Auxiliary specifications enable comparison of different social states by each member of society in preference satisfaction. These help define "Pareto efficiency", which holds if all alternatives have been exhausted to put at least one person in a more preferred position with no one put in a less preferred position. Bergson described an "economic welfare increase" (later called a "Pareto improvement") as at least one individual moving to a more preferred position with everyone else indifferent. The social welfare function could then be specified in a "substantively" individualistic sense to derive Pareto efficiency (optimality). Paul Samuelson (2004, p. 26) notes that Bergson's function "could derive Pareto optimality conditions as "necessary" but not sufficient for defining interpersonal normative equity." Still, Pareto efficiency could also characterize "one" dimension of a particular social welfare function with distribution of commodities among individuals characterizing "another" dimension. As Bergson noted, a welfare improvement from the social welfare function could come from the "position of some individuals" improving at the expense of others. That social welfare function could then be described as characterizing an equity dimension.