A comment on the axiomatics of the Maxmin Expected Utility model

Maxmin Expected Utility was first axiomatized by Gilboa and Schmeidler (1989) in an Anscombe–Aumann setup Anscombe and Aumann (1963) which includes exogenous probabilities. The model was later axiomatized in a purely subjective setup, where no exogenous probabilities are assumed. The purpose of this note is to show that in all these axiomatizations, the only assumptions that are needed are the basic ones that are used to extract a cardinal utility function, together with the two typical Maxmin assumptions, Uncertainty Aversion and Certainty Independence, applied only to 0.5:0.5 mixtures. For the purely subjective characterizations, this means that assumptions involving an unbounded number of variables can be replaced with assumptions that involve only a finite number thereof.