Why should a lottery be used in the allocation of an indivisible good to which participants in the lottery have an equally strong claim? Stone argues that when indeterminacy arises, in which it is impossible to satisfy the equality condition requiring like cases to be treated alike, the impartiality principle suggests that the agent responsible for the allocation task should not intend to favor one over another on the basis of invalid reasons. In this article, I argue that the impartiality (...) principle is neither sufficient nor necessary to explain the fairness of lotteries. Instead, the fairness of lotteries is explained by the sanitizing effect that lotteries generate to screen out the reactive attitudes of resentment and indignation that claimants might otherwise have if they do not obtain the good in question. (shrink)