G. L. S. Shackle, Review of Kenneth J. Arrow’s Social Choice and Individual Values (1951)

G. L. S. Shackle’s journal book review presents Arrow’s achievement as a decisive clarification of the foundations of welfare economics. Its movement is compact: an appraisal of mathematical method and exposition leads into a reconstruction of the social-choice problem, followed by the impossibility result and the alternatives it leaves open. Shackle’s central judgment is that Arrow’s formalism earns its place by establishing constraints that any welfare economics without interpersonal comparisons of utility must acknowledge.

A logically inescapable framework of formal truths, within which all development of welfare economics (so long as it eschews interpersonal comparisons of utility) must proceed, is here established once for all.

The parenthetical qualification defines the reach of this praise. Shackle is not claiming that Arrow has settled every question about social welfare; the achievement concerns a framework that takes individual preference orderings as its basis while excluding comparisons of utility between persons. Within that framework, he regards the result as exceptionally complete. Symbolic reasoning is justified not simply by its elegance but by the precision and finality it makes possible. His jigsaw-puzzle analogy distinguishes the difficulty of constructing the proof from the lesser, though still demanding, task of checking it. He also praises Arrow’s prose: mathematical virtuosity and intelligible exposition reinforce one another.

Shackle then explains a social welfare function as a rule assigning a social ordering of alternative states to each set of individual orderings. The problem is whether such a rule can satisfy five apparently reasonable requirements together. It must produce consistent answers despite unrestricted diversity of preferences; raising an alternative in an individual’s ranking must not lower it socially, other things remaining equal; the social ranking of two alternatives must remain unaffected by changes that leave their individual pairwise rankings unchanged; no pair must receive a fixed social ranking regardless of individual preferences; and no individual’s ordering must independently determine the social ranking of any pair. The progression makes clear why Arrow’s result is troubling: the conflict arises among requirements presented as expressions of generally accepted values, rather than among obviously objectionable demands.

The kernel of Dr. Arrow's book is the proof that no social welfare function can meet all these conditions at once.

Shackle reports the General Possibility Theorem as applying when there are at least three alternatives that individuals may rank freely. Under the responsiveness and independence requirements, a consistent social ordering must then be imposed or dictatorial. His exposition directs attention to unrestricted diversity as the pivotal difficulty. A rule cannot, in general, both reflect freely varying individual preferences and maintain the specified consistency while avoiding those two outcomes. The review thus treats the theorem as a boundary on the ambition to turn individual judgments into a coherent collective judgment, not as a recommendation for imposed or dictatorial choice.

The concluding discussion identifies two avenues of escape: abandon consistency in the social welfare function, or restrict the individual orderings. Shackle gives particular weight to Arrow’s concluding chapters on restrictions, reporting their result as the necessity and sufficiency of a fundamental similarity in individuals’ attitudes toward classifying social alternatives. This shifts the question from the ingenuity of an aggregation rule to the pattern of agreement among those whose preferences it aggregates. The review notes the philosophical and moral interpretation of this requirement without developing an independent account of it.

Dr. Arrow has shown that a book on the foundations of economic theory can be written at a sustained level of absolute rigour and yet, for those who will take trouble, be intelligible and a delight to read.

The closing judgment joins the review’s two concerns: the substantive limits of social choice and the value of rigorous exposition. Shackle’s contribution is an unusually clear, strongly affirmative account of why Arrow’s theorem matters, preserving both its conditional scope and the demanding intellectual work needed to understand it.