Glen Whitman asks whether Buchanan & Tullock "scooped" Rawls and his device of a "veil of ignorance" by introducing the device of a "veil of uncertainty" into their contractarian choice procedure in the Calculus of Consent. My answer is "sort of." It is clear from the footnotes of A Theory of Justice that Rawls knew Calculus, and much of Buchanan's work beside. They are not cited when the veil of ignorance is introduced, however. Instead, Rawls cites Harsanyi's 1953 paper, "Cardinal Utility in Welfare Economics and in the Theory of Risk Taking," in which Harsanyi introduces the idea that social welfare consists in the state of the world all individual's would prefer should they be in a state of uncertainty about their identity. (I think it works like this: if you are equally likely to be anybody, then your expected utility is the total utility of the world divided by the number of people in it. So, being a rational maximizer, you prefer the world with the most utility in it, or something like that.)
B&T don't cite Harsanyi, however. They cite Hayek in the Constitution of Liberty where he is making the point that equality under the law, and the rule of law, requires that law be general, and not framed with particular cases or persons in mind.
Rawls does cite Calculus, but in in order to distinguish what B&T mean by "constitutional choice" from what Rawls means by the "constitutional convention" in his four-stage sequence. It's worth quoting the footnote [p. 173, rev. ed]:
The idea of the four-stage sequence is part of a moral theory, and does not belong to an account of the working of actual constitutions, except insofar as political agents are influenced by the conception of justice in question. In the contract doctrine [i.e., in Rawls's scheme], the principles of justice have already been agreed to, and our problem is to formulate a schema that will assist us in applying them. The aim is to characterize a just constitution and not to ascertain which sort of constitution would be adopted, or acquiesced in, under more or less realistic (though simplified) assumptions about political life, much less on individualistic assumptions of the kind characteristic of economic theory.
This points up a tension that runs throughout Rawls's work between his penchant for moral idealization and his claim to be looking for a "realistically utopian" theory at the "limits of the realistically practicable." Here Rawls rejects B&T's behavioral assumptions. If he did not, B&T would likely have an impossibility theorem for the politics Rawls prefers, which is how descriptive theories can defeat normative aspirations, and Rawls would be left with something utopian in the pejorative sense.
But that's an aside. The point is that it is more likely that Rawls is drawing on the more explicit methodological machinery of Harsanyi than on B&T in Calculus, although he was obviously acquainted with that book, and it may have reinforced the theoretical need for a device for modeling impartiality like the veil of ignorance. In any case, they were both "scooped" by Harsanyi. But then again, the kernal of the veil of ignorance is there in impartial spectator theories, and in the categorical imperative.