human decision-making.