The purpose of this comment is to show that Nehring’s methodology does not prove helpful in finding ways of extending other classical social welfare orderings. I show indeed that the corresponding state-independence property becomes incompatible with the interim Pareto criterion for a very large class of common priors, as soon as the social welfare ordering satisfies the strict Pigou-Dalton transfer principle (strict PD for short). I also show that his impossibility result in the absence of a common prior extends to any social welfare ordering that satisfies PD. The Pigou-Dalton principle states that transferring utility so as to reduce inequality should never hurt from a social perspective. Strict PD requires that the resulting utility profile is socially strictly preferred. PD is often viewed as a very appealing axiom in social choice theory, and indeed all the classical social welfare orderings (e.g. utilitarian sum, egalitarian minimum, and Nash product) satisfy it. The utilitarian criterion has the distinctive property of satisfying PD, but not its strict variant.