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Serge-Christophe Kolm Introduction When some people are treated more or less favourably than others without a seemingly valid reason, this inequality arouses a judgement of injustice which is conveyed in the term ‘inequality’. Such inequalities are a major issue for judging societies or policies and are often compared across time or societies, in particular by the media and politicians. Such comparisons are a priori highly problematic, however, since given any two unequal distributions of some item, one can most of the time show that any one is more unequal than the other and the converse, with reasons, comparisons and measures which, a priori, may all seem convincing. Does, for instance, growth tend to augment or diminish income inequality? Balanced growth followed by a fiscal partial redistribution of the gains diminishes inequality measured by ratios, but may augment inequality measured by differences. Inequality based on ratios is not changed when the pair 0.01 and 1 becomes the pair 0.1 and 10. Inequality based on differences is not changed when the pair 1 and 2 becomes the pair 11 and 12. Does a transfer from richer to poorer diminish inequality? It augments the pairwise inequalities between the richer and the still richer or equally rich and between the poorer and the still poorer and equally poor. One can pass from the income distribution of Australia to that of France (adjusted for population) by a sequence of such transfers, and yet Australia, with its large homogeneous middle class, seems a more egalitarian society....