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by Paul Christiano 231 days ago | Vladimir Slepnev likes this | link | parent

Without reading closely, this seems very close to UDT2. Is there a problem that this gets right which UDT2 gets wrong (or for which there is ambiguity about the specification of UDT2?)

Without thinking too carefully, I don’t believe the troll bridge argument. We have to be super careful about “sufficiently large,” and about Lob’s theorem. To see whether the proof goes through, it seems instructive to consider the case where a trader with 90% of the initial mass really wants to cross the bridge. What happens when they try?



by Abram Demski 230 days ago | Paul Christiano likes this | link

The differences between this and UDT2:

  1. This is something we can define precisely, whereas UDT2 isn’t.
  2. Rather than being totally updateless, this is just mostly updateless, with the parameter \(f\) determining how updateless it is.

I don’t think there’s a problem this gets right which we’d expect UDT2 to get wrong.

If we’re using the version of logical induction where the belief jumps to 100% as soon as something gets proved, then a weighty trader who believes crossing the bridge is good will just get knocked out immediately if the theorem prover starts proving that crossing is bad (which helps that step inside the Löbian proof go through). (I’d be surprised if the analysis turns out much different for the kind of LI which merely rapidly comes to believe things which get proved, but I can see how that distinction might block the proof.) But certainly it would be good to check this more thoroughly.

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