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jimrandomh comments on Bayesian Doomsday Argument - Less Wrong Discussion
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There is a decision-theoretic caveat here. While you may be "just as likely" to be anyone, the amount of influence you have over utility, for most utility functions involving the universe as a whole, varies depending when you were born. People born earlier in the history of humanity have a greater influence, and therefore, you should weight the possibility that you were born early more highly.
You should weigh the importance of your choices more highly.
This doesn't mean future stuff doesn't matter; but it makes it so it's not an obvious choice.
Suppose you do something that has a chance of saving the world. Suppose there have been 100 billion people so far. The expected amount you'd do is ∫k/n dn = ln(n2/n1) If there's less than 200 billion people, that's k ln 2. If it's less than 210^40, that's k ln 210^29. It works out to being about 100 times as important. That seems like a lot, but charity tends to work in orders of magnitude difference.
I'm not sure how good a value 10^40 is, but I think the order of magnitude is within a factor of two, so the predicted value would be within that.