This is a significant revision of a paper which first appeared as Working Paper 98-26, CRÉFA, Département d’économique, Université Laval, Canada.We investigate the properties of a family of social evaluation functions and inequality indices which merge the features of the family of Atkinson (1970) and S-Gini (Donaldson and Weymark (1980, 1983), Yitzhaki (1983) and Kakwani (1980)) indices. Income inequality aversion is captured by decreasing marginal utilities, and aversion to rank inequality is captured by rank-dependent ethical weights, thus providing an ethically-flexible dual basis for the assessment of inequality and equity. These ocial evaluation functions can be interpreted as average utility corrected for the illfare of relative deprivation. They can alternatively be understood as averages of altruistic well-being in a population. They moreover have a simple graphical interpretation.We thank the Social Sciences and Humanities Research Council of Canada and the fonds pour la Formation des Chercheurs et l’Avancement de la Recherche of the government of Québec for their financial support.