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Donny comments on Harry Potter and the Methods of Rationality discussion thread, part 14, chapter 82 - Less Wrong Discussion
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Or, instead of your mind being distributed across multiple processors, a horcrux is a copy. And if you're killed, you survive not as a ghost, but by virtue of the fact that there's still a copy of you extant and functioning in the world. The same way uploading counts as survival.
Which means that by filling the world with horcruxes, Voldemort is executing the Hansonian strategy of flooding the labor market with EMs.
ETA: Hey, would Voldemort care what happened to a copy of himself? Perhaps the "power Voldemort knows not" is TDT. :)
Well, I've solved the story. Harry defeats Voldemort by tricking him into doing the "rational" thing and defecting against himself. Posting this in a new, unedited comment just in case it turns out to be more than a bad joke.