  We consider the psychological effect of preference reversal and show that it
finds a natural explanation in the frame of quantum decision theory. When
people choose between lotteries with non-negative payoffs, they prefer a more
certain lottery because of uncertainty aversion. But when people evaluate
lottery prices, e.g. for selling to others the right to play them, they do this
more rationally, being less subject to behavioral biases. This difference can
be explained by the presence of the attraction factors entering the expression
of quantum probabilities. Only the existence of attraction factors can explain
why, considering two lotteries with close utility factors, a decision maker
prefers one of them when choosing, but evaluates higher the other one when
pricing. We derive a general quantitative criterion for the preference reversal
to occur that relates the utilities of the two lotteries to the attraction
factors under choosing versus pricing and test successfully its application on
experiments by Tversky et al. We also show that the planning paradox can be
treated as a kind of preference reversal.
