Inequality as experienced difference: A reformulation of the Gini coefficient

Inequality is typically measured as the degree of dispersion of a distribution of individual attributes, say, wealth, as is captured for example by the Lorenz curve, and its associated statistic, the Gini coefficient. But both the economics and social psychology of experienced inequality are better expressed by differences between an individual and others. There is a natural way to do this using the standard definition of the Gini coefficient as one half the mean difference among individuals, relative to the population mean wealth. Here we show that reformulating the Gini coefficient as a measure of experienced inequality on a complete social network yields a computational algorithm that, unlike the conventional one, is consistent with this definition and irrespective of population size varies from 0 (no differences among individuals) to 1 (one individual owns all the wealth). Our proposed measure also avoids a downward bias in the standard algorithm, which for small populations can be substantial. Because social networks are far from complete, the pairwise comparisons based on social interactions in which people routinely engage may support a level of experienced inequality that either exceeds or falls short of the Gini coefficient measured on a hypothetical complete network. We illustrate this fact with empirical estimates for a farming community in Nicaragua.