A rather curious claim, I have to say.
There is a group of people, and you are clearly not in their group - in fact the first thing you know, and the first thing they know, is that you are not in the same group.
Yet your own subjective probability of being blue-doored depends on what they were told just before being killed. So if an absent minded executioner wanders in and says "maybe I told them, maybe I didn't -I forget" that "I forget" contains the difference between a 99% and a 50% chance of you being blue-doored.
To push it still further, if there were to be two experiments, side by side - world C'' and world X'' - with world X'' inverting the proportion of red and blue doors, then this type of reasoning would put you in a curious situation. If everyone were first told: "you are a survivor/victim of world C''/X'' with 99% blue/red doors", and then the situation were explained to them, the above reasoning would imply that you had a 50% chance of being blue-doored whatever world you were in!
Unless you can explain why "being in world C''/X'' " is a permissible piece of info to put you in a different class, while "you are a survivor/victim" is not, then I can walk the above paradox back down to A (and its inverse, Z), and get 50% odds in situations where they are clearly not justified.
I don't understand your duplicate world idea well enough to respond to it yet. Do you mean they are told which world they are in, or just that they are told that there are the two worlds, and whether they survive, but not which world they are in?
The basic class idea I am supporting is that in order to count myself as in the same class with someone else, we both have to have access to basically the same probability-affecting information. So I cannot be in the same class with someone who does not exist but might have existed, because he has no access to any ...
EDIT: This post has been superceeded by this one.
The doomsday argument, in its simplest form, claims that since 2/3 of all humans will be in the final 2/3 of all humans, we should conclude it is more likely we are in the final two thirds of all humans who’ve ever lived, than in the first third. In our current state of quasi-exponential population growth, this would mean that we are likely very close to the final end of humanity. The argument gets somewhat more sophisticated than that, but that's it in a nutshell.
There are many immediate rebuttals that spring to mind - there is something about the doomsday argument that brings out the certainty in most people that it must be wrong. But nearly all those supposed rebuttals are erroneous (see Nick Bostrom's book Anthropic Bias: Observation Selection Effects in Science and Philosophy). Essentially the only consistent low-level rebuttal to the doomsday argument is to use the self indication assumption (SIA).
The non-intuitive form of SIA simply says that since you exist, it is more likely that your universe contains many observers, rather than few; the more intuitive formulation is that you should consider yourself as a random observer drawn from the space of possible observers (weighted according to the probability of that observer existing).
Even in that form, it may seem counter-intuitive; but I came up with a series of small steps leading from a generally accepted result straight to the SIA. This clinched the argument for me. The starting point is:
A - A hundred people are created in a hundred rooms. Room 1 has a red door (on the outside), the outsides of all other doors are blue. You wake up in a room, fully aware of these facts; what probability should you put on being inside a room with a blue door?
Here, the probability is certainly 99%. But now consider the situation:
B - same as before, but an hour after you wake up, it is announced that a coin will be flipped, and if it comes up heads, the guy behind the red door will be killed, and if it comes up tails, everyone behind a blue door will be killed. A few minutes later, it is announced that whoever was to be killed has been killed. What are your odds of being blue-doored now?
There should be no difference from A; since your odds of dying are exactly fifty-fifty whether you are blue-doored or red-doored, your probability estimate should not change upon being updated. The further modifications are then:
C - same as B, except the coin is flipped before you are created (the killing still happens later).
D - same as C, except that you are only made aware of the rules of the set-up after the people to be killed have already been killed.
E - same as C, except the people to be killed are killed before awakening.
F - same as C, except the people to be killed are simply not created in the first place.
I see no justification for changing your odds as you move from A to F; but 99% odd of being blue-doored at F is precisely the SIA: you are saying that a universe with 99 people in it is 99 times more probable than a universe with a single person in it.
If you can't see any flaw in the chain either, then you can rest easy, knowing the human race is no more likely to vanish than objective factors indicate (ok, maybe you won't rest that easy, in fact...)
(Apologies if this post is preaching to the choir of flogged dead horses along well beaten tracks: I was unable to keep up with Less Wrong these past few months, so may be going over points already dealt with!)
EDIT: Corrected the language in the presentation of the SIA, after SilasBarta's comments.
EDIT2: There are some objections to the transfer from D to C. Thus I suggest sliding in C' and C'' between them; C' is the same as D, execpt those due to die have the situation explained to them before being killed; C'' is the same as C' except those due to die are told "you will be killed" before having the situation explained to them (and then being killed).