The major changes to the bargaining game introduced in "Distributive Justice" and carried over into A Theory of Justice are rather dramatic. They are four in number:
(1) Rawls introduces the famous Veil of Ignorance, which is a brilliant literary device designed to capture what we mean when we say that judges must be "disinterested" -- i.e., that they must make decisions without taking into consideration their own interests or situation. This takes care of the problem that some participants in the Bargaining Game are, and know they are, among the more talented members of society, while others are, and know they are, among the less talented. But this fix comes with its own problems.
Stripped of any knowledge of who they are, the players in the Bargaining Game now have no reason at all to bargain, or indeed to do anything else. This will be clear if we keep in mind the analogy to judges. Judges, in their judicial capacity, are not supposed to have an agenda [think Confirmation Hearings for Supreme Court nominees and all the blather about "activist justices" who "make law from the bench."] So if the individuals under the veil of ignorance know nothing at all about who they are, they can have no ends, no purposes, save perhaps the goal to render decisions fairly when they are presented with cases. Hence these individuals have no reason to bargain about anything at all. The self-interest Rawls has equipped them with is vacuous. Rawls is thus forced to endow the individuals in the Original Position with some sorts of purposes, specific enough to make them care what they get from the agreement being hammered out, but not so specific as to recreate the problems that invalidated the first version of his theory.
(2) Rawls' solution is to state that the individuals in the Original Position know that they have Life Plans. And since it wouldn't do to allow them to have the life plan of a religious hermit, for example [because then they would not care how much stuff they got out of the bargain, or even whether they had civil rights and protections], Rawls stipulates that the Life Plans posited for the individuals in the Original Position require for their accomplishment certain rights and abilities, powers and endowments [i.e., some stuff]. Bu this creates a new raft of problems, of an especially intractable sort, because the sorts of rights and abilities, powers and endowments required for the fulfillment of one Life Plan may be quite different from those required for the fulfillment of a different Life Plan. If your Life Plan is to become a Professor of Philosophy, then access to higher education for all those sufficiently talented is going to loom large in your budget of things you are bargaining for. But if your Life Plan is to become a champion surfer, higher education may drop way down in your list of desiderata.
[Notice, by the way, that built into Rawls' conception of Life Plans is a particular substantive historical, and cultural, and social conception of individual personality and the good life. I do not have time to go into this in the detail that it deserves, so I will simply refer you to the classic discussion in Karl Mannheim's Ideology and Utopia, Chapter IV, of the chiliastic, liberal-humanitarian, conservative, and socialist-communist forms of the Utopian Mentality and the orientation to time itself. Rawls, to put it in shorthand, assumes that everyone in the Original Position has a liberal-humanitarian orientation toward time, which is simply part of the larger fact that his entire theory is an ideological rationalization of capitalist social democracy. But I digress.]
To get over the problem posed by the diversity of possible Life Plans, so that he can get back to his theorem, Rawls now makes another assumption, and this one is, technically speaking, a whopper.
(3) since they do not know which particular Life Plans they have, Rawls asserts [he never offers anything remotely like an argument for it] that one can create an index of the heterogeneous basket of basic stuff that anyone would need to pursue whatever Life Plan he or she might turn out to have, something Rawls calls an Index of Primary Goods He then simply assumes that everyone in the Original Position has positive, albeit declining, marginal utility for the Index of Primary Goods. He assumes this, not because it is plausible [he never offers any arguments for any of this], but because unless he assumes it he won't have a hope of invoking the tools and techniques of modern economic theory with which he thinks he can prove his "theorem."
The problem of constructing an index of a heterogeneous assortment of rights and abilities, powers, and endowments is completely insoluble, as any honest economist will tell you. Indices like the Consumer Price Index or the Dow Jones Index are hopelessly flawed, and there is no way to fix them. Some of you may be quite familiar with this problem, others may have never heard of it before. I guess maybe I ought to say a word or two about the subject, even though it will slow us down some. The Consumer Price Index is constructed by putting together a list ["a market basket"] of consumer goods in specific proportions that is supposed to reflect the way most Americans spend their household income in a specified time, say a month: So much housing, so many pounds of potatoes, so many lamb chops, so many visits to the doctor, etc. Samples are then taken, and averaged out, of what these items are selling for in various stores, doctors' offices, etc, around the country. The same market basket of goods and services is then priced a month later. If the total cost of the market basket has increased by 1%, then it is said that there has been a 1% increase in the CPI, or that there has been a month to month inflation rate of 1%.
There are a gazillion problems with this index, all of which are totally unfixable. For example, suppose you have a thirty year fixed rate mortgage on your house. In that case, if housing costs rise dramatically [as they did in the 70's and 80's, for example], the Consumer Price Index, reflecting that rise, may shoot up dramatically. But you won't actually experience that rise, because a major component of your market basket of goods, namely housing, is fixed. The same sort of problem arises with regard to every element in the "market basket." The dramatic rise in health care costs will not affect you so long as you are healthy, but will affect you if you have a special needs child. if you are a vegetarian, a steady decline in the price of meat won't have any effect on your pocketbook. When I was a young man living in Cambridge, Massachusetts, lobster was cheap at the supermarket and steak was expensive. Now, when I shop for dinner, steak is cheaper per pound than all but the least expensive fish. Once again, Rawls unconsciously [I think] builds intro his supposedly universal theory the assumptions, presuppositions, and tastes of a particular social and economic class, which happens to be his.
(4) The last major change is a revision in the statement of the so-called "Difference Principle." Instead of inequalities working to everyone's advantage, they must now work to the benefit of the least advantaged members of society. This is a very significant change However, Rawls introduces it not by saying that he has changed his mind, or has been compelled by the logic of the bargaining game to alter the theorem, but rather by saying that this is a more reasonable "interpretation" of the original form of the principle. I confess that I find this rather weird and creepy. Rawls treats his own two principles, which he made up, as though they had been inscribed on tablets by The Lord God Himself, and thus required us to interpret them rather than change them. This is one of the strangest features of Rawls' entire discussion.