motivated his maximin principle for social choice through the artifact of the 'veil of ignorance': the assumption that individuals do not know their position in society. The Rawls maximin principle may be rationalized in terms of individuals identifying with the least will-off individual in each state. Analogously, we are concerned with the social choice criterion that is suggested, given the 'veil of ignorance' assumption, when individuals view themselves as potential occupants of each position in society. Identifying the 'position in society' of the individual with his or her rank in the income distribution, we arrive at the rank-dominance partial order on income distributions. We say that one income distribution rankdominates another income distribution if and only if the income in each position in the first income distribution is at least as great as the income in the same position in the second income distribution. Just as the assumption on the part of the individual that he or she is going to occupy the lowest rank suggests the Rawls maximin principle, so does the assumption on the part of the individual that he or she is just as likely to occupy any rank as any other suggest the rank-dominance criterion.
This note parallels the work of Atkinson (1970) -subsequently extended by and -on the measurement of inequality both in asking what social welfare function is implied by a particular partial ordering on income distributions and in applying work in the theory of choice under uncertainty to answer this question. To this end, we recall two results from the theory of choice under uncertainty. (The discrete versions of both theorems are stated.) * I wish to thank a referee for useful suggestions. The usual disclaimer applies.