Quantitative Predictions in Quantum Decision Theory

Quantum decision theory, advanced earlier by the authors, and illustrated for lotteries with gains, is generalized to the games containing lotteries with gains as well as losses. The mathematical structure of the approach is based on the theory of quantum measurements, which makes this approach relevant both for the description of decision making of humans and the creation of artificial quantum intelligence. General rules are formulated allowing for the explicit calculation of quantum probabilities representing the fraction of decision makers preferring the considered prospects. This provides a method to quantitatively predict decision-maker choices, including the cases of games with high uncertainty for which the classical expected utility theory fails. The approach is applied to experimental results obtained on a set of lottery gambles with gains and losses. Our predictions, involving no fitting parameters, are in very good agreement with experimental data. The use of quantum decision making in game theory is described. A principal scheme of creating quantum artificial intelligence is suggested.