I'm not clear on what you mean by "self-parts" here, but I'm assuming you mean something like basis states that contain people like you, which you can describe people in terms of. In which case I've already trodden this ground - no such objective account must necessarily exist, but such things can be useful, though you still wouldn't be able to get any two different peoples' idealized algorithms to agree on the edge cases.
I don't mean something that contains you, I mean something that you contain.
http://www.scottaaronson.com/blog/?p=1103
Eliezer's gung-ho attitude about the realism of the Many Worlds Interpretation always rubbed me the wrong way, especially in the podcast between both him and Scott (around 8:43 in http://bloggingheads.tv/videos/2220). I've seen a similar sentiment expressed before about the MWI sequences. And I say that still believing it to be the most seemingly correct of the available interpretations.
I feel Scott's post does an excellent job grounding it as a possibly correct, and in-principle falsifiable interpretation.