We propose and characterize a class of measures of welfare change that are based on the generalized Gini social welfare functions. In addition, we analyze these measures in the context of a second-order dominance property that is akin to generalized Lorenz dominance as introduced by Shorrocks (1983) and Kakwani (1984). Because we consider welfare differences rather than welfare levels, the requisite equivalence result involves linear welfare functions (that is, those associated with the generalized Ginis) only, as opposed to the entire class of strictly increasing and S-concave welfare indicators.