4 September 2017What would be the analogue of the Lorenz quasi-ordering when the variable of interestis of a purely ordinal nature? We argue that it is possible to derive such a criterionby substituting for the Pigou-Dalton transfer used in the standard inequality literaturewhat we refer to as a Hammond progressive transfer. According to this criterion, onedistribution of utilities is considered to be less unequal than another if it is judgedbetter by both the lexicographic extensions of the maximin and the minimax, henceforthreferred to as the leximin and the antileximax, respectively. If one imposes in additionthat an increase in someone’s utility makes the society better off, then one is left with theleximin, while the requirement that society welfare increases as the result of a decreaseof one person’s utility gives the antileximax criterion. Incidently, the paper provides analternative and simple characterisation of the leximin principle widely used in the socialchoice and welfare literature