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torekp comments on It's not like anything to be a bat - Less Wrong
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Let's look at examples where we know the 'right' answer:
Someone flips a coin. If it's heads they copy you a thousand times and put 1 of you in a green room and 999 of you in a red room. If it's tails they do the opposite.
You wake up in a green room and conclude that the coin was likely tails.
Now assume that in addition to copying you 1000 times, 999 of you were randomly selected to have the part of your brain that remembers to apply anthropic reasoning erased. You wake up in a green room and remember to apply the anthropic principle, but, knowing that you conclude that the group of people like you is only you. Nonetheless you should (I intuitively feel) still conclude the coin was likely tails.
Now assume that instead of random memory erasure, if the coin was heads the people in the red room forget about anthropics, and if the coin was tails the people in the green room forget about anthropics. You wake up in a green room and remember to apply the anthropic principle. Now it matters that you know to use the anthropic principle, and you should conclude with 100% certainty that the coin came up heads.
So, sometimes we need to consider the fact that the other people can apply the anthropic principle, and sometimes we don't need to consider it. I think I've confused myself.
I like this example because it has nice tidy prior probabilities. That's very much lacking in the Doomsday Argument - how do you distribute a prior over a value that has no obvious upper bound? For any finite number of people that will ever live, is there much greater than zero prior probability of that being the number? Even if I can identify something truly special about the reference class "among the first 100 billion people" as opposed to any other mathematically definable group - and thus push down the posterior probabilities of very large numbers of people eventually living - it doesn't seem to push down very far.