Purely subjective Maxmin Expected Utility

The Maxmin Expected Utility decision rule suggests that the decision maker can be characterized by a utility function and a set of prior probabilities, such that the chosen act maximizes the minimal expected utility, where the minimum is taken over the priors in the set. Gilboa and Schmeidler axiomatized the maxmin decision rule in an environment where acts map states of nature into simple lotteries over a set of consequences. This approach presumes that objective probabilities exist, and, furthermore, that the decision maker is an expected utility maximizer when faced with risky choices (involving only objective probabilities). This paper presents axioms for a derivation of the maxmin decision rule in a purely subjective setting, where acts map states to points in a connected topological space. This derivation does not rely on a pre-existing notion of probabilities, and, importantly, does not assume the von Neuman & Morgenstern (vNM) expected utility model for decision under risk. The axioms employed are simple and each refers to a bounded number of variables.