 Bergson (1938) and Samuelson (1947, 1981) occupy a special position, which may be described as a third way between old and new welfare economics. From the former, they retain the goal of making complete and consistent social welfare judgments with the help of well-defined social welfare functions. The formula W(U1(x),…,Un(x)) is often named a “Bergson-Samuelson social welfare function” (x is the social state; Ui(x), for i=1,…,n, is individual i’s utility in this state). With the latter, however, they share the idea that only ordinal non-comparable information should be retained about individual preferences. This may seem contradictory with the formula of the Bergson-Samuelson social welfare function, in which individual utility functions appear, and there has been a controversy about the possibility of constructing a Bergson-Samuelson social welfare function on the sole basis of individual ordinal non-comparable preferences (see in particular Arrow (1951), Kemp and Ng (1976), Samuelson (1977, 1987), Sen (1986) and a recent discussion in Fleurbaey and Mongin (2005)). Samuelson and his defenders are commonly considered to have lost the contest, but it may also be argued that their opponents have misunderstood them. Indeed, individual utility functions in the W(U1(x),…,Un(x)) formula are, according to Bergson and Samuelson, to be constructed out of individual preference orderings, on the basis of fairness principles. The logical possibility of such a construction has been repeatedly proven by Samuelson (1977), Pazner (1979), Mayston (1974, 1982). The fact that such a construction does not require any other information than ordinal non-comparable preferences is indisputable. Bergson and Samuelson acknowledged the need for interpersonal comparisons, but considered that these could be done, in an ethically relevant way, on the sole basis of non-comparable preference orderings. They failed, however, to be more specific about the fairness principles on which the construction could be justified. The theory of fair allocation (see  § 6)  may fill the gap.