Quantum-like generalization of the Bayesian updating scheme for objective and subjective mental uncertainties

In this paper we develop a general quantum-like model of decision making. Here updating of probability is based on linear algebra, the von Neumann-Luders projection postulate, Born's rule, and the quantum representation of the state space of a composite system by the tensor product. This quantum-like model generalizes the classical Bayesian inference in a natural way. In our approach the latter appears as a special case corresponding to the absence of relative phases in the mental state. By taking into account a possibility of the existence of correlations which are encoded in relative phases we developed a more general scheme of decision making. We discuss natural situations inducing deviations from the classical Bayesian scheme in the process of decision making by cognitive systems: in situations that can be characterized as objective and subjective mental uncertainties. Further, we discuss the problem of base rare fallacy. In our formalism, these "irrational" (non-Bayesian) inferences are represented by quantum-like bias operations acting on the mental state. (C) 2012 Elsevier Inc. All rights reserved.