What’s the Good of Equality?

A country’s income distribution can have many different shapes. It can be spread out or sharply peaked, skewed or symmetrical, perhaps even bimodal between the sexes. It is obviously impossible to capture all this variety in a single statistic such as the variance. But this is not the difficulty in measuring inequality. The purpose of an inequality measure is not to compress a lot of information into one number. There is often no need to do that anyway. If someone wants to know, say, whether income is more equally distributed now than it was ten years ago, there may be no difficulty about presenting her with the whole distribution for each date. The difficulty is that, when she has all this information, she may still not know whether the distribution has become more or less unequal.