I'll just cover three sections in this post, in order to finish up the sequence on the Self-interest theory, S.
In these sections, Parfit argues that S might tell us to believe things that are not true. For example, S might tell us to believe that it is rational to ignore threats, even though that is not in fact true, because it will lead to better results, at least some of the time.
Parfit's final statement about S, in section 9, is that even if S told everyone to believe some other theory, this would not mean that S was not in fact the best theory:
Suppose that S told everyone to cause himself to believe some other theory. S would then be self-effacing. If we all believed S, but could also change our beliefs, S would remove itself from the scene. It would become a theory that no one believed. But to be self-effacing is not to be self-defeating. It is not the aim of a theory to be believed. If we personify theories, and pretend that they have aims, the aim of a theory is not to be believed, but to be true, or to be the best theory. That a theory is self-effacing does not show that it is not the best theory.
That's it for S. The next sections deal with Consequentialism, C.