On a dilemma of redistribution

McKenzie Alexander presents a dilemma for a social planner who wants to correct the unfair distribution of an indivisible good between two equally worthy individuals or groups: either she guarantees a fair outcome, or she follows a fair procedure (but not both). In this paper I show that this dilemma only holds if the social planner can redistribute the good in question at most once. To wit, the bias of the initial distribution always washes out when we allow for sufficiently many redistributions