I know I said that if the alien is infallible (whatever that entails) then the question is pointless as the answer is obvious, and I think a fair few people did. It's simply creating a proxy to make the same point I think. You don't need retro causality or to breach it, as common or garden probability will yield the same result, and with the same reliability.
Newcomb's Problem
- Thread starter Erik Mesoy
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Gogf
Indescribable
No, because it's actually always preferable to take both boxes, so you need some sort of mechanism to ensure the money is in box b. That mechanism is the duality of Perfs.
Ayatollah So
the spoof'll set you free
Correction: If you believe that your choice bears a determinative relation to the amount of money put in the boxes, choose box B. Which it probably does.
Edit: see this reference about time-symmetric determinism
Mise
isle of lucy
Yeah... so any rational person will choose only Box B...
Omega correctly predicts that you will choose Box B, because it is the only logical conclusion!
Erik Mesoy
Core Tester / Intern
I could probably pretend to be Omega just by giving everyone the box values they named here. It's not that hard to get 100/100 right by approaching the right people. 
Ziggy Stardust
Absolutely Sane
Would it change opinion of the people who choose "both boxes" if the alien has been playing this game for ages and allready predicted millions of outcomes succesfully and never has been wrong once?
Or is the amount of times he predicted accuratly irrelevant to you?
Or is the amount of times he predicted accuratly irrelevant to you?
Precisely!
"A&B is always best" is a contradiction, because Omega will know you'll always pick A&B and thus B will be empty => picking just B best, which contradicts the original statement.
Ah, I think I understand now. Indeed, it is irrelevant that you're losing or you're gaining the cost. It is indeed more accurate to say "highest expected value" rather than a positive expected value.
And for the purposes of comparison, think of it as a game instead of a lottery. I.e. you can only buy tickets in parallel, but not in series (i.e. 6 separate lotteries rather than 6 tickets for one lottery)... in fact that's why lotteries in real life have negative expected values.
Even if the alien isn't infallible, with an understanding of statistics, the answer is still obvious! We don't know that the alien is infallible, but we know it has been right 100 out of 100 times. That allows us to place some sort of certainty value to its accuracy (like 99%) and derive expected values.
It is apparent that the number of times predicted is more or less irrelevant to them. They are resting their hypotheses on the assumption that Omega has nearly no predicting abilities (with a greater than 50.05% predictive ability, the statistical analysis clearly shows that choosing only one box is better). Given the 100/100 data, this likelihood is extremely low. I doubt that they are analyzing it and saying "well, I'll assume that he has no predictive abilities on a 0.0001% chance, but I wouldn't assume that on a 0.000000001% chance". So an infallible alien should have no effect on the decision (given the amount of data in the 100/100).
Precisely. I think the idea that we need some extraordinary means to make a choice is not true.
Darth_Pugwash
wobble wobble
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This thread has been fun 
I still have to wonder though, how two-boxers can follow the two-box rationale even though it doesn't fit with the data given in the question. I mean, going by the two-box logic, of the people who two-box, 50% should be rich, and yet, they aren't. The rationale doesn't fit the data, hence there is something wrong with the rationale!
Because after all, if 100/100 observed two boxers get a thousand dollars, and 100/100 observed one boxers get a million dollars, how many boxes do you choose to take? There are no two-boxers who got $1,001,000, and no one-boxers who got $0, hence we have to assume that these two outcomes are either impossible or extremely unlikely!
Cheers guys
I still have to wonder though, how two-boxers can follow the two-box rationale even though it doesn't fit with the data given in the question. I mean, going by the two-box logic, of the people who two-box, 50% should be rich, and yet, they aren't. The rationale doesn't fit the data, hence there is something wrong with the rationale!
Because after all, if 100/100 observed two boxers get a thousand dollars, and 100/100 observed one boxers get a million dollars, how many boxes do you choose to take? There are no two-boxers who got $1,001,000, and no one-boxers who got $0, hence we have to assume that these two outcomes are either impossible or extremely unlikely!
Cheers guys
warpus
Sommerswerd asked me to change this
Logic > Statistical Analysis
The statistics in this thought experiment are meant to deceive you.
Mise said:
If it's always preferable to pick box b, then you might as well pick both boxes. That way you end up with the preferable box B AND another box on top.
Truronian said:
If Omega doesn't put any money in box B, then picking box B is not going to change the fact that there ain't any money in it.
Darth_Pugwash
wobble wobble
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To be a one-boxer, you pretty much accept that for all intents and purposes, Omega knows which choice you are going to make before you make it. 
The statistical analysis stems from logic. All statistics and mathematical principles are directly attained using an axiom or two, and a whole lot of logic.
The logic shows that since the chances of his prediction being wrong (i.e. that you'll get $1001000 if you choose both boxes) are extremely low, you should not choose such a course of action.
Fact of the matter is that: if you take one million one-boxers, they'll likely have 1000000*$990000 or more amongst them all, and if you take one million two-boxers, they'll likely have 1000000*$11000 or less amongst them all (and by likely, I mean "almost certainly"). So would you like to be in the population of one-boxers or two-boxers?
Obviously he meant it's always preferable to pick only box B.
Lemme try three ways to explain it to you...
1) You've got it the wrong way around. If Omega doesn't put any money in Box B, then you are not going to pick Box B.
2) If it helps, think of it like this. Picking Box B will indeed magically spawn $1000000 in it! It's true! It's just that this money will magically spawn in the past, when Omega was predicting your choice.
3) Yes it will. Picking Box B means that there was actually $1000000 in it, and Omega didn't leave it empty.
warpus
Sommerswerd asked me to change this
To be a one-boxer, you pretty much accept that for all intents and purposes, Omega knows which choice you are going to make before you make it.
Which would put serious doubts on the idea of free will.
I would just assume that he's cheating, and go with one box.
What, pray tell, would be "cheating"? We don't know how he makes his predictions, we only know the results of his past 100 predictions. For all we know, he could be using cloning, mind-reading, time-traveling, or just plain intuition and luck. So what exactly would be cheating?
Darth_Pugwash
wobble wobble
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It doesn't nessesarily rule out free will if we postulate Perfy's simulation hypothesis!
So yeah, pretty fun scenario, but one-boxing is the best choice.
So yeah, pretty fun scenario, but one-boxing is the best choice.
warpus
Sommerswerd asked me to change this
There is nothing to suggest that the statistical data presented to you has not been fudged with in order to present to you a seemingly paradoxical situation.
Defiant47 said:
The fact is that as soon as the boxes are presented to me, and I am asked to make my decision, my decision is not going to affect the contents of the boxes.
At that point in time, previous statistics will not alter the contents of the box. If I select box B alone and I end up with a million dollars, I might as well have gone with both boxes - I would have ended up with more money. Or are you trying to say that the money would have mysteriously vanished from the box had I made a different decision?
Or maybe that I would have been unable to make that decision in the first place?
So I don't even have a say in the matter; the alien makes the decision for me. Whatever he decides, I will do.
I have no free will, and thus am not even making a decision. This sort of highlights one of the flaws with this thought experiment. It assumes that you have no free will OR that the alien is cheating (beaming money into the box or looking into the future)
That is true. We are assuming that the information regarding the 100/100 data is correct. But I have a feeling that this question is meant to be asked as "assuming that the information is true, what do you do?", so that is more or less moot.
The situation is not paradoxical. Data is available to make the desired choice rather obvious.
That is because the contents of the boxes are already determined based on your future choice.
That is more or less on the right track. If you select Box B, then it would have been better to choose both boxes to get the extra $1000. However, if you would have chosen both boxes, then Box B would have nothing (because your decision would be correctly predicted). If you choose both boxes, the money was never in Box B to begin with.
Actually, no, whatever you decide, he predicts.
Let's suppose that we're good friends, and you tell me that in a rock-paper-scissors game, you always choose rock first (and you pretty much do), at least for the first game. A week later, we have a rock-paper-scissors game. Does my prediction that you'll choose rock first deprive you of your free will?
Suppose that I make a complete psychological profile on my mother. I analyze her such that I can say with a lot of certainty that if I told her "I want to kill myself", she would become worried. I then go and tell her "I want to kill myself". Does my prediction that she would become worried deprive her of her free will?
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