Could you clarify these in detail, please? You probably should have made the post rather than me- your version seems a lot better.
As for myself, I want to try and get philosophical ideas together to encodify a purely selfish agenda because I'm still considering whether I want to try and push my brain (as far as it will go, anyway) towards that or a more selfless one. Trying to find a way to encode a purely selfish agenda as a coherent philosophical system is an important part of that- which requires an idea of personal identity.
To be honest, part of the reason I waited on making the post was because I was confused about it myself :P. But nevertheless. The following questions probably need to be either answered or dissolved by a complete theory of identity/consciousness; the first is somewhat optional, but refusing to answer it shunts it onto physics where it becomes much stranger. I'm sure there are others questions, too - if nobody responds to this comment I'll probably make a new post regardless.
Although Elizier has dealt with personal identity questions (in terms of ruling out the body theory), he has not actually, as far as I know, "solved" the problem of Personal Identity as it is understood in philosophy. Nor, as far as I know, has any thinker (Robin Hanson, Yvain, etc) broadly in the same school of thought.
Why do I think it worth solving? One- Lesswrong has a tradition of trying to solve all of philosophy through thinking better than philosophers do. Even when I don't agree with it, the result is often enlightening. Two- What counts as 'same person' could easily have significant implications for large numbers of ethical dilemnas, and thus for Lesswrongian ethics.
Three- most importantly of all, the correct theory has practical implications for cryonics. I don't know enough to assert any theory as actually true, but if, say, Identity as Continuity of Form rather than of Matter were the true theory it would mean that preserving only the mental data would not be enough. What kind of preservation is necessary also varies somewhat- the difference in requirement based on a Continuity of Consciousness v.s a Continuity of Psyche theory, for example should be obvious.
I'm curious what people here think. What is the correct answer? No-self theory? Psyche theory? Derek Parfit's theory in some manner? Or if there is a correct way to dissolve the question, what is that correct way?