Confused about the doomsday argument, please help
The doomsday argument says I have only a 10% chance of being within the first 10% of humans ever born, which gives nonzero information about when humanity will end. The argument has some problems with the choice of reference class; my favorite formulation (invented by me, I’m not sure if it’s well-known) is to use the recursive reference class of “all people who are considering the doomsday argument with regard to humanity”. But this is not the issue I want to discuss right now.
Imagine your prior says the universe can contain 10, 1000 or 1000000 humans, with probability arbitrarily assigned to these three options. Then you learn that you’re the 50th human ever born. As far as I can understand, after receiving this information you’re certain to be among the first 10% of humans ever born, because it’s true in every possible universe where you receive such information. Also learning your index doesn’t seem to tell you very much about the date of the doomsday: it doesn’t change the relative probabilities of doomsday dates that are consistent with your existence. (This last sentence is true for any prior, not just the one I gave.) Is there something I’m missing?