A debate about the concept of the welfare of a community (or "social welfare")started in the 1920s with the publication of Pigou's "Economics of Welfare" . Pigou observed that a unit increase in income adds more to the welfare of poor man than it adds to that of a rich man, and concluded that social welfare would be increased by a transfer from the rich to the poor. The first dissent came in 1938 from Lionel Robbins, who argued that Pigou's analysis was faulty because it required interpersonal comparisons of welfare, and urged a return to the "unanimity rule" which had been proposed by Vilfredo Pareto - which stated that it could not be assumed that welfare would increase unless there would be some gainers and no losers  - along with the associated concept of Pareto-efficiency. That was followed in 1939 by a proposal by Nicholas Kaldor to escape the interpersonal comparison problem by adopting a "compensation principle" under which a change would be deemed to increase efficiency if it could increase the welfare of its gainers after they had compensated the losers . That proposal was endorsed by Sir John Hicks , and became known as the the "Kaldor-Hicks criterion", but it was widely rejected by other economists as implying an ability to make interpersonal comparisons of welfare. (The claim that such comparisons could be avoided if the compensation was actually the paid, encountered objections arising from the formidable difficulties of determining the correct payments). An elaboration of the Hicks-Kaldor criterion known as the Scitovsky criterion was open to similar objections.
The next development was the Arrow-Debreu proof that, (on the assumptions noted in the main article) an interacting system of markets could reach an equilibrium in which all markets clear simultaneously  (known as the "existence theorem" and referred to in some texts as the first fundamental theorem of welfare economics) and the publication of the two theorems set out in the main article . Kenneth Arrow considered the possibility that a ranking of a community's preferences could be arrived at democratically, and his conclusion was his "impossibility theorem" which demonstrated that no acceptable voting system could be devised which guaranteed a ranking consistent with the preferences of its members , thus founding the discipline known as social choice theory.
It has been argued that, not only are the welfare theorems unrealistic; some of their assumptions actually lead to misleading conclusions. In the 1960s, William Baumol discussed the consequences of reversing the assumption that there are no "external economies" and concluded that the effect of acknowledging the existence of economic interdependence is often to nullify the conclusions of theories that ignore it. . He argued that the laissez-faire proposition that well-informed citizens can most effectively look after themselves is a truism in the absence of any mutual dependence, but that it will often be false if there is significant interdependence. But although that argument undermines much of the theory of welfare economics, Baumol also argued that welfare economics can nevertheless enable practising economists to provide politicians with useful advice
Is this normative economics?
Some textbook authors maintain that welfare economics belongs to the category of "normative economics" because it is concerned with what ought to be. However, it is possible (as William Baumol has argued) to consider what government actions would best serve the interests of the governed without maintaining that those actions ought to be taken. Alternatively it is sometimes claimed that applied welfare economics is necessarily normative because it cannot reach useful conclusions without adopting value judgements. That claim can be countered by maintaining that the value judgments that are used are not the product of the theories of welfare economics (or of its practitioners) but are preferences expressed by the community or its representatives. If those counter-arguments are accepted, it must be concluded that welfare economics is a user, not a generator of normative propositions, so that it is misleading to refer to it as normative economics.
- Arthur Pigou,: The Economics of Welfare Macmillan 1932 (first published: 1920)
- Lionel Robbins: "Interpersonal Comparisons of Utility", Economic Journal December 1938
- Vilfredo Pareto: Manual d’Economic Politique, Manuel Giard 1927
- Nicholas Kaldor "Welfare Propositions in Economics and Interpersonal Comparisons of Welfare" Economic Journal 49 1939
- John Hicks: "The Foundations of Welfare Economics", Economic Journal September 1939
- Kenneth Arrow and Gerard Debreu: "The Existence of an Equilibrium for a Competitive Economy", Econometrica, vol. XXII 1954
- Kenneth Arrow: "An Extension of the Basic Theorem of Classical Welfare Economics", Proceedings of the Second Berkeley Seminar on Mathematical Statistics and Probability University of California Press 1951
- Kenneth Arrow: "A Difficulty in the Concept of Social Welfare", Journal of Political Economy 58(4) August, 1950
- William Baumol: Welfare Economics and the Theory of the State, Chapter 12, page 180 (summary), Harvard University Press, 1965. (accessible online to Questia subscribers)