Quantum Decision Theory

We present a “quantum decision theory” (QDT) of decision making based on the mathematical theory of separable Hilbert spaces on the continuous field of complex numbers. This mathematical structure captures the effect of superposition of composite prospects, including many incorporated intentions, which allows us to describe a variety of interesting fallacies and anomalies that have been reported to characterize the decision making characteristics of real human beings. QDT characterizes entangled decision making, non-commutativity of subsequent decisions, and intention interference. These features, although being quantum in their description, have natural and concrete transparent interpretations. We demonstrate how the violation of Savage’s sure-thing principle (disjunction effect) can be explained quantitatively as a result of the interference of intentions, when making decisions under uncertainty. The sign and amplitude of the disjunction effects in experiments are accurately predicted using a theorem of interference alternation that we derive, which connects aversion-to-uncertainty to the appearance of negative interference terms suppressing the probability of actions. The conjunction fallacy is also explained by the presence of the interference terms. A series of experiments are analysed and shown to be in perfect agreement with a priori evaluation of interference effects, without adjustable parameter: we predict that, on average, the classical probability estimations for actions are reduced by 0.25 in the presence of competition between different intentions and in the presence of uncertainty. This quasi-universal “interference-quarter law” is found in remarkable agreement with the available experiments on the disjunction and conjunction effects. The conjunction fallacy is also shown to be a sufficient condition for the disjunction effect and novel experiments testing the combined interplay between the two effects are suggested.