A couple of days ago, I wrote a post about Rawls' difference principle. My main conclusion was that Rawls' argument for the difference principle relies on the mistaken assumption that there is such a thing as a rational preference; it assumes that minimaxing behind a veil of ignorance is more rational than following any other strategy, such as maximising expected utility. (As a friend of mine points out, someone who believes there is such thing as a rational preference will not necessarily accept my conclusion.)
However, I made one mistake in my analysis. This mistake does not affect my conclusion, but I think it is worth discussing anyway. In particular, I stated that Premise 2 of Rawls' argument for the difference principle is tantamount to the claim that it is rational to play a minimax strategy when faced with a veil of ignorance. This is wrong. What I should have said is that Premise 2 is tantamount to the claim that it is rational to play a minimax strategy and to be inequity-averse when faced with a veil of ignorance.
Premise 2 (again, please correct me if I've got it wrong) is as follows. An individual faced with a veil of ignorance would only want to deviate from perfect equality if doing so would improve the position of the least well-off people in society. More generally, an individual faced with a veil of ignorance would only want some amount of inequality, rather than no inequality, if introducing that inequality would improve the position of the least well-off people in society. In other words, she would want to maximise the position of the least well-off, whilst keeping inequality as low as possible.
By way of illustration, consider the diagram below. An individual who simply had a preference for minimaxing would be indifferent betweeen Scenarios 2 and 3. Conditional on maximising the position of the least well-off people in society, she would be indifferent to the amount of inequality in the rest of the distribution. However, an individual who not only had a preference for minimaxing, but was also inequity-averse, would prefer Scenario 2 to Scenario 3. The least well-off do just as well in Scenario 2 as they do in Scenario 3, but there is less inequality overall in Scenario 2.
If my interpretation of Premise 2 is correct (please tell me if it isn't), Rawls is arguing that a rational individual behind a veil of ignorance would have a preference against scenarios where she could be--on average--better off, and--at worst--no worse off. He is arguing that, conditional on maximising her minimum utility, she would prefer to have lower expected utility. Even if (unlike me) you believe that preferences can be rational, it seems rather irrational to want less expected utility rather than more.
One response I can think of (which is not totally unreasonable) is as follows. The different scenarios behind a veil of ignorance do not correspond to different distributions of utility, but to different distributions of the social and economic determinants of utility (i.e., status, income etc.). And although it might be irrational to want less expected utility, it is not irrational to want less expected income. This is because if you happened to be one of the least well-off people in society, you would want the most well-off people to have as little income as possible.
A counter to this argument is as follows. Even if it is not irrational to be concerned about your relative income, and accepting that there are diminishing marginal returns to income, it is not true that, for all combinations of degree of concern over relative income and rate of decrease of marginal utility, you would strictly prefer less inequality to more inequality. In other words, holding minimum income constant, it is possible to imagine some increase in inequality that you would prefer. At this point, the debate would presumably come down to what degrees of concern over relative income and rates of decrease of marginal utility were reasonable to postulate.