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Manfred comments on Selfish preferences and self-modification - Less Wrong Discussion
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Then we have the problem of deciding what counts as a decision. Even very minor changes will invalidate a broad definition like "body movements", as most body movements will be different after the 2 diverge.
My prefered diverging point is as soon as the cloning happens. I'm open to accepting that as long as they are identical, they can cooperate, but that can be justified by pure TDT without invoking "caring for the other". But any diverging stops this; that's my Schelling point.
The trouble is, of course, that if you both predictably (say, with 98% probability) switch to defecting after one sees 'A' and the other sees 'B', you could just as easily (following some flavor of TDT) predictably cooperate.
This issue is basically the oversimplification within TDT where it treats algorithms as atomic causes of actions, rather than as a lossy abstraction from complex physical states. This is a very difficult AI problem that I'm pretending is solved for the purposes of my posts.