The distinction between "average" and "classical" utilitarianism is meant to show a difference between two possible interpretations of the initial situation. The "classical" view is taken by Rawls to involve taking the arrangement of institutions on the grounds of what results from absolute weighted sums of expectations of representative people. So, on this ground, when the number of people in society increases, so also does the total utility. By contrast, the "average" doctrine is so called as it directs society to maximise not the total but the average utility. So it would then be no longer true that increases in population correlate to increases in utility since we would instead be measuring percentages of increase in utility for specified groups and these would not require increases in the sizes of the groups in question.
Now the difference in question between these variants of utilitarianism essentially affects not static but dynamic populations. So the "classical" conception, in its preference for increases in population sacrifices any specific commitment to the levels of utility for specific individuals. And Rawls takes this to mean that the "classical" position would be rejected in the original position. A reason for this is that it would appear plausible, on adoption of the "average" principle, to specify a set level below which averages of utility for given persons should not fall. Given an assumption of self-interest this would appear to be the view most likely to appeal to the parties in the reasoning situation of the "original position".
The reasoning by which the "average" principle is arrived at in the "original position" is next examined. Rawls assumes that our parties are trying to work out what society should be like and, given the conditions of the "original position", it is safe to assume that there are no violent differences in preferences. To make the situation conform to the constraints of the "original position" the parties have to assume that they have no knowledge of where in the social situation the possession of given talents will lead them. If the reasoners then add the assumption that their preferences are not merely the same as those of others but that any given person has an equal chance of being any individual then they will be identical in scope with the average utility of the society.
If we then drop the assumption that we know anything about preferences we arrive at the introduction of the veil of ignorance. Since, in this situation, the appeal of the average principle of utility is still plausible, it has been shown that contractarian reasoning can produce the "average" principle of utility, a principle that does not, unlike the "classical" principle, enjoy a "teleological" element or the intuitive appeal of the idea of maximising the good. In the original edition of Theory Rawls puts this thus: "The average principle appeals to those in the initial situation once they are conceived as single rational individuals prepared to gamble on the most abstract probabilistic reasoning in all cases". This sentence is excised from the "revised" edition.
In the "revised" edition rather than formulate the principle of utility as concerned with the "satisfaction of desire" as appears to be assumed in the formulation of the first edition, it is instead understood in terms that are more familiar from economics, namely, as "a way of representing the choices of economic agents". However, this still enables the notion of "average" utility to be formulated, and particularly gives further scope to rational risk-aversion.
Having given an argument that shows that the "average" principle is the form of utility that would have appeal in the "original position", however, Rawls goes on to argue against its being the principle that would be chosen in this situation. In doing so, Rawls keeps the point that interpretation of principles in this situation, whilst hypothetical, is sufficiently grounded to enable choice of a principle as authenticated. The first point that Rawls invokes concerns the maximin principle as the choice being made is one that is based under conditions of uncertainty (at least once the veil of ignorance has been invoked). This leads to people having to assume that the principle of insufficient reason applies (in which we have to assume any given outcome is roughly equivalent in its chance of occurring with any other given outcome).
Once the veil of ignorance has been invoked, suggests Rawls, the two principles of justice will be more appealing than the principle of average utility since they will involve protection of our liberties and a reasonable standard of life. A basic reason for taking these principles to be a better guide than that of average utility concerns what the assumptions underpinning the latter include. Rawls suggests that they include the view that there would be some means to ensure that the favours of society were evenly distributed over time. (In a sense, then, the problem with the principle of average utility might be that it promises too much!) However, not only is it the case that these assumptions are large ones for individuals to make concerning their own welfare, they also neglect the problem of ensuring that general social decisions are made in ways that advance some sense of social justice.
One of the reasons why the average principle cannot really advance any sense of social justice is that it must leave out of account not merely what conceptions of the good are held by others but also that any conceptions are held at all. The final stage in the reasoning for the principle of average utility in the "original position" can allow no appeal to this notion as it is not capable of being assessed by quantitative appeals. As Rawls put this in the "revised edition": "The parties are conceived as having no definite highest-order interests or fundamental ends by reference to which they decide what sorts of persons they care to be. They have, as it were, no determinate character of will. They are, we might say, bare-persons".
This characterisation effectively repeats a general problem Rawls has with utilitarianism, that of "abstracting from the separateness of persons" as he put it in the Chapter I consideration of "classical utilitarianism" but its statement here is meant to show that "average utility" could not meet the standards of the original position as it would leave out something essential. So, on the one hand, average utility presupposes a calculation that lacks specificity in relation to the "original position" and, on the other hand, it lacks a full conception of the parties engaged in reasoning.