[QUOTE=Indistinguishable]
All I need for my justification for picking only one box is for “I picked one box” to be much better evidence for “There was a million dollars in the box” than “I picked two boxes” would be. Accurate prediction is good enough for this. This is equivalent to the very definition of accurate prediction.
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If this was true, it would still be true if the boxes were transparent. Your ignorance about the contents of the box has no impact whatsoever on the skills of the predictor or the contents of the box.
[QUOTE=Indistinguishable]
As for your proof, it shows that if people always take the box with the money, no predictor could accurately predict this and put the money in the other box. Sure. But this doesn’t rule out accurate predictors who don’t try to set up such situations, or accurate predictors who set up such situations in a world where, for whatever reason, players don’t always take the box with the money. Accurate prediction is not, in itself, contradictory (of course it isn’t). And I’m not sure what reverse causation has to do with anything; apparently, “reverse causation” is just a phrase for “ultra-(guaranteed?) accurate prediction”? Even that isn’t contradictory in itself, of course; it’s only contradictory for it to be put to use in such fixpoint-lacking situations as your example. Your example does something, something significant even, but it doesn’t completely destroy the possibility of ultra-accurate prediction (and since this seems to be what you equate with “reverse causation”, it doesn’t completely destroy the possibility of reverse causation).
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Reverse causation does NOT mean “ultra-accurate prediction”. It means, as related to predictions, “predictions that cannot be wrong because when the predicted event finally occurs, the prediction alters the past to change the prediction itself so as to ensure the accuracy of the (altered) prediction.”
Naturally, this “changing the past, altering the prediction” thing is the only way that you can increase your “odds” that there is currently $1000000 in the box, because, of course, if you can’t change the past to change the prediction, then you can’t effect the contents of the box, which were put there in the past due to that prediction. You seem to understand this at some level, since you realize that if you knew the contents of the boxes, your choice would have no effect on those contents. The real question there is, sure, your knowledge effects how sure you are in your decision, but what does your knowledge have anything to do with the actual contents of those boxes? And shouldn’t the contents of the boxes be the source of your decision, not your fears or faith in the predictor?
I believe that we both agree that reverse causation is impossible, certainly in the context of this scenario and very probably in regular ordinary life (my proof is only one of many, many possible contradiction scenarios) - the primary difference between us is that you don’t yet realize that unless your decision has the power to reach back in time and toggle the contents of the box, it simply doesn’t have the power to toggle the contents of the box - and that only by toggling the contents of the box can your decision effect whether you will get the extra million or not.
[QUOTE=Indistinguishable]
Why shouldn’t I take the action that gives me the most reason to believe in the truth of my desired outcome? As for when you say “any free choice you make in the matter is not really subject to correlation”, wha-buzzah?! This seems to be denying, among other things, that anyone can make any predictions, with any level of accuracy, about free choices. Surely you don’t mean that; indeed, you’ve explicitly said you don’t believe that.
You don’t think a free choice can be correlated with anything? The very fact that we can make fairly accurate predictions about quite a lot of human actions which would normally be considered free choices suggests that quite a lot of free choices do have correlations with previous events.
What is the way that correlations work? Certainly, in terms of the math, conditionalizing on either end of a correlation gives an increased probability of the other end.
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I know a little about correlations, and they only occur when 1) one thing has a relatively consistent causal effect on the way the other thing turns out, or 2) when two things are both effected in a relatively consistent and causal way by one or more shared causes. Now, since we agree that there is no reverse causation, we can also agree that correlations are caused by cases where subsequent consequences of the prior event(s) interfere with the outcome of the later event(s). So, one of these must apply:
A influences B
or
Z influences both A and B
(Cases where things seem to line up due to random change are not technically correlations, since they don’t actually co-relate.)
Now, the structure of the problem leaves essentially no way for the prediction to effect your decision, unless you want to talk about incidental effects that are not part of the original scenario such as the friend watching the predictor withdrawing the cash. Absent such additions, it seems impossible, and therefore unlikely, that the predictor’s choice is going to alter your choice or make it for you.
The other alternative, with the shared prior cause Z, has a few better options, since it allows the primary thing effecting your decision (ie: you) to influence the prediction as well - as in, the predictor can watch you, study you, read what you’ve typed into this web forum, etc, and use that to influence his prediction. However, for such an analysis to be a perfectly effective predictor, you must be deterministic–that is, unable to make a surprising unexpected decision. If the analysis driving the prediction is not perfectly effective and you are thus able to make an unexpected decision, then the predictor is fallible – a condition which makes it theoretically possible to walk away with the full $1001000, which I think you’d agree is the optimally optimal outcome. Note that the statement of the problem explicitly allows for the possibility that the predictor is fallible, by not guaranteeing perfect accuracy. (Of course it certainly doesn’t guarantee that the predictor is fallible, either.)
So, if you check through this, I have determined based on my analysis of the situation and my knowledge of how correlations actually relate, that either I and probably a large swath of the universe around me are deterministic, or the predictor is fallible. This is important to know.
If I am predetermined, then I am not really making the choice, (as there is no choice), and due to that I feel that predetermination does not match Newcomb’s scenario very well. I also feel that the results are not particularly interesting or relevant, since all decisions a deterministic entity makes are in some sense optimal, since no other outcomes were possible. So I don’t really worry much about the predetermined case.
That leaves only the case were the future is malleable and not truly predictable, and in which therefore the predictor might be wrong, which is a nice thought, but not one we should get too worked up over (as the predictor has been pretty accurate so far.) More importantly, this is a scenario were, as we both agree, there is nothing that you can do to change the contents of the box. (Since that requires reverse causality, which is impossible.) Your choice about which boxes to take does not and cannot increase your probability of getting the million. Since, y’know, causes and correlations don’t work like that.
[QUOTE=Indistinguishable]
I’m not saying the future is fixed, as such, to such extent that this means anything, but it seems natural to say that the truth value of a statement explicitly tied to a specific time is independent of the time at which its truth is evaluated. It’s not like the statement “Global warming will kill us all in the year 3800” can flip-flop in truth value over time, unless by flip-flopping you’re referring to the fact that sometimes we know and sometimes we don’t, in which case, the same can happen with statements about the past.
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I’m saying that a truth value about the year 3800 doesn’t have a truth value prior to the year 3800. It has a probability. After the year 3800, it doesn’t have a probability anymore. It instead has a truth value.
That is, unless the universe is deterministic (and this problem uninteresting). In that case, there are no probabilities, there are only facts, fixed truth values, nothing ever changes (when looking at time as being the fourth dimension, anyway), nothing surprising ever happens, ho-hum, yawn, wake me up when it’s over - not that you’ll have any choice about whether or not to wake me up anyway.
[QUOTE=Indistinguishable]
Well, of course, we both think our solutions maximize our take. I think mine maximizes my take because it maximizes the probability that I discover a million.
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And I think that mine maximizes my take because it is certain, with absolute 100% perfect probability, to give me the maximum amount of money that I can cause myself to get by making this decision. 'Cause we both agree that my current decision isn’t going to retroactively put more money in the box, yo.
[QUOTE=Indistinguishable]
If I could see the contents of the sealed box, I would take both boxes, same as how I would smoke if I knew the value of my smoking/lung cancer-gene. Once having access to that information, it would no longer be the case that my actions could increase the evidence for my desired outcome.
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This is by far the most interesting part of your post; since it thoroughly validates the proof by cases:
If you knew that the million was there, then you choose both boxes.
If you knew that the million was missing, then you choose both boxes.
Now, I take one look at this and say to myself, “Self, this guy doesn’t care whether the money’s in there or not; either way, he’s going to take both boxes. So why does he need to look? He already knows what to do in either case.” To me, you’ve already agreed with my position, and just haven’t realized it yet.
Still, you clearly haven’t realized that you agree with me yet, so here are a few more questions for you to think on.
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Suppose you came into the room to make your choice, and the boxes were opaque, but you were allowed to open them and look inside them if you want. Now, if you open them, you’ll know what’s inside, and then that’ll be like the glass box scenario and so you’ll choose both boxes, regardless of the actual contents of the boxes. Now, as you stand there with your hand on the lid of the box, you know without opening it how you’ll choose if you do open it; the actual contents of the box are irrelevant. So, do you actually need to open the box? What, if anything, would that actually change, regarding your final decision?
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Suppose you came into the room, made your choice of one box, and then after making your choice were allowed to open the boxes. (You know, to get your money out.) At that point, seeing that there actually was the million in the box, would you regret not taking the thousand as well? After all, you now have that knowledge you need for the glass box conclusion of wanting to take both. Or, god forbid, what if your box was actually empty? Would you regret not taking the thousand? Is there any result where you wouldn’t end up regretting that you chose only one box, and left the thousand on the table?
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Suppose a close trusted friend you knew looked in the boxes. Now, you don’t have the knowledge of what’s in the boxes, but your friend does. Is that enough for you to feel like you were in the glass box scenario? (If you asked, he would tell you to take both boxes, since your friend is in the glass-box scenario now; but that doesn’t tell you anything about the actual contents of the box, or anything informative really.)
3b) Suppose a perfect stranger looked in the two boxes. Would their glass-box knowledge be enough for you? (Note of course that regardless of what they see in there they’d tell you to take both boxes, since they have glass-box knowledge, so there’s really no point in asking their opinion.)
3c) Suppose the predictor had knowledge about what was in the boxes. Would the knowledge that, were they you, they’d know to take both, be enough reason for you to take both?
On preview:
[QUOTE=Indistinguishable]
As it happens, I’m cool with branching multiple future possibilities, but I’m also cool with branching multiple past possibilities. Just as tomorrow’s coin flip corresponds to two branches of the future coming out of today, the bit on my hard drive which I erased yesterday corresponds to two branches of the past coming out of today.
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How would that work? Does it matter if you remember what the bit was? What if somebody else who isn’t you remembers? And what does the bit care about your knowledge or memory of it anyway?
Really, this makes no sense to me. How to you arrive at the conclusion that it is not the case that what happened, happened? Is there any evidence for this? I mean, since I don’t subscribe for one instant that a particular past event cares what you or anyone else remembers or thinks about it, your position would seem to imply that past events flip and toggle willy-nilly, whether you remember them or not. This would seem to put a kibosh on facts. I mean, one moment we had done a moon landing, the next, it was a fake. One minute there was a holocaust; the next: denied. One minute I lived long enough to reach the current date, the nex
