Modeling Decision Making

Abstract

Quantum-like modeling of decision making was triggered by three types of psychological experiments that showed the conjunction and disjunction fallacies and the order effect, challenging the application of classical probability theory to cognition [1, 2, 3]. Quantum probability theory was found to be able to account for such phenomena [4, 5, 6]. The essential mathematical aspects of quantum theory that came in handy were the representation of states by vectors in a Hilbert space rather than by points in phase space and the generally non-commuting structure of the operators acting on such states. However, quantum theory was developed to deal with microscopic entities like electrons and atoms that showed coherence effects (such as interference and entanglement) absent in macroscopic objects like chairs and tables. It is far from clear how the human brain, a hot and noisy macroscopic system, can act as if it were a quantum information processor. Quantum information processing is possible only if one uses qubits or quantum bits. A qubit is the basic unit of quantum information. Unlike the classical binary bit physically realized with a two-state (on-off) device, a qubit is a two-state quantum mechanical system. It is the simplest quantum system displaying the peculiarity of quantum mechanics, namely the superposition of two orthogonal states. One can also have qutrits and other multiple state systems. These provide an inherent parallel processing capacity to quantum computers which classical computers do not have. This should enable them to solve certain problems much faster than any classical computer using the best currently known algorithms.