It is possible I have missed an important point you are making, but here is how I interpret what you wrote:
Observer #1 in this scenario is a special class because he knows that he was created before Doomsday. Because of this, he knows that his retrospective probability for heads is 50% because he was created regardless of the coin’s outcome.
In our world, the timing of Doomsday is not so well-defined that we can say whether we’re in the same position as Observer #1 or not. Maybe we have lived past the most likely Doomsday scenario, and maybe we haven’t.
It is possible I have missed an important point you are making, but here is how I interpret what you wrote:
Observer #1 in this scenario is a special class because he knows that he was created before Doomsday. Because of this, he knows that his retrospective probability for heads is 50% because he was created regardless of the coin’s outcome.
In our world, the timing of Doomsday is not so well-defined that we can say whether we’re in the same position as Observer #1 or not. Maybe we have lived past the most likely Doomsday scenario, and maybe we haven’t.
Edit: grammar