In this 1967 paper Rawls introduces the notion of the "veil of ignorance" for the first time, some 4 years after he first described the "original position". The first interesting thing about this paper is the way the first sentence describes human society as "a more or less self-sufficient association" thereby implicitly aligning political life in general with the notion of association. It's also worthy of note that Rawls points out instantly that society, is characterized as much by conflict as identity of interests and that it is this that requires some kind of equilibrium point to be aimed at.
After making these opening points Rawls quickly dispatches utilitarianism as a possible standard for social arrangements, not least because a loss of freedom for some is not made right by a general sum of advantages for others. This prompts him to specifically present his own doctrine, by contrast to the utilitarian one, as contractarian. It is after this that Rawls discusses original agreement and mentions the "veil of ignorance" for the first time. However, despite invoking this notion, Rawls makes as yet little use of it, mentioning for example that he will not here attempt to show that his two principles of justice would be chosen in the original position (thus the "veil of ignorance" lacks, as yet, methodological significance).
The two principles of justice that Rawls subsequently introduces are, however, themselves more detailed than previously though the principle of liberty continues to have a clear connection to Kant's supreme principle of right. The second principle is more detailed and reads as follows:
inequalities as defined by the institutional structure or fostered by it are arbitrary unless it is reasonable to expect that they will work out to everyone's advantage and provided that the positions and offices to which they attach or from which they may be gained are open to all
This second principle clearly comes in two parts with the second part being one of openness to talents. The notion that inequalities are only to be tolerated if they are to the advantage of the "representative man" opens some significant questions.
Rawls is clearly aware of this and mentions at this point Hume's influential critique of social contract theory which was to the effect that criteria of the kind invoked in the second principle turn out not to be meaningful since, it is quite conceivable, that even slaves are "better off" in some sense than they would be in a state of nature. Rawls also mentions the emptiness of assessing social outcomes on the grounds of efficiency alone as appears occurs on Pareto optimality criteria. So justice has to be clearly distinguished from efficiency.
In responding to these points Rawls makes a key modification of the second principle in favour not of the "representative man" in some general sense but rather in relation to the "least advantaged" and in so doing he describes, for the first time, the first part of the second principle as the "difference principle". It is the "most unfortunate representative man" to whom we have to justify inequalities now. By this means Rawls aims to meet the standards of efficiency in the sense of attaining a sense of Pareto optimality and marrying it to the standard of justice.