Social welfare orderings for ratio-scale measurable utilities

This article characterizes all of the continuous social welfare orderings which satisfy the Weak (resp. Strong) Pareto principle when utilities are ratio-scale measurable. With Weak Pareto, on both the nonnegative and positive orthants the social welfare ordering must be representable by a weakly increasing Cobb-Douglas social welfare function while on the whole Euclidean space the social welfare ordering must be strongly dictatorial. With Strong Pareto, on the positive orthant the social welfare ordering must be representable by a strictly increasing Cobb-Douglas social welfare function but on the other two domains an impossibility theorem is obtained.