The doomsday assumption makes the assumptions that:
We are randomly selected from all the observers who will ever exist.
Actually, it requires that we be selected from a small subset of these observers, such as “humans” or “conscious entities” or, perhaps most appropriate, “beings capable of reflecting on this problem”.
They are wiped out by a catastrophic event, rather than slowly dwindling
Well, for the numbers to work out, there would have to be a sharp drop-off before the slow-dwindling, which is roughly as worrisome as a “pure doomsday”.
Actually, it requires that we be selected from a small subset of these observers, such as “humans” or “conscious entities” or, perhaps most appropriate, “beings capable of reflecting on this problem”.
Well, for the numbers to work out, there would have to be a sharp drop-off before the slow-dwindling, which is roughly as worrisome as a “pure doomsday”.