  The Quantum Decision Theory, 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 the Quantum Decision Theory. Different types of discounting
effects are analyzed and shown to enjoy a straightforward explanation within
the suggested theory. 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 decay to a strictly positive constant 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.
