Physics of risk and uncertainty in quantum decision making

The Quantum Decision Theory (QDT) developed recently by the authors is applied to clarify the role of risk and uncertainty in decision making and in particular in relation to the phenomenon of dynamic inconsistency. By formulating this notion in precise mathematical terms, we distinguish three types of inconsistency: time inconsistency, planning paradox, and inconsistency occurring in some discounting effects. While time inconsistency is well accounted for in classical decision theory, the planning paradox is in contradiction with classical utility theory. It finds a natural explanation in the frame of QDT. Different types of discounting effects are analyzed and shown to enjoy a straightforward explanation within QDT. We also introduce a general methodology based on self-similar approximation theory for deriving the evolution equations for the probabilities of future prospects. This provides a novel classification of possible discount factors, which include the previously known cases (exponential or hyperbolic discounting), but also predicts a novel class of discount factors that do not decay to zero for very large future time horizons. This class may be useful to deal with very long-term discounting situations associated with intergenerational public policy choices, encompassing issues such as global warming and nuclear waste disposal. PACS: 89.65.-3 Social and economic systems 89.70.Hj Communication complexity 89.75.-k Complex systems 03.67.Hk Quantum communication e-mail: [email protected] b e-mail: [email protected]