I do have an idea for a reasonably Extropian future which is consistent
with this argument being valid. What if almost everyone in the future
is a "mental descendant" of someone alive today or in the near future?
That is, they all have memories which extend back to the present day.
This would imply that most population growth ultimately becomes a matter
of mental duplication in some form, perhaps as uploads make copies
of themselves. There could be variations where people merge their thoughts
or change them, but for the argument to work they must retain a basic sense
of identity back to the present.
Then the doomsday argument is less effective because almost everyone
throughout human history will have been exposed to this argument at around
the point it was created, within a few decades of the year 2000. Hence
the fact that we are living through this moment is unsurprising since
virtually everyone in history will also have lived through this moment,
and have the same memories of it that we do, or soon will.
I am not 100% sure this argument works; maybe the doomsdayers would
suggest that even assuming my projected history is true, we should
find ourselves surprised to actually be conscious at this point in our
timelines, rather than at the later points when we are more numerous.
However I think this assumes a model of time which is not at all clearly
valid.
Hal