Rawls, however, starting from the same premises, derives the statement that society should maximize min ui. The argument seems to have two parts: first that in an original position, where the quality of an entire life is at stake, it is reasonable to have a high degree of aversion to risk, and being concerned with the worst possible outcome is an extreme form of risk aversion; and, second, that the probabilities are in fact ill defined and should not be employed in such a calculation. The first point raises some questions about the meaning of the utilities and does not do justice to the fact that, at least in Vickrey and Harsanyi, the utilities are already so measured as to reflect risk aversion. [...] 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 an 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. KJ Arrow (1973) reviewing Rawls's Theory of Justice in Journal of Philosophy, 251. [I thank MA Khan for renewing my interest in the review.--ES]
It says something about the then-impoverished state of political philosophy that it was an economist who reviewed Theory of Justice in Journal of Philosophy. In the famous review of Rawls, Arrow recognizes that Rawls has embraced a key insight of Frank Knight's; the denial that probabilities can be assigned to certain decisions under conditions of genuine uncertainty. What exact bits of Rawlsian text Arrow has in mind is left unclear, but I think it is obvious he must have in mind the following two features of Rawls’s approach (i) there is some role for epistemic uncertainty in the origin position, where one has no knowledge of “the likelihoods of the possible circumstances” (1971: 134); and (ii) that for Rawls it is crucial that one is “taking a chance” (on which person one will be) in the original position (1971: 165). [1]
Observing Rawls's debts to Knight must have annoyed Arrow because twenty years before in a very important review article (it's been cited over 700 times), he had ridiculed Knight's approach; rather than treating Knight's position -- that there is a genuine distinction between unmeasurable uncertainty and improbable risk -- as respectable and distinctive, Arrow (1951) claimed that “Knight’s uncertainties seem to have surprisingly many of the properties of ordinary probabilities, and it is not clear how much is gained by the distinction [between risk and uncertainty]”. (417)
In his review of Rawls, Arrow implies that Knight's defense of the distinction (between uncertainty and risk) relies on a controversial assumption: that the only legitimate way to conceive of probability is as something objective. Granted this assumption, Arrow can simply respond (as he already done in 1951: 428-432) by suggesting (echoing Savage) that for decision-making purposes we can treat probabilities as subjective. As an aside, unlike Arrow, Savage, worries in The Foundations of Statistics, that with this move “we must be prepared to find reasoning inadequate to bring about complete agreement.” (1954: 7).
Again, Arrow can't really bring himself to really grapple with Knight's position even when confronted with Rawls's reliance on it. For, Knight's position -- and here (recall) Knight is in substantial agreement with Keynes (who has dropped out of the discussion [despite then still being the towering figure of the public image of economics]) -- is to argue that there are plenty of circumstances in which assigning even subjective probabilities is utterly ungrounded. (You may say in the language of contemporary decision-theorists, these are cases where it would be irrational to bet.) By implying that the embrace of genuine uncertainty relies on an objective notion of probability (which can be treated as unsophisticated and old-fashioned), Arrow can pretend that his position is more sophisticated (with a "long history" in its back).
Arrow (correctly) notes that even Rawls cannot rely too much on Knight's position because Rawls, too, embraces a decision procedure (not unlike the one familiar from Arrow's own "particular tradition of intellectual thought: that of welfare economics" (246)) with a representative agent-model in which some consensus is generated. (Recall from Rawls (who engages with earlier Arrow in context), "By assuming certain general desires, such as the desire for primary social goods, and by taking as a basis the agreements that would be made in a suitably defined initial situation, we can achieve requisite independence from existing circumstances. The original position is so characterized that unanimity is possible; the deliberations of any one person are typical of all." Theory of Justice) But this procedure is unstable according to Arrow because -- irony of history -- Knight was right after all: "empirical knowledge is after all uncertain, and even in the original position individuals may disagree about the facts and laws of the universe." (255) That is to say, "Rawls transfers the problem to the area of factual disagreement." (255)
One might think that the previous paragraphs need not be articulated. For the conventional wisdom is that in his famous (1975) review, Harsanyi shows that Rawls position cannot withstand technical scrutiny. But this is only so because Harsanyi (like many Bayesians after him) assumes away what even Arrow grudgingly had to concede that there is a "recurrent and unresolved controversy." To be sure: Harsanyi allows that in Rawls "the participants would be uncertain about what their personal circumstances would be under any particular institutional framework to be agreed upon." (594) But, rather than acknowledge the existence of (Knightian) uncertainty, Harsanyi goes on to conflate "the two parts" of Rawls's argument that Arrow had correctly diagnosed. In effect, Harsanyi simply ignores the second part; thereby, Rawls's use of maximin is not the (purported) one that Harsanyi effectively demolishes.
[1] For a good defense of the significance of uncertainty in the original position, see Angner, E. (2004). Revisiting Rawls: A Theory of Justice in the light of Levi's theory of decision. Theoria, 70(1), 3-21.
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