This rule is rational under certain conditions. First, we do not know the probability of each circumstance under each decision. This make it impossible to calculate expectation of gain. Second, the worst off position chosen by maximin rule is good enough that we are not eager to get more than that. Third, the worst positions under other alternatives are unacceptably bad. Under the second and third assumptions we are inclined to secure the minimal acceptable result above all. Thus we use the maximin rule. Rawls thinks that original position satisfies these conditions.
As for the first assumption, we donŐt know anything about the probability of each outcome by the veil of ignorance. We do not know even exact values of outcomes. To consider second and third assumption, we should recall the alternatives among which we are choosing. We restricted the alternatives to the theories which are actually proposed as serious theories. Among them, most dominant ones are classical and average utilitarianism, and two principles of justice. Among these alternatives, the two principles of justice assure us a minimal acceptable outcome, due to the first principle and the difference principle (And under the condition of moderate scarcity, the worst off position under this alternative is acceptable by the definition of "moderate"). We can also assume the law of diminishing marginal utility as a psychological fact. According to this law, when we have already had enough, adding more goods does not increase our utility a lot. Thus we are not eager to get more than minimal enough outcome. Third assumption is understandable if we think about other dominant alternatives, namely classical and average utilitarianism. Under these alternatives, someone can be unacceptably worse off for the sake of maximizing utility. Utilitarians say this cannot happen because of diminishing marginal utility, but this is only a conjecture. We cannot risk the secure minimal outcome by such a conjecture. Therefore, the second and third assumptions are satisfied in the original position.