Following Kolm (1969) and Atkinson (1970) there is a wide agreement in the literature to appeal to the Lorenz curve for measuring inequality. A distribution of income is typically considered as being no more unequal than another distribution if its Lorenz curve lies nowhere below that of the latter distribution. Besides its simple graphical representation, much of the popularity of the so-called Lorenz criterion originates in its relationship with the notion of progressive transfers. It is traditionally assumed that inequality is reduced by a progressive transfer; that is, when income is transferred from a richer to a poorer individual without affecting their relative positions on the ordinal income scale. The principle of tranfers, which captures this judgement, is closely associated with the Lorenz quasi-ordering of distributions of equal means. Indeed half a century ago, Hardy et al. (1952) demonstrated that if a distribution Lorenz dominates another distribution, then the former can be obtained from the latter by means of a finite sequence of progressive transfers, and conversely.1 This relationship between progressive transfers and the Lorenz quasi-ordering constitutes the cornerstone of the modern theory of welfare and inequality measurement. As a consequence, the literature has concentrated on Lorenz consistent inequality measures; that is, indices such that a progressive transfer is always recorded as reducing inequality or increasing welfare.
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