Nike Zeus
Warlord
The strategy for picking box B is based on the conclusion from experimental data that the aliens are capable of predicting which box you will pick. You agree that if the aliens can do this, then picking box B is a better idea?
Newcomb's Problem
- Thread starter Erik Mesoy
- Start date
warpus
Sommerswerd asked me to change this
No, because the premise of this thought experiment is impossible unless the aliens can teleport money into the box.
If the aliens can predict which box I will pick, then it doesn't matter what box I pick.
Obviously they can't do such a thing, and so it makes more sense to pick both boxes.
Nike Zeus
Warlord
100 experimental trials say they can do such a thing. Ignoring experimental evidence in favor of your current perception of what is and isn't possible doesn't seem very scientific.
Everyone who followed your reasoning (Assuming the aliens are never teleporting money in and out of boxes, if they are the problem is meaningless) ended up with $1,000. What makes you special?
Everyone who followed your reasoning (Assuming the aliens are never teleporting money in and out of boxes, if they are the problem is meaningless) ended up with $1,000. What makes you special?
Because you have decided to take both boxes, the opaque box will most likely have $0.
Because I have decided to take only the second box, the box will most likely have $1m.
Omega doesn't magically teleport the money. He has you figured out, and he'll have you figured out to be the two-boxer you are (most likely).
warpus
Sommerswerd asked me to change this
Well, if you're just going to repeat what you said in your last post without actually addressing my points, then I have nothing left to add.. except for..
You're wrong!
You're wrong!
Gogf
Indescribable
Nobody is ignoring the evidence. The evidence states that the alien is either a very good guesser or a very good figure-outer. If he's a good guesser, then whichever one I pick doesn't affect what his guess was. If he's a good figure-outer, then he already has me pegged as a two-boxer or a one-boxer, and whichever box I pick won't matter.
The "pick box b" argument seems to be predicated on the assumption that, having heard this problem before, you can consciously change yourself into a one-boxer and thereby force the alien to put the money in. Of course, nothing is stopping you from switching back to being a two-boxer and taking the extra $1,000.
Excepts he would have seen that coming and so you lose $999,000.
I don't see why an alien that has supernatural money boxing ability won't also have supernatural predicting ability.
Erik Mesoy
Core Tester / Intern
Read the OP, the alien has been right 100 out of 100 times so far.
He'd say box B, and then he'd start dictating a book about what a generally Newcomblike agent should look like before realising that he had an AI to build.I'd call Eliezer Yudkowsky and ask him what to do.
I disagree. I want a million dollars more than I want a thousand dollars. Picking box B will get me a million dollars, while picking both boxes will get me a thousand dollars. Therefore, it makes logical sense to take box B.
Well, then assume that he's offering happy puppies, days of life extension, birthday cake, computing power, or something else that isn't really subject to inflation. Actually, assume Omega is offering unadulterated utility, if you like.
Inflation is beside the point of the problem.---
This problem is awesome to me in the way it can engender so much insistence that one's own choice is obvious and the other choice is silly.
"I don't understand why everyone believes [that]."
"Ignoring experimental evidence"
"You're wrong!
""Sounds stupid to me"
"There's no reason"
"Of course there's good reason"
"I'll just assume that you're afraid to confront the truth"
"The logical fallacy is that"
"...irrelevant. You would have to be pretty foolish..."
"I think you went off the rails a bit"
"it is ALWAYS better to take the extra $1,000."
Now, I'm a one-boxer, and I'd like to consider the situation after the alien has visited all of us here. In retrospect, my choice was obvious and disagreeing was silly.
I got a million dollars, and those of you who are two-boxers didn't. You got a thousand dollars. Why did you pick both boxes??
Darth_Pugwash
wobble wobble
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You would pretty much only take both boxes if you weren't convinced of Omega's predictive powers... if he had only predicted 25/100 people's choices correctly then it would make sense to go for two boxes, but since he has guessed 100/100 correctly, you can fairly safely assume that he got you right as well, so there's no reason not to go for the one mega-money box.
Basically if you take one box you are accepting that Omega pretty much knows what you are going to do before you do it, if you take two boxes then you're saying that Omega can't have predicted you correctly despite the question stating that Omega is pretty much the Chuck Norris of predicting.
Kinda interesting problem but it's ultimately a loaded question. If 100/100 two boxers got a thousand dollars, and 100/100 one boxers got a million dollars, then how many boxes do you choose to take?
Basically if you take one box you are accepting that Omega pretty much knows what you are going to do before you do it, if you take two boxes then you're saying that Omega can't have predicted you correctly despite the question stating that Omega is pretty much the Chuck Norris of predicting.
Kinda interesting problem but it's ultimately a loaded question. If 100/100 two boxers got a thousand dollars, and 100/100 one boxers got a million dollars, then how many boxes do you choose to take?
Gogf
Indescribable
If he saw it coming, then my box b is empty and I might as well take the $1,000.
The alien can predict what I naturally would pick with very high accuracy, certainly, but he can't retroactively change what's in the box after the scenario is set up.
Darth_Pugwash
wobble wobble
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Yeah but the question pretty much states that the last 100 people to follow the two box line of reasoning got $1,000, not $1,001,000. Are you really the exception that gets rich?
You can turn the logic over in your head as much as you want, but the numbers still say that 100% of two boxers thus far have lost out on $999,000. You can't wrangle your way out of odds like that.
You can turn the logic over in your head as much as you want, but the numbers still say that 100% of two boxers thus far have lost out on $999,000. You can't wrangle your way out of odds like that.
If you know that, then you'd pick one box.
If the Alien knows what you would pick it really becomes a waste of time asking the question, at least from an external perspective. If there is any doubt which with a 100% success rate there doesn't seem to be. Then there are either expectations that if you pick both boxes then you will always get $1000 no matter what is in the boxes. The alien knows who will pick 1 box and who two automatically. Or the Alien is stupendously lucky with his guesses.
To be frank if you aren't a dumb ass, and know former results the only rational solution is to pick 1 box. If you don't know the former results, you may well go for two, even though you could stand to lose $999,000.
It all depends on the preconditions you set though. Without knowing those, then the whole question becomes meaningless, and I personally highlight the third option in this exercise, giving the alien the finger and saying " you never saw that one coming did you reptile face!"
In that case this is a zero sum game, where you refuse to play because it's stupid and you have better things to do.
Or even better tell the alien that if you don't give him the $1,001,000 then you have a 48 in your coat pocket and you will spread his green ass across the side walk and take the money anyway.
In essence though it's not about the choice you make, it's about the conditions of the experiment, for each given preconditions, there is only one rational choice given probability or at the very worst a 50/50 chance, which doesn't seem to be the case with the OP. But unless you know what they are in every instance. Then you could very well be here all day.
It seems to me that picking two boxes is only the best idea if it's not something you'd naturally do, however if it's not something you'd naturally do then why would you do it?
Kennigit
proud 2 boxer
The whole point is that it does not matter in any way what your choice is: as the rules are explained to you, the alien does not change the value in the boxes. There is no trying to "trick" the alien. I would choose both boxes, and I would expect to probably find only 1,000 dollars.
Here are the scenarios:
If Omega thinks I am a two boxer, and I take just box B, I get $0.
If Omega thinks I am a two boxer, and I take both boxes, I get 1,000 as opposed to 0.
If Omega thinks I am a one-boxer, and I take just box B, I get 1 million.
If Omega thinks I am a one boxer, and I take both boxes, I get an extra 1,000 dollars.
No matter what, choosing both boxes gives me 1,000 dollars more.
Here are the scenarios:
If Omega thinks I am a two boxer, and I take just box B, I get $0.
If Omega thinks I am a two boxer, and I take both boxes, I get 1,000 as opposed to 0.
If Omega thinks I am a one-boxer, and I take just box B, I get 1 million.
If Omega thinks I am a one boxer, and I take both boxes, I get an extra 1,000 dollars.
No matter what, choosing both boxes gives me 1,000 dollars more.
Darth_Pugwash
wobble wobble
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Under the premise of the question the two bolded scenarios are much more likely than the unbolded scenarios.
The premise of the question is that the alien is a either a perfect predictor of box-preference, or an almost perfect predictor of box-preference. Hence whichever choice you make, it is likely that the alien will have predicted it before hand. No matter how you arrive at your chosen choice, it is likely that he predicted that choice. Examples:
Person A has an IQ of 50 and chooses box B becuase his first name starts with a B; the alien has predicted this and person A gets $1,000,000.
Person B has an IQ of 100. He was going to choose box B but at the last moment he changes his mind and chooses both boxes; the alien has predicted this and person B gets $1,000.
Person C has an IQ of eleventybillion and through careful deduction concludes that the only reasonable choice is to choose both boxes; the alien has predicted this and person C gets $1,000.
It doesn't matter how you choose, the assumption given in the question is that the alien has a very high chance of anticipating your choice no matter what your choice is, and no matter how you make it. All that matters is which box you choose.
Well, if you're just going to repeat what you said in your last post without actually addressing my points, then I have nothing left to add.. except for..
You're wrong!
Sorry, I didn't realize that they were so identical (my two posts). How have I not addressed your points? If I am right, then you are wrong, so please show me wrong.
Let us assign a 99% accuracy to Omega's predictions.
This has a 1% chance of happening (taking one box contingent)
Expected value = 0.01*0 = 0
This has a 99% chance of happening (taking both boxes contingent)
Expected value = 0.99*1000 = 990
This has a 99% chance of happening (taking one box contingent)
Expected value = 0.99*1000000 = 990000
This has a 1% chance of happening (taking both boxes contingent)
Expected value = 0.01*1001000 = 10010
Under the assumption that the alien has 99% chance of success:
The expected value of taking one box (one box contingent) is $990000. The expected value of taking two boxes (both boxes contingent) is $11000. I.e. if a million people choose one box, then each will have on average $990000; and if a million people choose two boxes, then each will have on average $11000.
Hmm... this is getting me thinking. For what percentage prediction chance does choosing both yield the same thing (indifference point)? I predict 50% just from an overview, but I'll go through the math.
One box = (1-x)*0 + (x)*1000000 = 1000000x
Two boxes = (x)*1000 + (1-x)*1001000 = 1001000 - 1000000x
Indifference point: E(one box) = E(two boxes)
1000000x = 1001000 - 1000000x
2000000x = 1001000
x = 1001000/2000000
x = 0.5005 = 50.05%
Thus, a person should choose one box if he or she believes that the alien's likelihood to be correct is greater than 50.05%. A person should choose two boxes if he or she believes that the alien's likelihood to be correct is less than 50.05%.
Given the data, the likelihood that the alien's likelihood to be correct is less than 50.05%, is extremely low.
If we all decide to flip coins to decide, we might gum up this hoighty-toighty alien's statistics.
Erik Mesoy
Core Tester / Intern
Not the way I think he works... and if he's a superintelligence, he can probably come up with more ways than that to avoid it.
The only serious such problem is Perfection's attempt to sneak around the problem with a source of quantum randomness. To which I suggest that Perf does not generally carry such a source around with him on a daily basis, and will not have one available when asked to pick between box B and both boxes.
Ayatollah So
the spoof'll set you free
The only reason I participated in this thread about a ridiculous hypothetical situation is because Erik Mesoy posted it and I consider him to not be stupid. However, I am baffled at how much there could actually be worth discussing here. If the alien was right with the first 100 instances, he's greater than 99% likely to be correct on the next instance. So the obvious and only logical choice is box B. So what is there to discuss? And I fail to see how this may be "the most controversial dilemma in the history of decision theory", as Erik Mesoy said in the opening post.
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