Bergson and Samuelson did not specify which fairness principles justify constructing utility functions from preference orderings.

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,