A Paradox on Social Welfare: Kenneth Arrow and the General Possibility Theorem
In Chapter 1 it was shown that a welfare analysis consisted of tracing implications from a set of value judgments, the most notable of which was the postulation of a particular schema of ends whose fulfillment is deemed desirable. We saw that the welfare function is an analytic tool which is especially convenient for making explicit the special set of value judgments involved in any such analysis and in enabling their implication to be examined. We posed two problems. First, what sets of values can, in the context of actual behavior, lead to useful social orderings? Second, how do we choose that particular set of values which will give rise to the most useful social ordering for a given community?
The substantial contribution to welfare economics by Kenneth Arrow is directed precisely to these questions. 1 His innovation in analysis and presentation by using the methods of symbolic logic, and the very high level of abstraction his contribution incorporates, is at one and the same time a danger and an opportunity. On the one hand, there is the great ease with which one can misunderstand the argument; on the other, there is the possibility of making valid interpretations on more than one level.____________________