John Rawls' veil of ignorance ("VOI") from A Theory of Justice (1971/1999) has assumed that rational, self-interested agents will choose the fairest principle of social justice for society if they do not know who they are, their social status, their ancestry, or their talents. They know nothing not only about their own social position but they know nothing of others' social position either. Behind the VOI agents do not know their place in society or know their ability to change society. Because they do not have this knowledge, the assumption is that agents behind the VOI will treat others fairly and impartially because everyone is equally situated. Likewise, the assumption is that others, too, will treat you equally well when they are behind the VOI. The person behind the VOI will choose the fairest principle of social justice because everyone would accept and agree to the principle if they found themselves facing a similar choice under the same conditions.
Given that those people who are behind the VOI have little knowledge about themselves and others, one question we may have is whether such people are capable of having desires. Some desires, after all, are the product of social influence. For example, we might want x because our neighbors have x or we want to wear y because our favorite celebrity wears y. Human nature seems to be naturally social, and we draw likes and dislikes from those who surround us. Desires are rarely not subject to outside influence.
One might contend that our desires are our desires. By this the person may mean that what I want is not subject to social control. I can form and maintain my desires independent of any social or outside influence; it is after all, to adopt terminology from Anscombe, a matter of fitting the world to suit me. The direction of fit for desires from me to the world. While this is no doubt true that desires are a matter of fitting the world to my whims, the whims and wants themselves are at least partially dependent upon others. Think here of our affinity for board games or video games or any hobby in which we engage. One story that we may tell of our likes is that they enable us to be social because these are interests shared by others.
If desires are not individualistic, then choosing one principle over another behind the VOI either has to be completely arbitrary or has to account for our desires, which seem to be off-limits for you behind the VOI. It can't be that we choose principles of justice arbitrarily because those wouldn't be fair for ourselves or others. Arbitrary choice gives up on our ability to use reason to decide what the best principle of justice is, and behind the VOI it seems that Rawls at least wanted us to take up principles of good reasoning to decide what the best principles are.
That leaves us with having to account for desires behind the VOI. The kind of principles that are fairest and most just would be the ones that we would want to live under once the VOI has been removed. This suggests, however, that the VOI does not necessarily remove oneself from all outside influence. Wanting some principle over another principle is often a reflection of some kind of social social influence. It might be the case that a rational, self-interested agent wants what would be best for her and others like her if they found themselves in the least well-off position. But this presumes that she interprets outside influence correctly and that she wants that kind of principle of justice to be instituted by the resulting government or political system.
We have to think that it is possible for the agent behind the VOI to have misinterpreted what her desires are and what others' desires are. If agents take others to say that society ought to maximize the least well-off's position and they've misinterpreted others' desires, then they might be wrong to presume that this is a good principle - for themselves and for others. So, there seems to be reason to think that there is no correlation between one's own desires and finding a principle of social justice using the VOI.