Mapping the Exact Relations between Overall Inequality and Inequality between Subgroups

Samuel Kotz, George Washington University

Social scientists study two kinds of inequality: overall inequality (as in income inequality) and inequality between subgroups (as in racial inequality). This paper analyzes the connections between these two kinds of inequality. The paper proceeds by exploring a set of two-parameter continuous probability distributions. We define a general inequality parameter, which governs all measures of inequality (such as the Gini coefficient), and we link the general inequality parameter to the gap between the means of subdistributions. In this way we establish that as overall inequality increases, inequality between subgroups increases also.