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Yvain comments on Pascal's Muggle: Infinitesimal Priors and Strong Evidence - Less Wrong
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Imagine someone makes the following claims:
Then they threaten, unless you give them $5, to kidnap you, give you the immortality drug, stick you in the spaceship, launch it at near-light speed, and have you stuck (presumably bound in an uncomfortable position) in the spaceship for the 3^^^3 years the universe will last.
(okay, there are lots of contingent features of the universe that will make this not work, but imagine something better. Pocket dimension, maybe?)
If their claims are true, then their threat seems credible even though it involves a large amount of suffering. Can you explain what you mean by life-centuries being instantiated by causal nodes, and how that makes the madman's threat less credible?
Are you sure it wouldn't be rational to pay up? I mean, if the guy looks like he could do that for $5, I'd rather not take chances. If you pay, and it turns out he didn't have all that equipment for torture, you could just sue him and get that $5 back, since he defrauded you. If he starts making up rules about how you can never ever tell anyone else about this, or later check validity of his claim or he'll kidnap you, you should, for game-theoretical reasons not abide, since being the kinda agent that accepts those terms makes you valid target for such frauds. Reasons for not abiding being the same as for single-boxing.
That requires a MTTF of 3^^^3 years, or a per-year probability of failure of roughly 1/3^^^3.
This implies that physical properties like the cosmological constant and the half-life of protons can be measured to a precision of roughly 1/3^^^3 relative error.
To me it seems like both of those claims have prior probability ~ 1/3^^^3. (How many spaceships would you have to build and how long would you have to test them to get an MTTF estimate as large as 3^^^3? How many measurements do you have to make to get the standard deviation below 1/3^^^3?)
If what he says is true, then there will be 3^^^3 years of life in the universe. Then, assuming this anthropic framework is correct, it's very unlikely to find yourself at the beginning rather than at any other point in time, so this provides 3^^^3-sized evidence against this scenario.
I'm not entirely sure that the doomsday argument also applies to different time slices of the same person, given that Eliezer in 2013 remembers being Eliezer in 2012 but not vice versa.