This article explores the Rawlsian goal of ensuring that distributions
are not influenced by the morally arbitrary. It does so by bringing discussions of distributive justice into contact with the debate over
moral luck initiated by Williams and Nagel. Rawls’ own justice as
fairness appears to be incompatible with the arbitrariness commitment,
as it creates some equalities arbitrarily. A major rival, Dworkin’s version of brute luck egalitarianism, aims to be continuous with ordinary ethics, and so is (a) sensitive to non-philosophical beliefs about free will and responsibility, and (b) allows inequalities to arise on the basis of option luck. But Dworkin does not present convincing reasons in support of continuity, and there are compelling moral reasons for justice to be sensitive to the best philosophical account of free will and responsibility, as is proposed by the revised brute luck egalitarianism of Arneson and Cohen. While Dworkinian brute luck egalitarianism admits three sorts of morally arbitrary disadvantaging which correspond to three forms of moral luck (constitutive, circumstantial, and option luck), revised brute luck egalitarianism does not disadvantage on the basis of constitutive or circumstantial luck. But it is not as sensitive to responsibility as it needs to be to fully extinguish the influence of the morally arbitrary, for persons under it may exercise their responsibility equivalently yet end up with different outcomes on account of option luck. It is concluded that egalitarians should deny the existence of distributive luck, which is luck in the levels of advantage that individuals are due.