We revisit the well-known decomposition of the Gini coefficient into betweengroups, within-groups and overlap terms in the context of two groups in which the incomes in one group may be scaled and that group's population weight modified. In this more general setting than usual, we focus on the...

The `Vast majority of incomes ratio (VMIR)' $R_0$ is the ratio of the average income $\mu_0$ of a poorest majority $p_0$ of the population to the overall average income $\mu$. Another measure of equality is $E_0\equiv(1-G)$ where $G$ is the Gini coefficient of inequality of the distribution....