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CronoDAS comments on Avoiding doomsday: a "proof" of the self-indication assumption - Less Wrong
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What bugs me about the doomsday argument is this: it's a stopped clock. In other words, it always gives the same answer regardless of who applies it.
Consider a bacterial colony that starts with a single individual, is going to live for N doublings, and then will die out completely. Each generation, applying the doomsday argument, will conclude that it has a better than 50% chance of being the final generation, because, at any given time, slightly more than half of all colony bacteria that have ever existed currently exist. The doomsday argument tells the bacteria absolutely nothing about the value of N.
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.
The fact that every generation gets the same answer doesn't (of itself) imply that it tells the bacteria nothing. Suppose you have 65536 people and flip a coin 16 [EDITED: for some reason I wrote 65536 there originally] times to decide which of them will get a prize. They can all, equally, do the arithmetic to work out that they have only a 1/65536 chance of winning. Even the one of them who actually wins. The fact that one of them will in fact win despite thinking herself very unlikely to win is not a problem with this.
Similarly, all our bacteria will think themselves likely to be living near the end of their colony's lifetime. And most of them will be right. What's the problem?
I think you mean 16 times.
Er, yes. I did change my mind a couple of times about what (2^n,n) pair to use, but I wasn't ever planning to have 2^65536 people so I'm not quite sure how my brain broke. Thanks for the correction.