similar to the Doomsday argument.

Just to jump in here - the solution to the doomsday argument is that it is a low-information argument in a high-information situation. Basically, once you know you're the 10 billionth zorblax, your prior should indeed put you in the middle of the group of zorblaxes, for 20 billion total, no matter what a zorblax is. This is correct and makes sense. The trouble comes if you open your eyes, collect additional data, like population growth patterns, and then never use any of that to update the prior. When people put population growth patterns and the doomsday prior together in the same calculation for the "doomsday date," that's just blatantly having data but not updating on it.