Here is one presentation of such an argument, but keep in mind these points:
1. The strongest argument for redistribution is when redistribution boosts economic growth and benefits all or most of society. That is by no means always the case, but it is sometimes true and of course it is not a Rawlsian argument.
2. The second strongest argument for redistribution is that it is sometimes intrinsically better if a poor, needy person has a resource, as opposed to a wealthier person having that same resource. That is in fact what most people think, no matter what argument they give you.
3. As we’ll see, the Rawlsian argument is parasitic upon #2, so why not use #2 directly? Admittedly, #2 is a difficult conclusion to establish in a scientific manner, but the Rawlsian gloss, upon examination, makes it weaker not stronger. It does however make the argument look a) more academic, and b) apparently more in line with neoclassical economic modes of thinking.
4. Most political philosophers, or indeed most philosophers, are not Rawlsians, even if they have been influenced by Rawls, which is frequently the case. So why should you, if you’re an economist, be a Rawlsian? Is it that you read Rawls and the critics, sided with Rawls, and then sat down to derive its implications? Or did you find it a convenient rationalization for something you already believed or wanted to believe?
4b. Rawls is almost always invoked selectively, rarely being applied across national borders or across the generations, cases where it yields screwy results. Rawls himself hesitated to approve of economic growth, because it does not maximize the well-being of the original “worst off” generation, which of course has to do some saving. He had sympathies with the idea of Mill’s stationary state. It’s fine to reject those conclusions, as indeed you should, but again maybe you’re not really a Rawlsian. You are a selective Rawlsian, if that.
4c. Most people — rightly I might add — believe just as much in redistribution or maybe more when the position of the unfortunates is certain in advance. How many times have you heard social immobility cited as a problem that requires redistribution for its solution? That argument is fine on its own terms, but again we’re back to #2. The funny thing about econo-Rawlsians is that they want to cite the uncertainty of the wealth distribution as a reason for redistribution, and then they wish to turn around and cite the certainty of the wealth distribution as yet another reason for redistribution!
Yes, maybe you can apply a Rawlsian transform to those situations with certain allocations, using a “…but*if* these people were all behind a veil of ignorance…” But look, a Rawlsian transform is appropriate with only some probability, so if you adhered to Rawls as the “most likely correct moral theory,” you still in these cases of certain distributions ought to believe in less redistribution. But that is not how people’s opinions are structured, nor is it how they should be structured, so in other words again we are not really Rawlsians but rather again motivated by #2.
5. When it comes to redistribution as social insurance, the biggest problems with the Rawlsian method is this. People have all sorts of preferences across the distribution of income. Some are merit-related, some liberty-related, some non-Rawlsian-fairness related, some insurance-related, maybe even some rooted in prejudice. The list of motives and reasons is long. As the veil is typically used by economists, it strips away all of those preferences but…the preference for insurance. So it is no wonder that the final construct produces an argument for insurance. You get out of the construct what you put into it.
6. If you already believe in #2, #5 won’t bother you much. But #2 is doing the real work here.
7. Almost everyone stops applying #2 at some point or margin. For instance, do you always and everywhere favor boosting the scope of the Obamacare mandate? It would save lives. If you don’t favor increasing the mandate, are you a despicable killer? In fact what I observe is people taking the status quo, and its current political debates, as a benchmark of sorts, and choosing sides, yet without outlining the “stopping principles” for their own recommendations. That’s a pretty sure sign a person is not thinking about the issues clearly.
8. Even #2, which I think of as a kind of “brute egalitarianism,” isn’t as straightforward as you might think. We do not always apply it to people in other countries, wealthy people who are poor in net terms because they are about to die, ugly men who cannot get sex, and many of the disabled. Just about everyone is more of a particularist, situation-based egalitarian than they like to let on.
In sum, the arguments for (some limited) redistribution are stronger than the arguments for Rawls.