People die in revolutions fighting inequalities. “People are free and equal in rights” is the political basis of democratic societies, and these rights may more or less include rights to have consumption or income. Inequality, notably of incomes, is related to practically all important problems of society, often as cause or as effect. Yet one generally has to compare situations in which inequality prevails: when is one less unequal than another? Even the simplest examples reveal the puzzle. Does the transfer of one dollar from a richer to a poorer person 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? The ...

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