This paper provides an axiomatization of linear inequality measures representing binary relations on the subspace of income profiles having identical total income. Interpreting the binary relation as a policymaker’s preference, we extend the axioms to the whole space and find that they characterize linear social evaluation functions. The axiomatization seems to suggest that a policymaker who has a linear measure of inequality on a subspace should have a linear evaluation on the whole space. An extension of the preferences reflected in the Gini index to the whole space is represented by a linear combination of total income and the Gini index. Journal of Economic Literature Classification numbers: D30, D31, D60, D63, D81.