Justice for the symbolically inclined

This book is a synthesis of work on distributive justice carried on in the past 50 years by economists and political philosophers. Originally conceived as a textbook for graduate students in economics, it is important in its own right and can be recommended to anyone with an interest in the subject who does not black out at the sight of a symbol and is prepared to take the proofs on trust. Theories of Distributive Justice demonstrates just how far the level of discussion has been raised in the past 25 years. It is instructive to compare it with Amartya Sen's Collective Choice and Social Welfare, its equivalent in 1970. Even where the same people are discussed (Kenneth Arrow, John Nash, John Rawls), the points made about them are different and far deeper. Of course, the notion of progress is relative to a paradigm, and it is possible to hold that the entire research programme is misguided. But the increased sophistication displayed in the book takes a form that should reassure sceptics, since John Roemer insists that formalisation must be subordinate to concerns generated within political philosophy. Much of his criticism of earlier work focuses on the inadequacy of its normative basis.

Thus, in his first chapter Roemer points out that Arrow's impossibility theorem shows only that if you start with sufficiently impoverished information you cannot get much out of it. But why, he asks, should anyone suppose that (even where it can be done) aggregating individual preference orderings over states of the universe will tell us anything worth knowing about those states of affairs? We can easily specify preference profiles that produce a winning outcome according to the deliverance of a social welfare function - for example, an outcome that is preferred by a majority to all alternatives. But that outcome may be one in which an ethnic minority is killed. Clearly, we need access to such facts to determine the contribution of a state of affairs to social welfare in any interesting sense.

In the next chapter Roemer defends the Nash bargaining solution against alternative axiomatic approaches using the same limited utility information (von Neumann-Morgenstern utilities) and reports recent work that meets the objection commonly made to the Nash solution that it lacks microfoundations. But he claims that the Nash solution can produce counterintuitive results, an example being the following. Suppose with probability p I get a silver dollar and you get nothing while with probability l-p you get a Rolls-Royce and I get nothing. What probability should we agree on? (If we do not agree, neither of us gets anything.) On plausible utility assumptions, Nash says we should agree to toss a fair coin, but Roemer thinks it obvious that the probability should be heavily weighted towards me. The reasoning is presumably that I have little to lose from failure to agree; but it can equally well be said that I have little to gain from intransigence. (We have to accept there is no way I can get a part of that Rolls-Royce within the specified game.) So perhaps Nash is right after all. The fact is that the example is so peculiar that intuitions drawn from our everyday experience with bargaining are highly unreliable. Roemer concludes by saying that bargaining solutions can have normative significance only if the bargaining situation is so heavily modified to reflect ethical constraints that the results could be more conveniently and perspicuously derived directly from the constraints.

Chapter three, which is the most technically demanding, picks up from a point made in the previous chapter: that the uniqueness of the Nash solution disappears as soon as richer utility information is admitted, and asks what happens when we add information about the characteristics of goods (for example, is this food essential to nutrition or merely nice to eat?). Roemer's answer is that "there will be I no argument that deduces one solution or mechanism as the consequence of a small number of clear, appealing axioms. Philosophical integrity will require us to move beyond the 'single characterizations' of social choice and axiomatic bargaining theory."

The next chapter is primarily devoted to a demonstration that John Harsanyi's derivation of utilitarianism from choice under uncertainty is invalid. The key point again turns on utility information: there is no way of getting from von Neumann-Morgenstern utilities (defined for individuals over lotteries) to utilitarianism, which requires strong interpersonal utility information. This does not impugn the point (made later in the context of Rawls) that a risk-neutral "soul" denied knowledge of its identity would choose the utilitarian criterion if it wanted to maximize the expected utility of whomever it turned out to be. I believe it is this idea that provides spurious plausibility for Harsanyi's "proof".

The remaining four chapters are based on the work of political philosophers. Apart from one on Robert Nozick, these are primarily devoted to tracing the controversy about the relevance of personal responsibility to just distribution that has developed in the writings of John Rawls, Amartya Sen, Ronald Dworkin, G. A. Cohen and Richard Arneson. This is more accessible than the first chapters, though it contains some formal material. My view is that the story is not one of unequivocal advance and that Dworkin was right to hold people responsible for the choices they make from the opportunities open to them. But Roemer provides the materials on the basis of which readers can judge for themselves between Dworkin and his critics.

Theories of Distributive Justice is a remarkable achievement. I know of nobody else who combines Roemer's mastery of formal analysis with his respect for the integrity of political philosophy and his deep understanding of it.

Brian Barry is professor of political science, London School of Economics.