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?
Also: http://www.nickbostrom.com/papers/experience.pdf (has been open in a tab for a while now as Something I Really Should Read).
I have read this paper and it really isn't that much about identity. What Bostrom is interested in are questions like this: Do two identical brains in identical states of suffering or pleasure count as x or 2x units of suffering or pleasure? (Bostrom argues 2x). Bostrom is pretty much agnostic on whether the two identical brains are the same person. He doesn't make claims on whether the two brains are two separate people experience x units of suffering/pleasure each, or if they are one person experiencing 2x units of suffering/pleasure.