Preference rankings in the face of uncertainty

An agent may have to choose between actions based on incomplete knowledge of its environment. The incomplete knowledge is modelled as the local state of the agent, which represents the set of states of the environment that the agent deems possible. A policy determines a ranking (as a total preorder) of the set of actions as a function of the local state. A policy is maximin representable when it is based on a utility function via the maximin principle. The theory of Brafman and Tennenholz on necessary and sufficient conditions for policies to be maximin representable is sharpened, extended, and related to maximax and Laplace representability.