Agreement seems more likely on general rules for collective choice than on the later choices to be made within the confines of certain agreed-upon rules. … Essential to the analysis is the presumption that the individual is uncertain as to what his own precise role will be in any one of the whole chain of later collective choices that will actually have to be made. For this reason he is considered not to have a particular and distinguishable interest separate and apart from his fellows. This is not to suggest that he will act contrary to own interest; but the individual will not find it advantageous to vote for rules that may promote sectional, class, or group interests because, by supposition, he is unable to predict the role that he will be playing in the actual collective decision-making process at any particular time in the future. He cannot predict with any degree of certainty whether he is more likely to be in a winning or a losing coalition on any specific issue. Therefore, he will assume that occasionally he will be in one group and occasionally in the other. His own self-interest will lead him to choose rules that will maximize the utility of an individual in a series of collective decisions with his own preferences on the separate issues being more or less randomly distributed.Note that this was first published in 1962 (though it's possible changes were made in later editions), almost a decade before John Rawls's A Theory of Justice in 1971. Did Buchanan & Tullock anticipate Rawls's veil of ignorance?
Yes, I realize there are important differences, particularly vis-à-vis the thinness of the veil, but the similarity is nonetheless striking.