The Rational Foundations of Income Inequality Measurement

People die in revolutions fighting inequalities. inequalities. “Men are free and equal in rights” is the political basis of democratic societies, and these rights may more or less include rights to consumption or income. Inequality, notably of incomes, is related to practically all important problems of society, as cause or as effect. But one generally has to compare unequal situations: When is one less unequal than the other? Does the transfer of one dollar from a richer to a poorer diminish inequality, given that it certainly augments inequality between the relatively poor receiver and the still poorer and equally poor, and between the relatively rich giver and the still richer and equally rich? In another respect, if the two-person income distribution (2,4) is as unequal as the distribution (1,2) because the ratios of incomes are the same, is inequality also unchanged when the distribution (0.01,1) is transformed into the distribution (0.1,10) by the multiplication of all incomes by the same number 10? In the transfer case, whatever its effect on inequality the transfer from richer to poorer may be good because it alleviates one person’s poverty, or it may be just.