Psychological 'double-slit experiment' in decision making: Quantum versus classical.

This paper is devoted to justification of the application of quantum probability theory to problems of cognition, psychology, and decision making. Such applications are heavily based on quantum-like representation of interference of events that is formalized with complex probability amplitudes ("mental wave functions") and the Born rule for calculation of probability. In this paper, we present universal mathematical formalization of interference of events based on the calculus of intensities of interacting processes. Generally, this formalization leads to the nonlinear law of superposition of complex probability amplitudes with quantum linear superposition as a special important case. For intensities characterized by discrete occurrence of events, the formula for interference of intensities is transferred into the quantum-like formula for interference of probabilities. We illustrate the formalism by simple examples of possible applications of the calculus of intensities of processes to decision making and economics. We show that in special cases the classical (Kolmogorov) probabilistic model can give the same results as the quantum rule of summation of probabilities.