ABSTRACT
In 1905, Max Lorenz proposed a simple graphical means to summarize the inequality of wealth in a finite population of individuals. Known subsequently as the Lorenz curve, it has survived well and indeed still occupies a preeminent place in discussion of the quantification of inequality. It was a simple, but a very good, idea. Subsequent investigations have provided useful interpretations of why it does so well in capturing our conceptions of what really constitutes inequality. Some of these insights will be discussed below. The mathematical concept known as majorization arrived somewhat later on the scene. Its close relationship with the ordering proposed by Lorenz in his pioneering paper has been apparent for many years, although it is difficult to pinpoint precisely when this nexus was first noted. Nevertheless, the deep understanding of the majorization partial order developed initially by Hardy, Littlewood and Polya (1929, 1934), has been seamlessly transformed to give us a spectrum of useful results and viewpoints on the ‘true nature’ of Lorenz’s curve and its associated ordering of inequality in distinct populations or in populations viewed at different points in time. An important contribution to our understanding of the Lorenz curve, and an important reason for its continued and growing acceptance among economists, was found in Dalton’s (1920) careful discussion of criteria that might be arguably accepted as being clearly desirable features of any measure of inequality and of any method for comparison of inequality between populations. The Lorenz curve may well have flourished without the contributions of Dalton, Hardy, Littlewood and Polya but it could not fail to flourish in the presence of such inputs. Indeed it seems that very few people question the fact that nested Lorenz curves signal a clear differential in inequality. What has kept the field of income inequality full of lively controversy is the question of what to do when, or how to interpret situations in which Lorenz curves cross.
