Abstract: 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 cases the value of further investments in information gathering will be genuinely uncertain. If so, courts should defer to agencies’ second-order choices about informational investments on the same grounds that justify deference to agencies’ first-order choices under uncertainty. If the [Board of Immigration Appeals] proposed to narrow the class of deportable aliens eligible to seek [legal] relief by flipping a coin—heads an alien may apply for relief, tails he may not—we would reverse the policy in an instant. That is because agency action must be based on non-arbitrary, “relevant factors.” (Judulang v. Holder, 132 S. Ct. 476, 485 [2011] [Kagan, J.]) The sense in which I am using the term [“uncertainty”] is that in which the prospect of a European war is uncertain, or the price of copper and the rate of interest twenty years hence, or the obsolescence of a new invention, or the position of private wealth-owners in the social system in 1970. About these matters there is no scientific basis on which to form any calculable probability whatever. We simply do not know. Nevertheless, the necessity for action and for decision compels us as practical men to do our best to overlook this awkward fact and to behave exactly as we should if we had behind us a good Benthamite calculation of a series of prospective advantages and disadvantages, each multiplied by its appropriate probability, waiting to be summed. (Keynes 1937, p. 214)