Sensitivity aspects of inequality measures

Abstract

The purpose of this article is to study inequality measures with respect to their sensitivity to transfers. Sensitivity is studied by means of a particular directional derivative. We observe that inequality measures behave differently in the sense that the vectors for which this directional derivative is positive or negative differ according to the used inequality measure. It is shown that different averages, such as the arithmetic mean, the median, the harmonic mean and the geometric mean play an essential role in these investigations. We conclude that the use of this directional derivative introduces a battery of sensitivities in the class of inequality measures. This helps the information scientist to choose between otherwise acceptable measures.