It seems to me that most of the confusion that arises about sense of self and identify comes out of the desire for some hard line in the sand, some cutoff point beyond which some entity is or isn't "the same". Unfortunately, that model isn't compatible with what the universe has provided to us; we've been given a hugely complex system, and there's a point where jamming binary descriptors on it is going to break down. I view it largely as a "word mangling" problem.
I doubt I could write a useful paper or article on this, but I can give my viewpoint in the form of question and answer:
Is a perfect copy of me 'me'? Yes. We are both the same person, both me.
Is an imperfect copy of me 'me'? Maybe. It depends on the amount of difference between us and our utility functions.
Is an older/younger copy of me still 'me'? Maybe. It depends on the amount of difference between us and our utility functions.
If I create a perfect copy of me and wait a week, so that we both collect additional experiences, is that copy me? At this point in time, with high probability, yes, we are still both me. The differences between us acquired in the course of a week are not likely to be so huge as to make us different people.
How much of a difference would there have to be for us to be different people? Probably pretty big. I can't draw a line in the sand easily for this; a difference of 90% of my age is probably guaranteed to be a different person, and 0.1% is probably not.
If you have to choose between one of two copies to keep, how do you do so? Look through the differences between them, figure out which set of experiences is most valuable according to our utility functions, and keep that copy.
I largely ascribe to the 'identity as pattern' concept. My pattern happens to be stored as combined matter and data in physical body right now; it should be entirely possible and reasonable to move, store, and update that pattern in other media without losing my identity or sense of self. A copy of me as a .tgz archive sitting idle on a hard drive platter is still me; it's just in suspended animation. Similarly, a copy of me in a cryogenic vault stored as biological data is still me.
Look through the differences between them, figure out which set of experiences is most valuable according to our utility functions, and keep that copy.
What if the utility functions differ?
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?