On the consistent measurement of attainment and shortfall inequality

▶ Health status inequality rankings in terms of attainments and shortfalls can differ. ▶ For relative and intermediate inequality concepts, the rankings do differ. ▶ Only for the absolute inequality concept are consistent rankings possible. ▶ We find two classes of absolute inequality indices which yield consistent rankings. ▶ The only consistent and subgroup decomposable inequality index is the variance.