How should administrative law cope with genuine uncertainty, in which probabilities cannot be attached to outcomes? I argue that there is an important category of agency decisions under uncertainty in which it is rational to be arbitrary. Rational arbitrariness arises when no first-order reason can be given for the agency’s choice, yet the agency has valid second-order reasons to make a particular choice. When these conditions obtain, even coin flipping may be a perfectly rational strategy of decision making for agencies. Courts should defer to rationally arbitrary decisions. There is a proper role for courts in ensuring that agencies have adequately invested resources in information gathering, which may dispel uncertainty. Yet in some case...