Rational behavior under complete ignorance is described by means of requirements such as invariance of choice with respect to modifications of states of nature. Possible criteria necessarily involve intransitivities of indifference, and are incompatible with the ascribing of personal probabilities to events. Characterization of criteria shows that in first order approximation they take into account only the extremal possible outcomes of each choice; effects linked to events also come into play, although only in the second order, whereas an axiom system like that of Arrow and Hurwicz, which requires transitivity of indifference, excludes their being taken into account at all.