Arrow on Rawls

I'm curious about the contradictions between the utilitarian Pareto-optimal principle used by most economists and the difference principle / maximin / "veil of ignorance" principle ignored by most economists.

Vilfredo Pareto argued that a policy could only be efficient if it makes no one worse off. Cynically one could say that was a convenient theory for an Italian of noble blood to propose. John Rawls, on the other hand, argued that we should focus more on maximizing the well-being of the worst-off member of society. He called it the difference principle, economists call it maximin. To make this theory salient, Rawls proposed a "veil of ignorance": if you are about to enter the world but do not know who you will be, what kind of society do you want to enter?

Kenneth Arrow's critical review of Rawls' A Theory of Justice helped to convince me that Rawls' veil of ignorance is a useful social justice principle and that economists should bring it into decision-making. That is not the point Arrow was trying to make.

I'm no moral or political philosopher so maybe Arrow's arguments are more valid than I give them credit for, but I found them to be (1) a bit irrelevant since he immediately took things to their logical extreme instead of seriously considering the veil of ignorance as a useful decision making mechanism, and (2) a bit contradictory.

1. Logical extremes

One example of an argument employed by Arrow is that, as Pareto and Irving Fisher have argued, "there is no quantitative meaning for utility for an individual" -- it's an ordinalist position. "If the utility of an individual is not measurable, then a fortiori the comparison of utilities of different individuals is not meaningful ... Consider an individual who is incapable of deriving much pleasure from anything, whether because of psychological or physical limitations. He may well be the worst-off individual and, therefore, be the touchstone of distribution policy, even though he derives little satisfaction from the additional income." ... oversimplifying, I interpret this as: why house the homeless if one guy remains depressed? IMO Arrow is missing the point here.

2. Contradictions

Where Arrow is slightly contradictory he is at his most interesting. He was of course brilliant so there is a lot of good info even when I doubt the validity of his argument.

To take a step back, Rawls' argument that society should maximize the utility of the worst-off has two parts. First, in the original position where the quality of your entire life is at stake, it's reasonable to have high degree of risk aversion, and being concerned with worst possible outcome is an extreme form of risk aversion. Second, probabilities are in fact ill defined and should not be employed in such a calculation. Here Arrow points out:

"The second point is a version of a recurrent and unresolved controversy in the theory of behavior under uncertainty: are all uncertainties expressible by probabilities? The view that they are has a long history and has been given axiomatic justification by Ramsey and by L. J. Savage. The contrary view has been upheld by F. H. Knight and by many writers who have held to an objective view of probability; the maximin theory of rational decision-making under uncertainty was set forth by A. Wald specifically in the latter context. Among economists, G. L. S. Shackle has been a noted advocate of a more general theory which includes maximin as a special case. L. Hurwicz and I have given a set of axioms which imply that choice will be based on some function of the maximum and the minimum utility."

 And a few pages later, in defense of a utilitarian approach:

"As Ramsey and von Neumann and Morgenstern have shown, if one considers choice among risky alternatives, there is a sense in which a quantitative utility can be given meaning. Specifically, if choice among probability distributions satisfies certain apparently natural rationality conditions, then it can be shown that there is a utility function (unique up to a positive linear transformation) on the outcomes such that probability distributions of outcomes are ordered in accordance with the mathematical expectation of the utility of the outcome."

Near the end, explaining why there might not be a meaningful universal concept of justice:

"One problem is that any actual individual must necessarily have limited information about the world, and different individuals have different information."

Arrow casts doubt on Rawls' theory by saying that we can express decision making under uncertainty as a set of probabilities of futures outcomes. A few pages later he says we of course have limited information about the world, in other words it is impossible to express the future as a set of probabilities.

Maybe I'm misreading the argument, but it seems contradictory. In any event I need to read Rawls' book before I write more on this. Arrow's review is worth reading for his summary of decision making under uncertainty and his views on utilitarianism.