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brian_jaress comments on Avoiding doomsday: a "proof" of the self-indication assumption - Less Wrong
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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.