 Levi in fact tells a more complicated story about what a decision-maker is permitted to choose, in terms of a procedure that rules out successively more and more options. First, the procedure selects from all the options just the ones that are E-admissible. Next, the procedure selects from the E-admissible options just the ones that are P-admissible: options that “do best” at preserving the E-admissible options (the idea being that a rational agent should keep her options open). Finally, the procedure selects from the P-admissible options just the ones that are S-admissible: options that maximize the minimum utility. (Note that this last step involves maximin, not Γ-maximin.)