The Difference Principle

Rawls.

The difference principle is the second part of the second principle of John Rawls’s theory of justice. 

The first principle requires that citizens enjoy equal basic liberties. 

The first part of the second principle requires fair equality of opportunity. 

These rules have priority over the difference principle; the difference principle cannot justify policies or institutions that abrogate them. 

The difference principle governs the distribution of income and wealth, positions of responsibility and power, and the social bases of self-respect. 

It holds that inequalities in the distribution of these goods are permissible only if they benefit the least well-off positions of society.

These are Rawls' offerings as principles of justice.

The most widely discussed theory of distributive justice in the past four decades has been that proposed by John Rawls in A Theory of Justice, (Rawls 1971), and Political Liberalism, (Rawls 1993). 

Rawls proposes the following two principles of justice:

1. Each person has an equal claim to a fully adequate scheme of equal basic rights and liberties, which scheme is compatible with the same scheme for all; and in this scheme the equal political liberties, and only those liberties, are to be guaranteed their fair value.

2. Social and economic inequalities are to satisfy two conditions: (a) They are to be attached to positions and offices open to all under conditions of fair equality of opportunity; and (b), they are to be to the greatest benefit of the least advantaged members of society. (Rawls 1993, pp. 5–6. The principles are numbered as they were in Rawls’ original A Theory of Justice.)

Where the rules may conflict in practice, Rawls says that Principle (1) has lexical priority over Principle (2), and Principle (2a) has lexical priority over (2b). 

It is his claim that justice requires observation of these principles.

Ignore, for the moment, the senselessness of moral claims of all sorts, including claims about what justice requires.

Is it really plausible that justice requires that any number of better off people be deprived of any amount of income or wealth to prevent deprivation of some or even all of the worse off, no matter how few they may be, of even the tiniest amounts of the same?

Apparently it was to Rawls, but it isn't and hasn't been to most others aware of the question.

No utilitarian would buy that.

And is it in the least credible that a representative flock of even no more than normally egoistic rational individuals would, in the fiction of the original position, choose a regime committed to this behind Rawl's veil of ignorance?

No, IMHO.