This shows that inference "I think therefore I exist" is, in general, invalid. You can't update on your own existence (although you can use more specific info as parameters in your strategy).
Rather, you should look at yourself as an implication: "If I exist in this situation, then my actions are as I now decide".
This might be a dumb question, but couldn't the inference of your existence be valid AND bring with it the implication that your actions are as you decide?
After all, if you begin thinking of yourself as an inference, and you think to yourself, "Well, now, IF I exist, THEN yadda yadda..." - I mean, Don't you exist at that point?
If non-existence is a negative, then you must be existant if you're thinking anything at all. A decision cannot be made by nothing, right?
If Omega is making you an offer, Omega is validating your existence. Why would Omega, or anyone ask a question and expect a reply from something that doesn't exist? You can also prove to yourself you exist as you consider the offer because you are engaged in a thinking process.
It feels more natural to say "I think, therefore I exist, and my actions are as I now decide."
That said, I don't think anyone can decide themselves out of existence LoL. As far as we know, energy is the only positive in the universe, and it cannot be destroyed, only transformed. So if your conciousness is tied to the structure of the matter you are comprised of, which is a form of energy, which is a positive, then it cannot become a negative, it can only transform into something else.
Maybe the whole "quantum observer" thing can explain why you DO die/disappear: Because if Omega gave you a choice, and you chose to no longer exist, Omega is "forced", if you will, to observe your decision to cease existence. It's part of the integrity of reality, I guess - existence usually implies free will AND it implies that you are a constant observer of the universe. If everything in the universe is made of the same thing you are, then everything else should also have the same qualities as you.
Every other positive thing has free will and is a constant observer. With this level playing field, you really have no choice but to accept your observations of the decisions that others make, and likewise others have no choice but to accept whatever decisions you make when they observe you.
So as the reality of your decision is accepted by Omega - Omega perceives you as gone for good. And so does anyone else who was observing. But somehow you're still around LoL
Maybe that explains ghosts??? lol ;-D I know that sounds all woo-woo but the main point is this: it's very hard to say that you can choose non-existence if you are a positive, because so far as we know, you can't undo a positive.
(It reminds me of something Ayn Rand said that made me raise an eyebrow at the whole Objectivism thing: She said you can't prove a negative and you can't disprove a positive. I always thought it was the other way around: You can't disprove a negative (you can't destroy something that doesn't exist), and you can't prove a positive (it's fallacious to attempt to prove the existence of an absolute, because the existence of an absolute is not up for debate!).
Ayn Rand's statements were correct without being "true" somehow. You can't prove a negative because if you could it would be a positive. Where as you can't disprove a negative because if you COULD disprove a negative you would just end up with a double-negative?? Whaaat???
LOL Whatever, don't listen to me : D
mmm to clarify that last point a little bit:
If disproving a negative was possible (meaning that disproving a negative could turn it into a positive) that would be the same as creating something out of nothing. It still violates the Law of Conservation of Energy, because the law states that you cannot create energy (can't turn a negative into a positive)
<3
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).