This paper investigates preferences over menus, i.e., sets of alternatives, to analyze a decision maker who randomizes alternatives in a menu. We identify preferences for randomization, by studying anticipated utility from the viewpoint of subjective uncertainty. The effect of randomization in one's mind stems from several cognitive or psychological effects ranging from complements between alternatives to aversion to timing of earlier decision-making. The main axiom in our analysis is a monotonic condition for preferences for randomization, named as Randomization. We show that Randomization, along with other standard axioms, axiomatically characterizes the main result, that is, a random anticipated utility representation. In the model, the decision maker's subjective belief for the effect of randomization is uniquely identified. In addition, we characterize preferences for a desire to randomization, and an aversion to randomization, respectively.