  We study a generalized family of stochastic orders, semiparametrized by a
distortion function H, namely H-distorted stochastic dominance, which may
determine a continuum of dominance relations from the first- to the
second-order stochastic dominance (and beyond). Such a family is especially
suitable for representing a decision maker's preferences in terms of risk
aversion and may be used in those situations in which a strong order does not
have enough discriminative power, whilst a weaker one is poorly representative
of some classes of decision makers. In particular, we focus on the class of
power distortion functions, yielding power-distorted stochastic dominance,
which seems to be particularly appealing owing to its computational simplicity
and some interesting statistical interpretations. Finally, we characterize
distorted stochastic dominance in terms of distortion functions yielding
isotonic classes of distorted expectations.
