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).
The doomsday assumption makes the assumptions that:
We are randomly selected from all the observers who will ever exist.
The observers increase expoentially, such that there are 2/3 of those who have ever lived at any particular generation
They are wiped out by a catastrophic event, rather than slowly dwindling or other
(Now those assumptions are a bit dubious - things change if for instance, we develop life extension tech or otherwise increase rate of growth, and a higher than 2/3 proportion will live in future generations (eg if the next generation is immortal, they're guaranteed to be the last, and we're much less likely depending on how long people are likely to survive after that. Alternatively growth could plateau or fluctuate around the carrying capacity of a planet if most potential observers never expand beyond this) However, assuming they hold, I think the argument is valid.
I don't think your situation alters the argument, it just changes some of the assumptions. At point D, it reverts back to the original doomsday scenario, and the odds switch back.
At D, the point you're made aware, you know that you're in the proportion of people who live. Only 50% of the people who ever existed in this scenario learn this, and 99% of them are blue-doors. Only looking at the people at this point is changing the selection criteria - you're only picking from survivors, never from those who are now dead despite the fact that they are real people we could have been. If those could be included in the selection (as they are if you give them the information and ask them before they would have died), the situation would remain as in A-C.
Making creating the losing potential people makes this more explicit. If we're randomly selecting from people who ever exist, we'll only ever pick those who get created, who will be predominantly blue-doors if we run the experiment multiple times.
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".
Then what about introducing a C' between C and D: You are told the initial rules. Then, later you are told about the killing, and then, even later, that the killing had already happened and that you were spared.
What would you say the odds were there?
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).