  We study a sufficiently general regret criterion for choosing between two
probabilistic lotteries. For independent lotteries, the criterion is consistent
with stochastic dominance and can be made transitive by a unique choice of the
regret function. Together with additional (and intuitively meaningful)
super-additivity property, the regret criterion resolves the Allais' paradox
including the cases were the paradox disappears, and the choices agree with the
expected utility. This superadditivity property is also employed for
establishing consistency between regret and stochastic dominance for dependent
lotteries. Furthermore, we demonstrate how the regret criterion can be used in
Savage's omelet, a classical decision problem in which the lottery outcomes are
not fully resolved. The expected utility cannot be used in such situations, as
it discards important aspects of lotteries.
