A Characterization of Optimality Criteria for Decision Making under Complete Ignorance

In this paper we present a model for decision making under complete ignorance. By complete ignorance it is meant that all that is known is the set of possible consequences associated to each action. Especially there is no set of states that can be enumerated in order to compare actions. We give two natural axioms for rational decision making under complete ignorance. We show that the optimality criteria satisfying these two axioms are the ones which consider only the extremal consequences of actions. We compare our axioms with related ones from the literature.