[genshii]

I've been presented with this thought experiment before and I always feel like I'm missing something when other people talk about it. Why would you ever take both boxes?

The premise is that the predictor is always right. So whether you take one or both boxes, the predictor would have predicted that choice. We know from the setup that if the predictor said you would take the one box, it will have a million dollars. Therefore, if you take the one box it will have a million dollars in it (because whatever you choose is what the predictor predicted).

As an aside, I think whatever this says about free will or if you're actually making a "choice" is irrelevant in regards to if the million dollars is in the box. The way I see both choices is this:

You "decide" to take both boxes -> the perfect predictor predicted this -> the opaque box has zero dollars -> you get a thousand dollars

You "decide" to take the opaque (one) box -> the perfect predictor predicted this -> the opaque box has a million dollars -> you get a million dollars

If you want to consider the version of this where the predictor is almost perfect instead of truly perfect, I don't think that changes anything. Say it's 99% accurate or even 90% accurate.

You take the opaque box -> the predictor has a 90% chance of predicting this -> it follows that there's a 90% chance that the box has a million dollars -> you have a 90% chance of getting a million dollars

Had you picked both boxes, you have a 90% chance of not getting the million.

[Ethee]

As a one boxer myself this is the way I see it. The problem is presented as a value proposition, how do I walk out of this room with the most money? This typically prompts people to think of this as a statistics problem, and you genuinely can use statistics to 'solve' this, but that has nothing to do with what seems to be the problems underlying premise. Which is, do you actually believe that the predictor can even make that prediction? I think most people who take things logically at face value (like Veritasium watchers) would accept the premise as it's set up. I think for the two boxers there's some doubt they have about the predictors actual abilities, or they think they can 'outsmart' the predictor. The problem is setup in such a way however that it's fundamentally impossible to outsmart, which is I think what makes this problem so interesting.

[mcphage]

> Why would you ever take both boxes?

As near as I can tell, it boils down to this: no matter what the predictor has chosen, one you walk into that room, there's more money in both boxes, then there is in one box.

But it feels like half an analysis—focusing solely on what you decide, while ignoring the fact that the other side is deciding based on what you think they'll decide.

Maybe that's me being unfair, because I'm a solid one boxer.

I also disagree with the linked article—I don't think it matters at all how the predictor makes their decision, because the outcome really doesn't matter if it's 100% accurate or 99% accurate. Or even like, 80% accurate. There's no magic required for the experiment to work.

[vidarh]

Even if it's 50% accurate the benefit of picking both is marginal. If it's 50% accurate and you pick both boxes, 50% of the time you get nothing, 50% of the time you get 0.1% more. So unless you know that the predictor is worse than chance, you at worst suffer a meaningless loss if you pick one box.

[pinusc]

(To two-boxers) it's not half an analysis because once you walk into the room your choice is causally independent of the demon/AI/alien prediction.

There's something vaguely similar to the fallacy of proposed (Cooperate,Cooperate) solutions to the Prisoner's Dilemma. The arguments go as follows: (1) if we're both rational agents and we have the same information and same payoffs, we will make the same choice; (2) therefore, (Cooperate,Defect) and (Defect,Cooperate) are out of the question; (3) therefore, the only options are (Defect,Defect) and (Cooperate,Cooperate); (4) so I should Cooperate since it gives the better payoff. It seems to follow logically but (1) and (2) are problematic because you can't assume symmetrical solutions and thus eliminate asymmetrical outcomes, because that is essentially the same as saying "what I choose causally affects what my opponent chooses".

In the same way, one-boxing is irrational (for this argument, anyway; I'm undecided myself) because the prediction has already been made, and so your choice to one-box or two-box cannot have any causal relevance to the contents of the boxes. Even a perfect predictor cannot invert the flow of causality.

[mcphage]

> that is essentially the same as saying "what I choose causally affects what my opponent chooses".

No, it’s the same as saying “what my opponent thinks I will choose causally affects what my opponent chooses”, which is obviously true. Also, “what my opponent thinks I will choose is positively correlated with what I do choose”, unless my opponent isn’t very good.

[danbruc]

The thing is, you can not chose once you are in the room. The fact that an [almost] perfect predictor exists implies that your choice must already be fixed at the point in time the predictor makes its prediction. Or the other way around, if you could still choose both options once you are in the room, say by basing your choice on some truly random and therefore unpredictable event like a radioactive decay - at least as far as we know truly unpredictable - then the predictor could not [almost] perfectly predict your choice, i.e. an [almost] perfect predictor can not exist.

So what you really want is to be in a state that will make you chose one box and you want to already be in that state at the time the predictor makes its predictions because the predictor will see this and place the million dollars into the second box. And as we have already said, you can not chose to take two boxes afterwards as that would contradict the existence of the predictor.

[mcphage]

> So what you really want is to be in a state that will make you chose one box and you want to already be in that state at the time the predictor makes its predictions because the predictor will see this and place the million dollars into the second box.

Here’s the thing: no, I don’t. I’d much rather walk away with the easy million instead of risking it all for an extra thousand.

[danbruc]

You can only get a thousand - take both boxes - or a million - take only the second box, zero and one million one thousand are not possible - or at least unlikely - because that would require a misprediction by the predictor but we assume an [almost] perfect predictor.

[mcphage]

Then I for one choose the million.