Decision making when consequences are random

Abstract

The intricacy of decision making is often due to uncertainty about the data to base a decision upon, and the consequences that the decision implies. Commonly, decision options are rated based on their expected utility. This approach is intuitive and successful in many cases, but has difficulties when the utility to be associated with an action is unknown or at least uncertain. Both problems can be addressed by accepting randomness as an intrinsic part of the utility itself, leading to defining optimal decisions in terms of stochastic orders rather than upon benchmark figures (only). For one such (even total) stochastic order, we give a complete construction, accompanied by examples and procedures how to get a (stochastically optimal) decision. A discussion of how game theory can be put on top of the stochastic order, as well as how the ordering can be applied to general IT risk management closes the chapter.