Firstly, there’s a difference between “never” and “extremely rarely”.
That difference is so small as to be neglected.
And in the latter case, the question remains “and what do you do then?”. To which, it seems, you answer “choose the Right box”…? Well, I agree with that! But that’s just the view that I’ve already described as “Left-box unless there’s a bomb in Left, in which case Right-box”.
It seems to me that strategy leaves you manipulatable by the predictor, who can then just always predict you will Right-box, put a bomb in Left, and let you Right-box, causing you to lose $1,000.
By construction it is not, because the scenario is precisely that we find ourselves in one such exceptional case; the posterior probability (having observed that we do so find ourselves) is thus ~1.
It seems to me that strategy leaves you manipulatable by the predictor
… but you have said, in a previous post, that if you find yourself in this scenario, you Right-box. How to reconcile your apparently contradictory statements…?
By construction it is not, because the scenario is precisely that we find ourselves in one such exceptional case; the posterior probability (having observed that we do so find ourselves) is thus ~1.
Except that we don’t find ourselves there if we Left-box. But we seem to be going around in a circle.
… but you have said, in a previous post, that if you find yourself in this scenario, you Right-box. How to reconcile your apparently contradictory statements…?
Right-boxing is the necessary consequence if we assume the predictor’s Right-box prediction is fixed now. So GIVEN the Right-box prediction, I apparently Right-box.
My entire point is that the prediction is NOT a given. I Left-box, and thus change the prediction to Left-box.
I have made no contradictory statements. I am and always have been saying that Left-boxing is the correct decision to resolve this dilemma.
Except that we don’t find ourselves there if we Left-box. But we seem to be going around in a circle.
There’s no “if” about it. The scenario is that we do find ourselves there. (If you’re fighting the hypothetical, you have to be very explicit about that, because then we’re just talking about two totally different, and pretty much unrelated, things. But I have so far understood you to not be doing that.)
Right-boxing is the necessary consequence if we assume the predictor’s Right-box prediction is fixed now. So GIVEN the Right-box prediction, I apparently Right-box.
I don’t know what you mean by “apparently”. You have two boxes—that’s the scenario. Which do you choose—that’s the question. You can pick either one; where does “apparently” come in?
My entire point is that the prediction is NOT a given. I Left-box, and thus change the prediction to Left-box.
What does this mean? The boxes are already in front of you.
I have made no contradictory statements. I am and always have been saying that Left-boxing is the correct decision to resolve this dilemma.
You just said in this very comment that you Right-box in the given scenario! (And also in several other comments… are you really going to make me cite each of them…?)
I’m not going to make you cite anything. I know what you mean. I said Right-boxing is a consequence, given a certain resolution of the problem; I always maintained Left-boxing is the correct decision. Apparently I didn’t explain myself well, that’s on me. But I’m kinda done, I can’t seem to get my point across (not saying it’s your fault btw).
That difference is so small as to be neglected.
It seems to me that strategy leaves you manipulatable by the predictor, who can then just always predict you will Right-box, put a bomb in Left, and let you Right-box, causing you to lose $1,000.
By construction it is not, because the scenario is precisely that we find ourselves in one such exceptional case; the posterior probability (having observed that we do so find ourselves) is thus ~1.
… but you have said, in a previous post, that if you find yourself in this scenario, you Right-box. How to reconcile your apparently contradictory statements…?
Except that we don’t find ourselves there if we Left-box. But we seem to be going around in a circle.
Right-boxing is the necessary consequence if we assume the predictor’s Right-box prediction is fixed now. So GIVEN the Right-box prediction, I apparently Right-box.
My entire point is that the prediction is NOT a given. I Left-box, and thus change the prediction to Left-box.
I have made no contradictory statements. I am and always have been saying that Left-boxing is the correct decision to resolve this dilemma.
There’s no “if” about it. The scenario is that we do find ourselves there. (If you’re fighting the hypothetical, you have to be very explicit about that, because then we’re just talking about two totally different, and pretty much unrelated, things. But I have so far understood you to not be doing that.)
I don’t know what you mean by “apparently”. You have two boxes—that’s the scenario. Which do you choose—that’s the question. You can pick either one; where does “apparently” come in?
What does this mean? The boxes are already in front of you.
You just said in this very comment that you Right-box in the given scenario! (And also in several other comments… are you really going to make me cite each of them…?)
I’m not going to make you cite anything. I know what you mean. I said Right-boxing is a consequence, given a certain resolution of the problem; I always maintained Left-boxing is the correct decision. Apparently I didn’t explain myself well, that’s on me. But I’m kinda done, I can’t seem to get my point across (not saying it’s your fault btw).