We analyze relations between two methods frequently used for modeling the c
hoice among uncertain outcomes: stochastic dominance and mean-risk approach
es. New necessary conditions for stochastic dominance are developed. These
conditions compare values of a certain functional, which contains two compo
nents: the expected value of a random outcome and a risk term represented b
y the central semideviation of the corresponding degree. If the weight of t
he semideviation in the composite objective does not exceed the weight of t
he expected value, maximization of such a functional yields solutions which
are efficient in terms of stochastic dominance. The results are illustrate
d graphically.