In the post Outlawing Anthropics, there was a brief and intriguing scrap of reasoning, which used the principle of reflective inconsistency, which so far as I know is unique to this community:

If your current system cares about yourself and your future, but doesn't care about very similar xerox-siblings, then you will tend to self-modify to have future copies of yourself care about each other, as this maximizes your expectation of pleasant experience over future selves.

This post expands upon and attempts to formalize that reasoning, in hopes of developing a logical framework for reasoning about reflective inconsistency.