RobinZ comments on What makes you YOU? For non-deists only. - Less Wrong
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I think we have, at least in sketch form - here's Alicorn's nutshell summary, and here's mine. Both of our theories, if they are distinct, fit this intuition of yours - that a person is not destroyed and a new person created after a spell of unconsciousness - better that the thread of consciousness approach.
As for the rest, quite frankly you should expect to get weird results in weird situations like duplication. One weird result I expect is that, if you are duplicated, there will be two people afterwards, both of whose experiences suggest that they are DanArmak.
I took the time to think all this through before replying. I think I grok now your and Alicorn and the other posters' theory(s). And I pretty much accept it now. Thanks for your explanations.
The problem with my old approach, as I now see it, is the impossibility of empirically distinguishing it from infinitely many other possible theories. In such a situation, it is indeed best to choose an approach that optimizes outcome over all my configuration-descendants, because I might subjectively become any of them.
Of course, if I give up personal continuity, then the above statement becomes merely "because each of them will have memories indicating it is my descendant". But I am forced to this point of view due to the apparent impossibility of describing a personal continuity in terms of physics, which does not break down in the face of (arbitrarily short) lapses of consciousness.
Thanks again to everyone else who participated and helped convince me.