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Eliezer_Yudkowsky comments on Avoiding doomsday: a "proof" of the self-indication assumption - Less Wrong
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But they'll be well-calibrated in their expectation - most generations will be wrong, but most individuals will be right.
Woah, Eliezer defends the doomsday argument on frequentist grounds.
So we might well be rejecting something based on long-standing experience, but be wrong because most of the tests will happen in the future? Makes me want to take up free energy research.
Only because of the assumption that the colony is wiped out suddenly. If, for example, the decline mirrors the rise, about two-thirds will be wrong.
ETA: I mean that 2/3 will apply the argument and be wrong. The other 1/3 won't apply the argument because they won't have exponential growth. (Of course they might think some other wrong thing.)
They'll be wrong about the generation part only. The "exponential growth" is needed to move from "we are in the last 2/3 of humanity" to "we are in the last few generations". Deny exponential growth (and SIA), then the first assumption is still correct, but the second is wrong.
But that's the important part. It's called the "Doomsday Argument" for a reason: it concludes that doomsday is imminent.
Of course the last 2/3 is still going to be 2/3 of the total. So is the first 2/3.
Imminent doomsday is the only non-trivial conclusion, and it relies on the assumption that exponential growth will continue right up to a doomsday.