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cousin_it comments on indexical uncertainty and the Axiom of Independence - Less Wrong
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Here's a precise definition of "observer-moment", "trustworthiness" and everything else you might care to want defined. But I will ask you for a favor in return...
Mathematical formulation 1: Please enter a program that prints "0" or "1". If it prints "1" you lose $100, otherwise nothing happens.
Mathematical formulation 2: Please enter a program that prints "0" or "1". If it prints "1" you gain $10000 or lose $100 with equal probability, otherwise nothing happens.
Philosophical formulation by Vladimir Nesov, Eliezer Yudkowsky et al: we ought to find some program that optimizes the variables in case 1 and case 2 simultaneously. It must, must, must exist! For grand reasons related to philosophy and AI!
Now the favor request: Vladimir, could you please go out of character just this once? Give me a mathematical formulation in the spirit of 1 and 2 that would show me that your and Eliezer's theories have any nontrivial application whatsoever.
Vladimir, it's work in progress; if I could state everything clearly, I would've written it up. It also seems that what is already written here and there informally on this subject is sufficient to communicate the idea, at least as problem statement.