Social welfare functions with a reference income

A foundation of social welfare functions is considered with a given reference income (or utility): relative and absolute invariance of the underlying welfare ordering are defined to hold for societies with either all members having incomes below the reference income or all members having incomes above the reference income. These conditions, alongside standard properties of a social preference relation, provide reference income dependent extensions of traditional classes of welfare functions. Dalton's principle of positive transfers is incorporated, under which relative invariance leads to a class of piecewise (rank-)linear welfare functions, including the class of generalized Gini social welfare functions as a special case. To ensure quasi-concavity a new preference condition is proposed, which has the interpretation of aversion to income dropping below the reference income.