The first point that is made is that the point of view anyone would have within the original position ensures that there is no way of securing special advantages or, indeed, for putting up with special disadvantages. Given this point there is an automatic tendency (part of the "equilibrium" within the "original position") to favour equality of distribution. On these grounds Rawls refers immediately to the previous principles of equality of basic liberties, fair equality of opportunity and equal division of income and wealth.
However whilst this automatic tendency exists within the "original position" this is hardly sufficient to meet the fifth formal constraint of the concept of right, namely, that of finality. This failure to meet the criteria of finality is due to the point that Rawls makes against simple acceptance of an all-out commitment to egalitarianism and involves qualified reference to Pareto optimality since departure from a baseline of equality has not been shown to be inefficient in regard to the provisions of all. Further, whilst parties are mutually disinterested in the "original position", a point that ensures that no one has selfish motives, there are still reasons to recall the "circumstances of justice", circumstances that act as an additional constraint on the "original position", additional, that is, to the formal constraints arising from the concept of right.
It is when reference to these considerations of the "circumstances of justice" and Pareto optimality are brought into play that Rawls is able to qualify the initial result of preference for strict egalitarianism by reference to the difference principle. The difference principle is thus invoked as a reflective check upon the tendency towards an egalitarian equilibrium within the "original position". However, although it is such a check, it is meant also to meet Gerry Cohen's request for "justificatory community" since it sets the standards of justification for departure from commitment to baseline standards that are entirely egalitarian.
Now, this intuitive account of some basic reasons for pushing towards recognition of the two principles of justice is an initial description of the conditions of choice within the "original position". It is next supplemented by reference to a further consideration that will be thought to have weight in the process of reasoning that parties in this choice situation are engaged in. This is that, whilst the introduction of the "veil of ignorance" has ensured that the parties in question have no way of comprehending what specific interests they might have, they are aware that they will have some. By "interests" here Rawls means what Bernard Williams elsewhere called "commitments" as he has in mind the sense that people have "fundamental aims" and the security of the basic liberties is meant to ensure protection of such interests.
Finally, as part of the conception of "psychology" that Rawls has left outside the "veil" there is reason to assume that all parties have a higher-order interest in how their interests will be shaped by the basic structure. This point gives a preference again in the equilibrium to liberty of thought and action in how their interests can develop and strengthens the sense that such a commitment has lexical priority over the other pull towards equality. This provision of lexical priority for equal liberty is a second element of reflective check on the base equilibrium condition of equality (second, in order of introduction only, not necessarily second in the order of justification).
After giving these general considerations that make evident the plausibility of the two principles of justice Rawls next considers the means of making commitment to the two principles more systematically justifiable. This is attempted by reference to a rule thought available for consideration within the "original position" given that economic theories are open to be consulted there (are outside the "veil"). This is the "maximin rule" for circumstances of choice under conditions of uncertainty. The maximin notion means maximum minimorum and directs us to consider the worst that could happen to us under any proposed course of action and then to choose in light of this understanding so that the worst outcome available is one that is easiest to bear compared to the alternatives that could be considered.
The maximin rule is understood by Rawls to have a natural "conservative" bias in the sense that it militates against unnecessary risk. The reason for viewing the appeal to the rule as important under the conditions of the "original position" next have to be given. Rawls specifies three conditions that make appeal to this rule plausible. Firstly, there has to be a reason for discounting estimates of probabilities (since the worst possible outcome on one choice might be much less likely than that on another). Secondly, it has to be not worthwhile for the person making the choice to engage in risk with regard to a specified minimum threshold. In other words, it must not be worth their while to engage in speculations that have any potential to threaten this. This indicates that the third feature that makes appeal to the maximin rule plausible is that we are in a situation of "grave risk". The "paradigm situation" for following the maximin rule is when all these conditions are clearly and decisively met.
Having made these points Rawls next reviews the circumstances of the original position again. The introduction of the "veil of ignorance" meets the first condition of appeal to the maximin rule since it ensures that probabilities are discounted. The second consideration is met since a satisfactory minimum would be sufficient for all engaged in the "original condition", particularly if the commitment to equal basic liberties is accepted as given. Finally, the grave risks mentioned in the third consideration are clearly met if we consider that some principles could lead to extreme conditions including the institution of slavery or serfdom and we have no means of guarantee that we would not be ourselves in the least fortunate situation in such a system.
The maximin rule thus ensures that our caution in the "original position" is secured. Just as the introduction of the "veil of ignorance" accentuated attention to the generality constraints of the concept of right so the reference to the maximin rule ensures that we have greater reason to wish for conditions of stability (in which principles of justice secure the conditions of their own acceptance) are met. Appeal to the maximin rule is thus a way of enforcing the constraint of publicity.
The rest of section 26 departs from these considerations to present a general argument for conceding that "general facts" are required in discussing the arguments for the principles of justice. The "facts" in question are, however, no other than those that were included in the construction of the "original position" (circumstances of justice plus the thin theory of the good). More general facts than these cannot be considered and one of the reasons why is that they then invoke more complicated theoretical arguments that cut against simplicity of presentation and understanding.