  Decisions are often based on imprecise, uncertain or vague information.
Likewise, the consequences of an action are often equally unpredictable, thus
putting the decision maker into a twofold jeopardy. Assuming that the effects
of an action can be modeled by a random variable, then the decision problem
boils down to comparing different effects (random variables) by comparing their
distribution functions. Although the full space of probability distributions
cannot be ordered, a properly restricted subset of distributions can be totally
ordered in a practically meaningful way. We call these loss-distributions,
since they provide a substitute for the concept of loss-functions in decision
theory. This article introduces the theory behind the necessary restrictions
and the hereby constructible total ordering on random loss variables, which
enables decisions under uncertainty of consequences. Using data obtained from
simulations, we demonstrate the practical applicability of our approach.
