Generalizing the S-Gini family: Some properties

In the literature there are a number of generalizations of the Gini coefficient which inherit most of its appealing properties. These families allow the incorporation of different value judgments and all of them are more sensitive to transfers among the poorest individuals in society than to transfers among the richest. Consequently they fail to capture a fact with which perhaps not everybody agrees: it is always good for society to give much more additional income to the richest person than to the poorest one. The aim of this paper is to propose extensions of these generalizations of the Gini coefficient with measures which, preserving their properties, complete the information about all the inequality perceptions.