A quantum probability explanation for violations of 'rational' decision theory

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.

Figure 1

(a–f) The probability of defection under the unknown condition minus the average for the two known conditions, at six time points (note that time incorporates a factor of π/2; (a) time=0.75, (b) time=1.00, (c) time=1.25, (d) time=1.50, (e) time=1.75, (f) time=2.00). Negative values (blue) typically indicate an interference effect in the predicted direction.