[Excerpt] The comparison of alternative patterns of family income distribution, as in most social welfare judgments, is a difficult and sometimes controversial subject. An ideal method for the design of an ordinal measurement of inequality is an axiomatic approach whereby reasonable properties are explicitly postulated for a complete pre-ordering R defined on the income distribution space Ω+, the non-negative orthant of the n-dimensional real space Sn. Commonly used axioms are those of scale irrelevance (A1), symmetry (or anonymity) (A2), and the desirability of rank-preserving equalization (A3). While A1 isolates the 'distribution' of income from the overall 'level,' A2 emphasizes a 'democratic' principle in which all families are treated alike. The third axiom A3 states that equality increases when income is transferred from a relatively rich to a relatively poor family. This set of axioms, to be discussed briefly below, will be taken as the starting point of the present paper.