Axiomatic characterization of aggregate consumer surplus measures as social welfare indices

This paper proposes two types of equity-regarding social welfare indices which satisfy the Pigu-Dalton transfer principle in the neoclassical market model: one is the geometrically aggregated compensating ratios and the other is the geometrically aggregated equivalent ratios. The two proposed indices, as well as the well-known two types of arithmetically aggregated Hicksian variations, are used to define Arrovian social ordering functions which evaluate the price vectors and income distributions in the market model. It is shown that each of the four Arrovian social ordering functions can be characterized by the axioms in Arrovian form: Pareto, symmetry and an independence axiom weaker than Arrow's original independence axiom. It follows from the characterizations that the two proposed indices have solid normative foundations as social welfare indices even if the individual heterogeneity both in tastes and in incomes is admitted, and that the equity-regarding property of the indices comes from their respective independence axioms(variants of Fisher's commensurability axiom).