This paper addresses the impact of a subsidy—an increase in someone's income—on generalized Gini inequality indices. We show that for any distribution of income there exists a “pivotal individual” such that an increment given to an individual poorer (resp. richer) than himself, decreases (resp. increases) inequality. We characterize the pivotal individual for relative and absolute Gini indices. We show that normative prescriptions about the preferred level of inequality aversion can also be formulated in terms of the pivotal, namely the richest individual that we find just to compensate.