This is another question worth debating of it's own. When I tried to do this on my own, I started by trying to figure out the answer to as many coherent variants of the question as possible seperately. The ones I think most important:
-Which variation of personal identity is best valued from an ethical perspective (ethical question) -Which variation of personal identity is most intuitive out of all coherent theories
There are various ways of looking at it, but my argument for these two is that the first is a necessary component of an ethical theory and that the second closest fits the philosophical idea of 'the answer'.
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?