I don't see the argument against taking box B. If the statistics show that everyone who picked box B got the million, I don't see why you wouldn't. The only argument that I can come up with is, "Well, I'd rather not risk 99.99% odds. I'll take the certainty as opposed to the very unlikely risk of choosing B." I don't mean to sound snobbish, but that's not much of an argument.
Newcomb's Problem
- Thread starter Erik Mesoy
- Start date
Kennigit
proud 2 boxer
'Cuz this: "Before you make your choice, Omega has flown off and moved on to its next game. Box B is already empty or already full."
A two-boxer does choose box B. He also gets an extra 1k.
A two-boxer does choose box B. He also gets an extra 1k.
Not so. The problem assumes the direction of causality. It explicitly states that the entity moves on and does not take money from under box B if you pick both boxes.
Ziggy Stardust
Absolutely Sane
The superintelligence from another galaxy has a 100 out of 100 record of predicting the decision. Hard to argue with a succesrate like that.
What people are saying is: I know the superintelligence from another galaxy has been right 100 times, but now he will be wrong. And they defy these odds to win 1.000 and stand to lose 1.000.000.
What people are saying is: I know the superintelligence from another galaxy has been right 100 times, but now he will be wrong. And they defy these odds to win 1.000 and stand to lose 1.000.000.
Dragonlord
Fantasy Warlord
'Cuz this: "Before you make your choice, Omega has flown off and moved on to its next game. Box B is already empty or already full."
A two-boxer does choose box B. He also gets an extra 1k.
This.
Or, in other words: My taking Box A in no way influences whether there is a million under Box B or not - so there is no reason not to take the 1000.
Logic fail for anyone who leaves the 1000 lying!
Dragonlord
Fantasy Warlord
Nope, sorry. Souron said it:
Your decision to take Box A or not has no influence on what the alien has already done.
Ziggy Stardust
Absolutely Sane
I know, that's kind of hidden in the definition of "predicting".
You are betting against a 100 out of 100 succesrate, which is a statistical given. You stand to lose 1.000.000 and win 1.000.
You are betting against a 100 out of 100 succesrate, which is a statistical given. You stand to lose 1.000.000 and win 1.000.
We might end up going in circles with this.
But the fact of the matter is that you no longer have any effect on the box. The money either is or is not in there. You have no effect on the box. Therefore, your choice to take only Box B would have no effect on whether the money is in there or not.
Let's say the probability the alien left the money in Box B is "p".
If you take Box B, you have p probability of getting $1M, so the expected value is
1,000,000*p
If you take both Box B and Box A, you have not changed the value of p for Box B, because your choices have absolutely no effect on the existence of money inside Box B. Thus, the expected value is
1,000,000*p + 1000
I forgot what the quantifier was to allow us to use expected value, but there we have it. We should take both boxes.
Ironically, if we came to the conclusion that we should take only Box B, then we'd end up with $1,000,000; but this way we only get $1000. Such is life...
Dragonlord
Fantasy Warlord
Not at all, there is no bet of any kind involved on my part!
The million is already under Box B or not, regardless of what I do. Thus, picking up Box A has no effect on that probability whatsoever. Not taking Box A has only one effect: I am a 1000 poorer.
Actually, what this experiment really does is show how widespread superstition is - the belief that one can somehow, through reverse causality, influence the aliens decision. You can't. It's already happened. It's over. No matter what you do now.
Ziggy Stardust
Absolutely Sane
Ok, bear with me:
I think the problem in understanding here is accepting that the supernatural big-brained alien really has the power to predict your decision. There is no absolute proof he can do this, but there have been 100 observations which support that he can. So there is evidence he can, but it's not proven.
Now lets assume the Alien actually can predict what is going to happen. He puts down the boxes and efs off. Now the crux of the matter is not, the content of the boxes cannot be altered once the Alien has left, it's: has the Alien predicted your reaction accurately? In 100 of the 100 observations he did.
So what I am saying is: you are betting against whether the Alien can in fact predict the future. When the bastard of an alien takes a hike, he either has the content in the boxes reflect the choice you are about to make (in which case it's best to pick box B alone) or you are the 1st out of 101 cases where his prediction does not reflect your choice, in which case it would be best to pick both.
I think the problem in understanding here is accepting that the supernatural big-brained alien really has the power to predict your decision. There is no absolute proof he can do this, but there have been 100 observations which support that he can. So there is evidence he can, but it's not proven.
Now lets assume the Alien actually can predict what is going to happen. He puts down the boxes and efs off. Now the crux of the matter is not, the content of the boxes cannot be altered once the Alien has left, it's: has the Alien predicted your reaction accurately? In 100 of the 100 observations he did.
So what I am saying is: you are betting against whether the Alien can in fact predict the future. When the bastard of an alien takes a hike, he either has the content in the boxes reflect the choice you are about to make (in which case it's best to pick box B alone) or you are the 1st out of 101 cases where his prediction does not reflect your choice, in which case it would be best to pick both.
One thing worth pointing out: It's rather easy to imagine an alien with such predictive powers, if this alien prior to offering the two boxes ask you, in an anonymous way, which choice you would hypothetically make. So it doesn't take super powers to be good at predicting what people will choose.
Dragonlord
Fantasy Warlord
OK, I get your point.
Supposing the alien can actually predict the future (which I automatically rejected), then it gets even worse: he predicts your decision, which you in turn base on his predictions, an infinite regression ... that does, indeed, lead to the inescapable conclusion only to pick up Box B.
Ziggy Stardust
Absolutely Sane
Well, it doesn't say in the OP the alien actually asks you which box you will open, if it would then Derren Brown could be the alien.
OP says: Omega selects a human being, sets down two boxes in front of them, and flies away
Furthermore both options have been tried, not just always box B or always both:
Omega has been correct on each of 100 observed occasions so far - everyone who took both boxes has found box B empty and received only a thousand dollars; everyone who took only box B has found B containing a million dollars. (We assume that box A vanishes in a puff of smoke if you take only box B; no one else can take box A afterward.)
But you do accept Box A vanishing in a puff of smoke?
And this is not just an idle boast, the alien has 100 observations to back his claim. Now he could have been really lucky to get to 100 right predictions, but the chance is likely to be very low. He could also have used some trick, but then again, the trick has worked 100 out of 100 times. So you're still betting that you're the person with whom the alien's streak will be broken.
Not so, I don't know his prediction until I make my decision, not before. If he wouldn't have the 100 out of 100 success rate (for instance, if I'd have been the first person selected) I too would have rejected his claim to be able to predict the future and picked both boxes in a heartbeat.
Even a with non-alien normal person who plays some trick to pull off that success rate, I would chose box B, since the trick has been working 100% so far.
Rashiminos
Fool Prophet
Alright... Instead of choosing from money amounts, change the quandary as follows:
You have a terminal illness, and there are two boxes:
Box A contains something that is guaranteed to extend your life for one year.
Box B contains a cure if and only if the alien entity predicted you would take just Box B.
The alien has had a 100% success rate for predicting correctly for at least 100 people, and the alien has never predicted incorrectly.
Do you take both boxes, or just box B?
Dragonlord
Fantasy Warlord
Sorry, my mistake: I meant you make your decision based on his record of previous predictions, not the actual prediction. If the alien knows that, it makes his prediction even easier...
My supposition was (and is) that he can't predict the future (since that is not possible, in my world view... free will and all that) and he can't read my mind. If he can, and read what kind of person I am... well, that's another story.
lovett
Deity
- Joined
- Sep 21, 2007
- Messages
- 2,570
The point is that once the alien has buggered off it doesn't matter what your actual decision is. The contents of box B are already determined.
Given that, there are a number of options.
Firstly, let's say that the alien has predicted you take box B. In that case, there will be one million dollars in B and one thousand dollars in A. If you take just box B you will win a million dollars. If you take box A and B you will win $1,001,000. Your actual action bears no consequence on what is in the boxes.
Let's say the alien has predicted you take both boxes. In this case there will be no money in box B and $1000 in box A. Consequently taking only box B will lead to you being zero dollars richer, whilst taking both box A and box B will lead to you being $1000 richer.
We can write this in matrix form.
*********Just B**********Both
Just B****1,000,000*********0*
***************************
***************************
Both*****1,001,00******1,000**
Where the horizontal axis represents the alien's prediction and the vertical represents your actual behaviour. As we can see, 'both' strictly dominates 'just B'; the outcome is better every time.
It's perhaps clearer in the form of a sequential tree graph:
*****************/Just B (0)
****************/
****Both----------
**/*************\
*/***************\ Both (1,000)
*****************
(1)*************(2)
******************
*\****************/Just B (1,000,000)
**\**************/
***Just B-----------
*****************\
******************\Both (1,001,000)
The Alien is 'player one' (1). He plays either 'Both' or 'Just B'. You are player two (2) and play either both or just B. You do not know what the alien has played and nor can you affect the aliens play; your 'move' comes after that of the alien. That is, you don't know if you are playing with the top branch sub-game or the bottom branch sub-game. But again, we see that choosing Just B gives you an average pay-off of 500,000 whilst choosing Both gives you an average payoff of 501,000. And choosing Both is superior to choosing Just B in both games; you gain a higher payoff in both. Again Both strictly dominates just B because the game is sequential; your actions as player two do not affect those of player one, because his 'move' is before yours. The contents of box B are not decided by your actions.
Ziggy Stardust
Absolutely Sane
But you taking box A and B means that for the first time in 101 tries the alien predicted wrongly.
And again, taking only box B in this instant will mean that the alien has predicted wrongly for the first time in 101 tries.
I get all the calculations behind it, but all those calculations mean that, as I said from the start, you are betting the alien will have predicted wrongly for the first time in 101 tries. So regardless what the best choice would be in normal circumstances, in this case it's a rigged game. Either the alien has had incredible luck the last 100 tries, or he has some trick up his sleeve or he has indeed the powers to predict the future. Whether it's actually possible to predict the future is also irrelevant in the hypothetical scenario.
It seems all the people I'm arguing against throw away the factoid of 100 correct predictions beforehand because it doesn't suit the reasoning behind picking both boxes.
Similar threads
