Bergson’s Use of the Social Welfare Function
Bergson (Bergson, 1938, p. 310) described the object of his paper as being “to state in a precise form the value judgments required for the derivation of the conditions of maximum economic welfare which have been advanced in the studies of the Cambridge economists [Marshall, Pigou, Kahn and Edgeworth], Pareto and Barone, and Mr.
Lerner.” In other words, he was not challenging their approach, merely explicating it. He then simplified his notation by assuming there were two consumption goods, two types of labor, two non-labor inputs into production and that each commodity was produced in a single production unit. Ignoring non-economic variables that might affect welfare, he focused on an Economic Welfare Function (EWF), in which economic welfare was a function of each person's consumption of each of the two consumption goods (x and y), each person's supply of each type of labor in producing each consumption good (αx, bx, ay, by) and the quantities of non-labor inputs (C, D) used in producing each consumption good.
He then discussed the conditions under which Economic Welfare would be maximized, including the conditions derived by the three groups of economists mentioned earlier.
It was only when Bergson discussed the Pareto-Barone conditions that he referred to individuals' judgments of their own welfare. They assumed that if the quantities of consumption goods and labor supplied were
constant for all except the ith individual, “if the ith individual consumed the various commodities and performed the various types of work in combinations which were indifferent to him, economic welfare would be constant” (Bergson, 1938, p. 318). This implied that the EWF must take the form
where the functions S1(.) are individuals’ indifference loci.
It is notable, given more recent discussions, that Bergson did not discuss where his EWF might come from. It is simply a mathematical statement, the explanation of which is initially left open pending discussion later on, when he explains that welfare principles have to be based on the prevailing values of the community being discussed.
[O]nly if the welfare principles are based upon prevailing values, can they be relevant to the activity of the community in question. But the determination of prevailing values for a given community, while I regard it as both a proper and necessary task for the economist, and of the same general character as the investigation of the indifference functions for individuals, is a project which I shall not undertake here. (Bergson, 1938, p. 323)
This suggests not so much an imposed-from-outside welfare function as one that reflects the values of the community being analyzed, which is potentially vulnerable to Arrow’s critique.
As he had promised at the outset, Bergson analyzed the value judgments implicit in the conditions others had developed. He was particularly critical of the Cambridge economists’ use of the concept of utility that, he stressed, did not avoid the need to introduce ethical judgments. Rather, reference to utility served to conceal the role of value judgments.
[It] does not provide an alternative to the introduction of value judgments. First of all, the comparison of the utilities of different individuals must involve an evaluation of the relative economic positions of these individuals. No extension of the methods of measuring utilities will dispense with the necessity for the introduction of value propositions to give these utilities a common dimension. Secondly, the evaluation of the different commodities cannot be avoided, even tho this evaluation may consist only in a decision to accept the evaluations of the individual members of the community. (Bergson, 1938, p. 327)3
Utilitarianism introduces value judgments in a way that Bergson considered misleading, the reason being that statements about “the aggregative
3
Bergson added a third objection but these two are sufficient for the point being made here.
character of social welfare” or about “equality of marginal utilities when there is an equal distribution of shares, provided temperaments are about the same” sound like factual propositions even though they are not. Such language serves to conceal the value judgments being introduced. On the other hand, Bergson found difficulties in the writing of those, such as Pareto, Enrico Barone and Abba Lerner, who, in refusing to add up utilities, had turned their back on utilitarianism (Bergson, 1938, pp. 329-30). In rejecting utilitarianism they effectively excluded certain distributional issues from their analysis, without providing any justification for doing so.
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