Quantum Decision Theory

Quantum decision theory of decision making, based on the mathematical theory of separable Hilbert spaces, is presented. This mathematical structure allows us to quantitatively explain a variety of interesting fallacies and anomalies that have been reported to characterize the decision making of real human beings. The theory describes entangled decision making, non-commutativity of subsequent decisions, and intention interference. We demonstrate how the disjunction effect can be explained quantitatively by the intention interference, when making decisions under uncertainty. The sign and amplitude of the disjunction effect 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 intention interference. A series of experiments are analysed and shown to be in perfect quantitative agreement with apriori evaluation of the disjunction effect and conjunction fallacy, without any adjustable or fitting parameters.