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there is no such thing as a $1000 dollar bill, so you would be crazy not to go with the closed box,... then there is always the rocket-testing smart idea of lifting the closed box to see if it weighs at all

What about kicking him in the nuts to see if he really predicts stuff ?
This would add new data and thus would improve the chance of a good decision-making.

The human doesn't make a choice here. The alien does. Or rather, the human, by being a two-box human or a one-box human, directs the alien to put the million in or not. You make the choice long before you enter the room, through all the actions of your life that will make you the predictable being the puzzle stipulates that you are.

You think the alien can't exist? Actually, we could almost do this today. There are drugs, like Versed, which inhibit your ability to store long term memories. I could give you Versed, pose the problem to you, see what you do and then wait until it wears off. You will have no memory of the puzzle. (When this was done to me, I remember the injection, but nothing after that, even though I talked to people.)

Anyway, I give you the drug again. (If it weren't an injected drug you would have no way of knowing this is the 2nd time, for for this hypothetical imagine you think the injections are for something else.)

Anyway, now I can predict what you will do very accurately. Probably not as accurately as the alien, but so well that the result is very similar. Those who are the sort who pick one box become millionaires, those who aren't, don't.

Now imagine something better than Versed, something I can give you without telling you, something that doesn't sedate you or generate other visible effects, something like the Men-in-black pen that just erases a segment of memory if you will. It's not as science fiction as it sounds, the drug I describe is real and is used in medical procedures where they want you to be awake but not remember the horror.

Now do you understand the problem better? You understood it better the last time I explained it to you...

I'd take the $1,000 bill: one just sold at auction for $2.3 million. This paradox just vanished thanks to simple economics.

http://www.chron.com/disp/story.mpl/metropolitan/4405479.html

-John

I believe that such being cannot exist, and therefore the problem is a logical impossibility, but for different reasons than Martin Gardner.

One thing I can decide to do is flip a coin to decide. In order to predict what I will do, the being has to be able to predict how the coin will land. In fact, I can use something harder to predict than a coin: I can use something truly unpredictable, governed by quantum mechanics: I'll set up a single radioactive atom and observe whether it decays or not in 1 half-life.

In such a circumstance, the being can never be better than 50-50 with me, no matter how smart s/he is, so the paradox goes away.

Take neither box. You neither gain nor lose anything, and you got to meet a super intelligent being from another galaxy. Try asking the alien some questions rather than taking his box (this works with women, too).

This is not even hard. To solve it, just invert the order of events. First you choose, then the alien decides what goes in the closed box. It doesn't really matter which comes first, but it is easier to see. The alien has 99.9 percent chance of knowing your decision accurately. If you are greedy, you have a .1 % chance of fooling him, with expected value of $1K + .001*$1000K = $2K. If you are not greedy, the alien still has a .1% chance of getting it wrong, so the expected value of that decision is .999*$1000K = $999K. $999K > $2K so the greedy thing to do is not be greedy (now there's a real paradox!)

You take the closed Boxed. Risk reward ratio. If the predictive power of the alien is 100% then if you take the closed box as you are guaranteed a million dollars. If his predictive power is not quite perfect, but highly accurate, you are most likely to get a million dollars if you take the closed box. If the Alien does have 100% predictive power and you take both boxes you are only getting a thousand dollars. If his predictive powers are only extraordinarily good, then if you take both boxes, most likely you will only end up with 1,000 with a very small chance of getting 1,001,000. If the predictive power is 100% and you take the closed box, you get the million which is the highest possible outcome. If his predictive power is only very good, then you still take the closed box, because you are more likely to end up with a million then either the small chance of getting nothing or 1,001,000. If there was a 999 chance in 1,000 of risking a 1,000 to gain a 1,000,000 who wouldn’t take those odd. Certainly beats Vegas or the Stock Market. Of course this all takes on faith that you believe the alien is telling the truth that he has predicted the last 999 in a row.

Quit thinking so hard. Take both boxes. Not only do you then have $1,000 , you also have TWO BOXES!!

An extra $1,000,000 would be nice, but again, you get TWO BOXES!! And of course the $1,000.

A great day any way you look at it.

Paradox?
All this proves is that the superior being knows we a basically materialistic species fsacinated by all forms of material gain. No matter what happens he knows we are going to take something. In the end, he knows that he is superior because we fell for the scam, $1000 or $1,000,000 and will either 1) know enough to avoid this planet in the future or 2) know he has a couple billion fish to fry when he sets us up for a bigger scam.
Besides, I want to go behind the green curtain and see who this "superior alien" really is. Sounds like Oz to me.

The test is executed exactly the same way _only_ if each and every one of the 999 person was told the same "he has run this experiment with 999 people before, and has been right every time." before choosing.

Think, if you'd been the first one tested, would the alien have said "999" or "0"? The test is only same if he says "999" to everyone because telling that will affect the outcome.

Now, only way for him to say "999" and not lie is to posses time machine. If he has time machine, he knows what you will choose because he went and watched beforehand your choice.

Thus, choosing the closed box will give you 1 million dollars if telling the number of participants is part of the test.

I reckon an alien box is worth well more than $1000 so I'd take a chance on the single box...

Edited by author 12-15-2006 05:14 AM
Am I a complete idiot in thinking that if you choose both, and there is a million dollars in the closed box, you will end up with $1,001,000.00 and if there isn't the million, you still have the thousand? if you choose the box with the $1,000.00, then, well, you have $1,000.00 and no chance at the million?

It doesnt make any sense to me as to why someone would choose anything but both. the decision you make will not affect what is in the empty/million box, so why not take that AS WELL AS the thousand box?

Is the purpose of the question then, to show that when given a question like this people either dont care about the question and are simply happy with monetary gratification, or want to try to outsmart the alien, don't care about the money at all, and want to be different from the past 999 people questioned?

Not a paradox. It does not contain a logical conflict or circular argument such as "this statement is a lie".

If you believe, you take 1 box. If not, you take two. Simple as that, no conflict.

I'm a believer, and therefore broke.

Paradox? Where? I don't see it.

The alien has been right the previous 999 times, so there's a good chance he is right this time too.

Solution: take the closed box. You will then have one million. End of story.

It's very unlikely that the alien would be wrong. As there is a very, very high chance of the alien being correct, it would be stupid to take both boxes, because then you will end up with just a $1000 instead of one million, because the closed box would be empty.

However, if the alien was indeed wrong, and the box is empty, you can say you outsmarted a superior being. A thousand is a small sum to pay for such a privilege.

Allright, my assumption that this is truly a paradox in the classic sense is only correct if you consider the entire quote presented in post #1. As a whole, it contradicts itself, here: "Either way, if you take both boxes you get a thousand dollars more than if you take the closed box only."

If you only consider the first three paragraphs, i.e. up to and including "what would you do?", it isn't paradoxical in the sense that the situation is actually impossible. The question is still a bit philosophical, and I'm still not sure that you could _prove_ that one answer is better, but it _is_ much clearer in this case: Would you risk a million dollars for one thousand dollars, even though the futility of this endeavor has already been demonstrated over and over? Would you go against all odds, in the hope that afterwards you could say, "a highly superior being offered me a million dollars as a gift, but I tricked it and increased my earnings by one tenth of a percent"?

I'm tired, and I think I missed something, but if the alien can only predict your own decision, then can't you just flip a coin to void his knowledge? Would the odds not be back at 50/50? A level playing ground?

Personally, I'd probably be happy playing with a box, they make great spaceships.

Edited by author 12-14-2006 11:35 PM
This is only a paradox if there is a causal link between your decision in the present moment and the alien's prediction at some past time. That this is the case is not necessary, or even obvious; I predict right now that "The sun will rise tomorrow," but just because I have made this assumption every evening with unerring accuracy for my entire life, it is not the case that my prediction was "caused" by tomorrow's sunrise.

The million is either there or it is not; the prediction, accurate or not, has been made. Opening both is the only rational choice.

Msg 49: "always take both as you'll have the same chance of getting the million plus a gaurenteed thousand no matter what. this seems very simple to me, i hope someone can point out how i'm wrong."

The alien knows you think that way, so it won't put $1 million in the box.

We don't know how the alien managed to predict it (i.e. whether he used a special alien "make it be yesterday" device or just clever psychological analysis) but what we DO know is that he's predicted correctly on all prior attemps (all 999 of them) and although it's not stated explicitly, we should assume that the former participants had the same information as we do (ask the alien if needbe). There are those of us who think "the money's already been put in the boxes, so I have nothing to lose by opening both." To the alien, such people probably glow blue. One step ahead of you, no million in the box. Then there are those that think that out of those 999 people, at least some of them must have tried to second guess and trick the system. They all failed. Every one of them. For whatever reason, the alien was one step ahead of them. I too could risk 999 thousand dollars beliving that I can second guess better than they did for a potential gain of a measly 1 thousand dollars, or I could just assume that this alien is a lot cleverer than me and take the cool million. I'll make up the extra thousand in interest within a week if I invest cleverly (and maybe ask the alien financial advice, as he's clearly good at this type of thing). Such people to the alien probably glow red, so the million is prepared. Getting it right every time sounds relatively easy. Tricking the system sounds relatively hard as the sequential odds are against you, and your choices for tricking it are very limited.

Now if the numbers were more even, say 15 thousand dollars in one box and 50 thousand dollars in the other, and the alien only had a 70% success rate, then it would make for a more interesting problem.

We see that it's clearly not the case that everybody chooses the same course here, just from this thread. So the alien is not just lucky.

The confusion people have here is that they have an incorrect concept of what a choice is in the context of this problem. (Perhaps because they deny that there could ever be such an alien.)

In the context of this problem, you do not _make_ a choice. You _are_ a choice. The alien's accuracy suggests that a human's conclusion that she is weighing two options here is a false one. From the alien's viewpoint, you are no more likely to choose differently than the prediction than you will choose to suddenly freeze because of a bizarre entropic coincidence. (It could happen, but it's really unlikely.)

So there is no paradox. Predictable beings are presented with a problem and answer it just as predicted. The only paradox is in their illusion that they might do otherwise. The trick is the question asks you to decide which choice to take, when in fact the premise says you don't have that freedom.

We don't like the idea of being predictable and deterministic, of course, which is what vexes us.

But we can imagine ways in which we are slighly less predictable.

Imagine I present you with Uma Thurman and George Clooney, and you are completely heterosexual. I ask you to decide which one you want to have sex with. Now you might imagine that you could, if given an important enough reason, have homosexual sex, but in this puzzle you're completely heterosexual and find that unappealing or even repulsive. But that's really an illusion. Knowing you are straight, and knowing your sex, I can predict with extreme accuracy which of the two you will choose.

It's presented as a decision you can make, but in fact the decision is already inherent in your sexual orientation, and was before you entered the room.

This is not a paradox in the normal sense. In a true paradox, there is a lack of internal consistency -- like "What happens when an irresistable force meets an immovable object?". The answer to which is, if one exists the other by definition cannot -- the question asserts the existence of a logically impossible condition -- so it is simply a non-sensical question.

Newcomb's "paradox" is not a paradox in that sense; it is just a brain teaser. The key to Newcomb's is to consider the possible combinations of what the alien knows, and how it chooses to load the boxes based on that knowledge (or lack thereof); and to determine what is your optimal strategy based on these combinations of what the alien might be able to know & do.

Scenarios

1/A -- the alien IS able to accurately predict what you will select, and places the million-dollar bill in the SAME way he said he would.

1/B -- the alien IS able to accurately predict what you will select, and places the million-dollar bill in the OPPOSITE way he said he would

2/A -- the alien is NOT able to accurately predict what you will select, and RANDOMLY puts the million-dollar ball in the box or not based on a coin flip or other random process, or a non-random process you are not privy to

2/B -- the alien is NOT able to accurately predict what you will select, and NEVER puts the million-dollar bill in the box

2/C -- the alien is NOT able to accurately predict what you will select, and ALWAYS puts the million-dollar bill in the box

2/D -- the alien is NOT able to accurately predict what you will select, and puts the million-dollar bill in the box or not based on what most of the prior 999 people did in a way that favors you getting the million

2/E -- the alien is NOT able to accurately predict what you will select, and puts the million-dollar bill in the box or not based on what most of the prior 999 people did in a way that favors you NOT getting the million

... and any other variation you can think of. This works out better if you can define the scenarios in ways that are mutually exclusive & exhaustive.
 

The optimal strategy is obvious in each case --

1/A >>> Choose the closed box only

1/B >>> Choose both boxes

2/A >>> Flip your own coin

2/B >>> Choose both boxes

2/C >>> Choose both boxes

2/D >>> Ask the prior people what they did if you can; if not, then think of what an "average" person would do (which is not the same as the current analysis -- the average person isn't all that logical :) and do what that hypothetical person would do. Call this the "Family Feud" analysis :)

2/E >>> Opposite conclusion from 2/D


Your job is to figure out which is most likely. Just because the other player is an alien doesn't mean it actually has amazing powers, or is telling the truth. Maybe it is just a weird guy in a rubber mask :) You can choose one scenario if you feel strongly it is correct; or you can assign relative probability to each scenario and generate a random number to decide which of these to select (likelihood of selection weighted by the probability you assigned). This is the "utility function" approach and is actually the general case, because if you are absolutely sure one scenario is accurate it gets 100% of the probability in this utility function.

Or maybe there are other factors you aren't aware of that change the whole situaion -- maybe the alient always puts the million-dollar bill in the box, but has the super-power of being able to take the million-dollar bill out of the box psychokinetically if you grab the closed box :) Maybe your friends think you are a retarded monkey for believing in aliens in the first place and set you up for an embarassing Candid Camera segment.

Personally, I would choose the closed box. Not making $1000 is a small let down but the possibility of earning 1000x more (a life-changing amount) is very attractive. If I thought there was more than a 1-in-1000 chance the alien was telling the truth, then I would choose just the closed box.

p.s. Just because a decision is hard to make doesn't make it a paradox.

This is truly a paradox, in the classic sense of Zeno's paradox, Epimenides' paradox, and the Barber's paradox. (_Not_ in the sense of the Monty Hall "paradox", which has a logical, mathematically correct solution, but people will still argue endlessly about it, because the correct solution can appear counter-intuitive and is difficult to understand.) That is, the question per se contradicts itself, with the result that neither of its mutually exclusive answers is more correct than the other. The only real way to "solve" it is to point out the flaw in the reasoning of the problrm stated.

Which is this: On one hand, the "highly superior being" always predicts your decision and makes sure you cannot get away with over a million dollars. If the "highly superior being" already knows that you will take both boxes, before you even meet, then the million-box will be empty. On the other hand, the problem states that if there is money in both boxes, you could conceivably take them both. This is logically inconsistent, hence paradoxical.

From a scientific perspective, it's pointless to try to solve the puzzle, as it doesn't make sense to begin with. If it is worth contemplating at all, then as a philosophical question: Would you believe the story the "highly superior being" told you and attempt to take the box with the million dollars? Or would you be more of a realist, don't buy the crazy story that apparently violates the laws of nature, play it safe, and take all the boxes you are offered?

No matter which choice you make, you cannot prove that it really is better. A proof must be based on axioms that are part of the same formal system, but if the formal system is meaningless, then theorems inferred from it are meaningless, too. The answer "take both boxes" is not more meaningful or correct than the answer "fruit salad".

The answer seems simple and the key is that the alien isn't guessing what you're going to do - according to the premise, the alien knows what you're going to do. All you have to do, therefore, is decide to go for the million dollar option. As you will choose this option, the alien will have predicted you would do so, and have stuffed the box with the million dollars.

The problem has nothing to do with predictability or anything the alien says, just look at the physicality of it, the alien has already put the million dollars in the box (or not). Which box you choose therefore makes no difference to whether the million dollars is in the closed box or not, therefore it will always be better to take both boxes, in NO SITUATION is it better to just take the closed box, you'll either lose out on a $1000 and just get the million or get nothing.

just think of it this way, the 50/50 chance of getting the million is totally independant of whether you choose one or both boxes, because it has already been put in there before you made your descision, so always take both as you'll have the same chance of getting the million plus a gaurenteed thousand no matter what. this seems very simple to me, i hope someone can point out how i'm wrong.

The human in the experiment knows nothing about the alien, save that it has a 100% success rate at predicting human behavior. However when the experiment is done, the alien does not have a 100% chance of predicting what the human will do. For instance if you accurately predict the result of 999 coin tosses your chance of predicting the 1000th toss correctly is still 50%.

This means there is a 50% chance that the closed box will contain a $1,000,000. So the best choice would be to take both boxes as this will result in $1,000 and the 50% chance, whereas choosing the closed box only will result in the 50% chance only.

Wait a moment.

If the alien knows nothing about it's human subjects then it has achieved a 100% success rate through dumb luck alone. This is as likely as a human predicting 999 coin flips in a row. The alien must have engaged in a very in-depth analysis of the humans in order to predict their behavior with such accuracy. It probably knows them better than they know themselves.

Given this state affairs, I would choose the closed box as it is very unlikely that the alien has made it's only error in predicting my actions.

But if I did not know of the alien's predictive success I would have chosen both boxes. And the alien (if indeed it had studied me carefully) would no doubt have predicted this choice as well.

Edited by author 12-14-2006 08:30 PM
The alien can predict the future. He says that he HAS possibly put a million dollars in the closed box. Even your second rate magician could make the money vanish as soon as he opened the closed box. Why is a "superior being" traveling around the galaxy teasing us. He is obviously up to no good. I would say just take both boxes (they might be made of some cool alien material), don't worry too much about the money, and try not to get beat up by some alien punk looking for a fight. You still go $1000 his money, right? Anyway, the odds are even, so you have a better chance of getting his money by dressing up as a different person, conning him into asking you again.

The superior being has predicted what I will choose. He does this either by scientific reasoning (As one can predict with scientific accuracy that a pencil will fall downwards if it rolls off a desk) OR by some kind of supernatural, psychic power.

The first is based on scientifically sound data (Perhaps he has been observing me my whole life and knows me - and those other 999 people - that well) OR in the latter case, he recieved information that travelled back in time from the moment I make my decision.

Because of this, I would choose the single box, and I would get my million, because by choosing the single box I am either acting in a way that can be, and indeed has been, acurately predicted OR by choosing the single box, I send information back in time on which the being in the past bases his decion.

If you can find fault with my thinking (I am labourer, not any kind of professional thinking man), please let me know at jjnnww@gmail.com

Then again there are no such things as aliens. So, what appears to be the alien is probably Dick Cheney in a nice alien suit. He probably picked 999 greedy people who he used to work with, so naturally they went after the million. Cheney probably has a shotgun hidden in the alien suit, and he probably shot all 999 before you got there. So I'd either run like hell or shoot first.

Here's my analysis:

Either the alien has predicted that I will take the closed box (Pc), or he's predicted that I'll take both boxes (Pb). I don't know the relative probabilities of Pc and Pb.

Either I will take only the closed box (Tc), or I'll take both boxes (Tb).

So we have four combinations:
Pc + Tc = $1,000,000 for me.
Pb + Tc = $0 for me.
Pc + Tb = $1,001,000 for me.
Pb + Tb = $1000 for me.

It seems pretty clear to me that unless I believe that Tc => Pc, then whatever the relative probabilities of Pc and Pb, it's best for me to choose Tb and take both.

Now, if the alien is smart, he'll have done the same analysis, so he knows that the best thing for me to do is choose to take both. It's quite plausible that the last 999 humans did so, as predicted; much more plausible than the hypothesis that nobody took the risk-free money. So I should break the chain, and take just the closed box.

The analysis fail to recognize the most overlooked aspect: this is a highly superior being from another part of the galaxy.

So this raises new problems. Is it US currency? Canada, Australia, New Zealand, Bahamas, Barbados, Bermuda, Fiji, Hong Kong, Jamaica, and Singapore use 'dollars'.(List in not necessarily all inclusive or completely accurate.) So depending on which, this could extremely diminish the value.

Is it alien currency? If so does it have any value to me. Where the hell am I going to get it exchanged?!

Where did the alien get this money? Was it legally acquired? Is this money going to disappear into the galactic court system?

Doesn't he have cattle to mutilate and people to abduct?

What kind of boxes does he have? Are the from earth or another planet? I might really want two.

Is there any certainty the being is a "he"?

I'd let him keep the money if he could get me off this planet. But can I get BoingBoing away from Earth...

The problem doesn't say that the alien CLAIMS that he guessed right 999 of 999 times. The problem states that the alien DID guess right 999 of 999 times. This being the case, you don't need to make any kind of assumptions of whether the alien is being truthful or not. Many folks are making some assumptions that just aren't in the problem.

 Since I am a theologian by training with an interest in economic
theory, it appears to me that Newcomb's Paradox is just the window
dressing on the theological and philosophical problem of
predeterminism and foreknowledge, muddled together with an economic problem of rational-choice.

To answer Newcomb’s Paradox, it is helpful to describe the problem in
economic terms. The problem of rational choice was described to me by
economist Peter Boettke. In the Economist's Paradox, the researcher
solicits participants by offering them one cent out of a dollar.
Since something is logically better than nothing, rational-choice theory
dictates that the participant should choose the penny. Invariably,
however, participants try to bargain the researcher up to a 50/50
split. The outcome has occurred wherever the experiment is tried,
regardless of culture or other controlling factors.

Since the alien claims to have a prediction capacity of 100%, his
interest in the experiment is high. However, any solicited
participant has a high participation threshold. Intuitively, I believe most people realize that the “opportunity cost” (the intangible valuation of a person’s time, motivation, or experience) of participating in the
Economist’s Paradox implies that the researcher has overvalued the
experiment: the supply of “research units” ($1.00) is higher than the
demand; the money is simply a way of keeping score.

The participant was indifferent to the researcher’s problem before it
was presented, so what benefit is gained by simply accepting it as a
given? The researcher must lower the cost of participation by
increasing the incentive. The problem doesn’t change no matter what
amount of money is affixed to it. To put it another way, if you
consider an abstract unit of absolute supply (1), and a unit of
absolute demand (0), then the point at which supply and demand meet is
always (0.5).

Thus, one way to answer Newcomb’s Paradox would be to bargain the
alien up to $500,500 in the open box in order for you to fulfill his test.
If you choose both boxes, you have a 100% chance of gaining at least
half of the money. However, if you choose the closed box, you have at
most a 50% chance of gaining the same amount.

It doesn’t matter if the alien claims he has a 100% chance of
predicting your choice. From your point of view, you know with
certainty that he has at least half of the money to offer. Suppose he
had lied, and possessed only a maximum of $500,500? Then you have
already gained a 100% chance at all of the money. But if you take the
closed box, you have a 50/50 chance he is lying.

Of course, if the alien refuses to bargain at all, then you must
figure your opportunity costs into the process of convincing him to change
his mind. This will be individually determined by each person’s
experience and self-valuation. After a certain point (depending upon your
patience), it will be simply wiser to choose both boxes and move on
with your life.

Closed box, for sure. The paradox doesn't matter. It's how one values money. What is 1000 dollars? In LA, it's a month's rent. I have a month's rent. Another month's rent isn't going to change my life. Now, a million dollars? That's another matter, entirely. That's the opportunity to quit my job and "Live The Dream" as a full-time BoingBoing and Slashdot reader.

As Robert points out, this is not a logic problem. The fact that the predictor of your choice is so good at it is a *red herring*. All the hokum and hand-wringing about omniscience, backward causation, free will and the predictability of human behavior are *red herrings*! Take a close look at the payoff matrix, as a function of the relative dollar amounts and the predictive accuracy of the predictor. How good does he have to be in order for the paradox to arise? Not very good at all! Any psych grad student with a 20-question survey about your attitudes towards games and risk, that will take you under 5 minutes to fill out, will do just fine. Any reasonably streetwise con artist can also probably figure you out in under 30 seconds.

All it really boils down to is which arguments about maximizing expected utility versus maximizing minimum winnings sway you the most. It makes a difference whether you're risk-averse or risk-tolerant. It also makes a difference how many times you get to play the game; if you get to play many times, then maximizing expected gain may make a lot more sense than maximizing minimum payoff from a one-shot trial.

What's very interesting about this problem is not that there are two contradictory approaches to deriving a "rational" coursre of action, but that there are two camps of people that strongly adhere to the one camp or the other, and "rational" arguments don't work very well at causing people to switch camps. For some people, the negative impact of "losing" an otherwise certain $1000 has a huge negative utility that can swamp the dollar amounts involved. Those people are risk-averse; uncertain value is very steeply discounted against certain value. For others, the uncertain chance of winning a large amount of money greatly outweighs the uncertain chance of not winning anything at all, and the expected gain calculation is not seriously distorted by non-monetary considerations. This just goes to show that the expected utility payoff matrix is too simplistic an analysis of what human rationality really is.

The question is if the 999 humans that were tested before all had the same information about the problem as you have now. if they didn't and were not informed about "the catch" i.e. the previous outcomes, their decision is a simple one: $1000 for sure and a 50:50 chance for 1 million; they of course take both boxes. so the alien 999 times predicted they would take both boxes. so the other box was always empty. so you have to take both boxes because $1000 is as much as you can get.
in fact we have no information about wether the other 999 ppl had the same amount of knowledge that we have. this aspect of the problem is however an essential one as i have demonstrated.

Ryan Smith: $1000 notes were last issued in 1945 and stopped being circulated (officially) in 1969 -- but some still exist, and they are still legal tender.

Now, regarding the problem....me, I will take both boxes, thanks. I get $1000, whether or not said alien is telling the truth, and that's good. In fact, I'm not bucking for getting the highest amount of money, because of external factors -- I'm a dual US-UK citizen living in the UK. As it stands, I only pay UK taxes. However, if I ever make more than $80,000 in a year, I invoke s***loads of US taxes, on TOP of my UK taxes. Frankly, I just can't be bothered dealing with the IRS.

If I'm wrong, and the closed box actually DOES contain $1 million, then I can afford an accountant to help me offshore it quickly.

Either way, I don't lose out.

And thus do I thumb my nose at predicted motivations. ;-p

Ryan Smith
notes from $500 to $100000 were used,last printed around 1934
look them up

or try here
http://cgi.ebay.com/1934A-1000-RICHMOND-FE...3417QQrdZ1QQcmdZVie Item

Kiekeben is wrong about how scientific predictions work. He describes a process of induction, wherein one moves from singular statements about observation to general statements which provide predictions - a process which can only function if some principle of induction is assumed (which would be distasteful :-P). Another common version of the inductivist view is that each time the same observation is made it becomes more likely that it will be made again. This is also wrong; how could each sunrise be more probably (i.e. higher percentage chance of occuring) for each sunrise which has already happened?
A better description of scientific predictions is that based on observation we postulate universal statements which we assume to be true. We then deduce predictions from our new universal statements and compare those predictions to new observations. If the predictions are incorrect, our universal statement is shown to be wrong. If the predictions are born out, then we can use our universal statement to make more predictions (and to create technological applications of the theory) until the universal statement is falsified by experiment. If the stament/theory were true, that would never happen, but we have no way of knowing for sure that it wont happen eventually.

I don't think my nit-picking affects Kiekeben's eventual decision.
Effectively, the alien is testing how trusting each of his subjects is. The subjects are rewarded with a million dollars if they trust the alien. I say take the closed box, but don't trust him. He's an alien; his real motivations are probably totally inscrutable.

To my thinking, there is absolutely no paradox here.

Case 1)

If the alien (even though he has claimed to have predicted your actions) has already placed a certain amount in both boxes before you make your decision, and nothing can change that state once you make your decision, than the only logical answer is to take both boxes. There is absolutely no case whatsoever for taking one box (other than maybe to be proud enough to say that you did something other than what the alien predicted). The reason being that you will always get more or the same amount of money by taking both boxes. This is true regardless of how he made his prediction or what it was.

The above case seems to be the one described and to me there is only one correct answer. The dominance principle is the only one that makes sense in that case.

Case 2)

If there is a chance of the amount changing after you make your decision, than there's an element of chance. You could attempt to take the one he didn’t predict so that he will put the million dollars in the box. The correct decision in this case is up to the odds of correctly guessing the box that he didn't predict. If the odds are worse than 1:1000 than it's only worth taking the open box.

But this isn’t the case that was described.



The point is that his prediction means nothing in the case described (case 1). His prediction can be disregarded because it has no bearing on the outcome.

The only case in which you must bear in mind his prediction is in case 2. I didn't see it presented as an option

Am I missing something here? It seems pretty simple to me.

You have to take only one box.
Why ? Because you are doing the experiment twice. First you do it as you are being simulated by the alien, then you do it again in the real world. The best would be to take only one box the first time and both box the second time. But since you don't know if you are in the real world or just in the alien mind, you can't take the risk and so you have to take only one box.

The being claims that he is able to predict what any human being will decide to do.

(emphasis added)

All that's required it to remove our decision process from the game and you'll have a 1-in-2 chance of winning extra money.

How's that? By introducing chance into the equation, we remove the alien's ability to predetermine our chosen action.

For example, with a coin and a sharpie, we could write "both boxes" on one side of the coin and "closed box" on the other. Flip the coin and follow the directions.

If you don't take the closed box you will always wonder what would have happened if you did, so take it. It's worth $1000 to put your mind at ease forever, and you may get $1 million!

Kill the alien, take the $1000, sell the corpse to FoxTV for an Alien Autopsy TV special, and use its spaceship to conquer Botswana for its rich diamond industry.

Destroy both boxes. Remind him that people are always more complex than "superior beings" can easily predict.

"In the open box there is a thousand-dollar bill. "

Take the closed box only. Theres not such thing as a "thousand=dollar bill"

heh, in this day and age the alien would be reported to homeland security and his money seized. Can aliens from another plantet own money?

People have a problem with this paradox because they reject the premise that humans (ie. themselves) could be so predictable. However, that is the premise of the problem.

To understand this, imagine you have a primitive AI program on a computer under your control. You create a virtual environment for it where you pose this problem. You run the program up to the point where it makes a choice of boxes.

Then you rebuild the VR and put the money in the box based on the choice. And you run the AI again. You will predict very accurately indeed, and the right "choice" for the AI is the closed box.

I put "choice" in quotes because people have trouble reconciling choice and a deterministic mind like the AI. They refuse to believe they might have a mind so deterministic the alien could predict what it does so well.

It need not even be deterministic. The AI could include some quantum inputs so it is not perfectly predictable. However, we could run the AI 100 times and get a very good sense of the likely result. Now the choice depends on how much the AI knows about how random is decision processes actually are. If they are highly consistent, it should select the closed box and big reward. If they are highly random then the tester must be lying about the ability to correctly predict such beings 999 times in a row.

By revealing that the alien has been right 999 times in a row, the alien tells you that human decision making on this subject is indeed highly predictable to it. In which case the your choice was made long ago, a consequence of how your brain has grown and become you. The alien already knows how you will reason this out. You either already are the sort of mind that will take both boxes, or you already are the sort of mind that will take only the closed box. That's already happened. You will just be what you are, but if you are the sort of mind that will select only the closed box, you will be richer than if you are the sort of mind that takes both boxes.

This problem is not a strictly logical problem, at least not deductively so. To make it a deductive problem, replace the alien with (hypothetically speaking) God. By definition God's predictions are infallible, so we can eliminate the track record aspect and cut to the chase: God knows with absolute certainty which you will choose. Therefore, choose the closed one, you idiot.

The paradoxical angle arises from the problem whether you can rely on the alien's predictive claims. If you trust the alien, you take the closed box. If you don't, you take them both. This removes it from the realm of deductive reasoning and introduces an inductive element.

If we may assume that the alien's track record has been recorded and reported unimpeachably, then your confidence that the alien has predicted your own choice accurately should rise proportional to the success of his track record. The mechanism by which the alien predicts may be interesting, but is pragmatically irrelevant. 999 consecutive successes is a very persuasive record. Whether knowing you've been predicted influences your decision is irrelevant. The last hundred people tested have heard similarly persuasive stories, and they've been predicted accurately too.

Again, how he does it doesn't matter. The alien's error rate stands currently at worst at 1 in 1000, but is likely to be a lot lower, since a 1:1000 error rate would have been extraordinarily likely to manifest itself sometime during the first 999 attempts. We can easily chart out the odds in play here.

If you choose both boxes, there's at best a 1:1000 chance that you've fooled the alien. Multiply that chance by the value you're risking to figure out how much this choice is really worth. In this case, the total value of choosing both boxes is at best $2000.

If you choose the closed box, there's at least a 999:1000 chance that the alien predicted this correctly. You haven't got the "safe" $1000 to shore up the bottom line anymore, but the value of this option is still at least $999,000.

Therefore, factoring out irrational human decisionmaking processes, this problem is no different than if he walked up to you and said, "one of these boxes contains $2000 and the other contains $999K. Which one do you want?" With these odds it's not even an interesting conflict. If you choose anything other than the closed box, you're not deciding rationally. Your visceral concern over how the alien might be able to know what you'll do is not rational.

Given standard human guessing, of course, you're better off taking both boxes. The values of your options are $501,000 and $500,000 respectively in that case. Given the difference in values in play, the break-even point comes with even the slightest insight into how people will decide. A guesser who is right better than 50.05% of the time makes it more to your advantage to pick the closed box. A much more interesting examination of behavior will come from these very close cases, especially since such a small margin of success is very likely to be a statistical fluke.

We did read the information provided we have nothing better to do, this or work. So what is the box made of, is it alien also maybe a new element that we can sell along with the pictures. Have to go to ebay to search for the other 999 to 1998 possible alien boxes. Always take both boxes you get 2 alien boxes, a $1000 note (any average circulated $1000 note is worth $2000 and up) if the highly superior being from another part of the galaxy is wrong this time you also get the million. And your pictures posted on boingboing.net

Edited by author 12-14-2006 03:27 PM
jesse - the chances are *not* 1 in 2. Or rather - you don't know *what* they are.

Frankly, if I flip a coin and correctly guess the result 999 times correctly in a row, I'm cheating - the chance that I've done it by luck is vanishingly small. You know it, I know it - just because you don't know how I'm cheating doesn't mean that I must not be and the next result is a 50/50 chance.

(To put it another way - this isn't a proverbial 'fair coin toss' you talk about in probability. That would be 50/50, as you suggested.)

Likewise, the alien has been right 999 times in a row. We don't know how he does it, but he's doing it. It's a given of the problem (assuming the alien is lying is not really the spirit of the paradox - the question isn't 'can you trust aliens', it's 'is the universe deterministic').

[edited for clarity]

I think it's wisest not to make the question more complicated than it really is. Read the information provided carefully. If you buy the suppositions of the problem that are given, and what's the point of working on an answer if you don't, then the answer is to take the closed box only. There's no point in trying to understand how the alien predicts. If you buy that the alien was right 999 of 999 times, then there is a very very high probability that he will be right about you. Then by deciding to take the closed box only, you are doing what the alien knew you would do (regardless of how it knew that information), and walla, a million in your pocket!

Correct, bill. We crossposted. Easy (poster 9) may be onto something also.

 So the alien already knows you are going to shoot her and go through her pockets... OK, I ask, "what are the serial numbers of the bills in the box?"
Or, "what's in the box?"
"Cider!" - Nathan Detroit.

What series is the thousand dollar bill and is it uncirculated ?

I would take the closed box, without hesitation. By being the type of person who would take the closed box, I have already guaranteed that he will put $1M in it for me :) If I were the type to try and outwit the alien, he would already know that and only give me $1000. There is no paradox, assuming the alien can judge me as well as he claims.

On the other hand, is he good enough to predict the decay of a heavy atom? My buddy over here suggested to choose randomly, based on that. But maybe the alien would know you would try something like that, and simply not present you with the boxes at all :)

Let's assume that aliens can in fact predict how humans will choose between the two offers.

What if I decide by flipping a coin? Or by running a Scroedinger's cat type experiment?

Seems to be no problem to me. Take the $1000, take photos of the alien, sell them to the press for $1,000,000!

Seems to be no problem to me.

It all comes down to what you know about the alien. He claims to know all about you - maybe he does, but what do you know about him/her/it? Did you observe the 999 times? Did you make him do some cool alien tricks to prove his awesomeness? What is the motivation of a superior, possibly time-travelling omniscient-about-human-decisions alien, and does he care about money?

For you to KNOW that he is infallibly predictive of human actions would mean that you too are infallible about this guy's motivations. I would assume he's BS'ing you and take the grand. But I'm only human.

"But you *DO* know that I've been right 999 times in a row, and the chances that I can be right again are pretty good. "

Actually, the chances of you being right are still 1:2 if you don't know why you're getting it right.

Unless the alien is guaranteed to be correct about your decision or has the ability to modify the contents of the boxes after your decision there also leaves the possibility that the alien was incorrect in assuming you'd take both boxes (leaving the closed one empty) when in fact you just take the empty one. What is the result of this scenario? Do you just get screwed with the empty box and laughed at by the alien, or do you then get a million dollars out of it's pocket and the achievement of proving a supposedly superior being wrong?

Edited by author 12-14-2006 01:46 PM
danboy - he's an advanced alien from another galaxy; how do you know he *doesn't* have a time machine?

See - that's the point. Just because we don't know *how* he does his prediction doesn't mean that he can't.

If I tell you I can predict the flip of a coin, and do so correctly 999 times in a row, you still don't know how I did it - maybe I'm magic, maybe the coin is rigged, maybe something else. Maybe I'm just *really* lucky - but the chances of that are small, maybe smaller than me having a time machine. But you *DO* know that I've been right 999 times in a row, and the chances that I can be right again are pretty good.

The alien is the same case - I don't know how he makes his predictions. But he does, and with remarkable success.

If we take the premise of the argument to be correct - that he's a "superior being" from another galaxy with a proven track record - it seems silly to assume he can't predict our choice, just because we don't know how he does it.

The people who reason that the money is already in the boxes, he can't change it, and so they can go ahead and take both without changing the outcome are implicitly assuming that the alien can't really do what he claims to do - despite some fairly overwhelming evidence to the contrary. It's hubris, really - an admirable trait for a Perl programmer, but maybe not so good a way to win a million dollars from an alien.

For me - it boils down to "Will I bet $1000 I didn't have a few minutes ago that he's not lying, to win a million". I will.

I'd bet my buddy $1000 that the alien was wrong about me. Then take the closed box.

Perhaps I read this too quickly, but by telling about his predictions, and what the outcome will be based on his predictions, Isn't he creating a self fulfilling prophecy? Isn't he therefore guaranteeing you would take only the closed box? If he is not lying, and he always predicts right, he knows what I am going to do, regardless of my reason for doing it. By telling me he put the million in the box, if he predicted I would take only that box, I would be foolish to do anything but take the closed box.

The real question, as Tom points out, is "what do you lose by taking the closed box?" I think my reaction would be, "Well, you know I'm going to take the million dollars." The question is, how greedy does the alien think I am? I'd assume that he'd think that I would think (woo ... getting dizzy) that a million bucks was fine and that if I never collected $1,000 that I didn't have anyway I'd say, "Easy comes, easy goes," and move on. I'd basically have no reason to take the safe bet; I'd have no reason to try to double-guess the alien.

Now, if it was "a million dollars or nothing, and if you wind up with zero dollars then I'll kill you" then you have a paradox worth me thinking about. Then he becomes the Dread Pirate Roberts with his iocaine powder and poisoned wine and I become a sniveling Sicilian saying, "Ha ha! You fool! You fell victim to one of the classic blunders! The most famous is never get involved in a land war in Asia, but only slightly less well-known is this: never go in against a Sicilian when death is on the line! Ha ha ha ha ha ha ha! Ha ha ha ha ha ha ha! Ha ha ha..."

In short, there are more important paradoxes.

There has to be more information -

First I presume he has written his prediction on a piece of paper that he has agreed not to change with his magic powers.

Then, depending on his prediction and whether it is true or not, he will either place or remove the money from the closed box using his magic powers after you have made your choice and his prediction is revealed.

If the experiment is run this way, it is straightforward, and there is no problem with the predictive causality, which is what makes this a kind of silly riddle. You can play it safe and get $1000 for sure, or take a chance for a million. (I would take the chance.)

I'm concerned that the being merely claims to be able to predict the human's actions. What is the truth of the matter? Is there independant evidence of this remarkable claim. Can the alien predict or can the alien cause the million dollars in the box to disappear once the human has chosen so that it only appears to be correct? If, after some observation and experimentation, you become convinced that taking the single box will net you $1 million, then that is the logical strategy. If you have observed the run of 999 correct predictions then you might very well choose the single box. It would be a very expensive and elaborate practical joke to stop the performance just when you step up to the plate.

I don't see the paradox. The claim that the alien makes to be able to predict human choices (which may actually be true) and the claim that the alien has been right 999 times in a row (which may actually be true) are information which is difficult to use. You really need to calculate a proper payoff matrix: If I choose one, what is the probability of getting $0/$1,000,000. If I choose both, what is the probability of getting $1,000/1,001,000? That involves judgement and an evaluation of the truth of the claims. You might end up with $0 but still have made a rational choice.

Assuming that this being's prediction is based on his idea of what your logical choice would be then I would only take the closed box.

You take the closed box, always.

Why? Sure if you took both boxes you *could* win an extra $1000, or at least be guaranteed $1000, but if you take only the closed box then you are also guaranteed something. Either you win:

a) a million dollars.

or

b) the opportunity to prove highly superior being from another part of the galaxy is a liar or not as smart as he thinks he is (if the closed box has no money).

Either way you've *lost* no money. And either way you've got a good story to tell.

Unless this being has some sort of time machine you'd be a fool to do anything but take both boxes.

whatever is inside is already inside, so if you take both you get both...

am i missing something?

It seems pretty obvious to me to take the closed box. $1000 is substantial, but as it's 'found money' it won't hurt me much if I don't get it, and the potential payoff is very significant. Basically, I'm being asked to bet at excellent odds and high payoff if I trust the alien's predictive abilities. Oh, and if I trust that he's not just lying.

As you think about it, ask yourself:

1) What if the $1000 was only $1? would you change your action?

2) What if the alien claimed to predict, say, a flipping coin? and your choices were to take $1000 and walk away, or guess if his prediction was true - he's wrong, you get $1,001,000 and he's right you get bumpkus?

Edited by author 12-14-2006 12:32 PM
Franz Kiekeben (who is a very funny cartoonist) does a nice job of describing Newcomb's Paradox, which I've enjoyed contemplating, on and off, for many years.

A highly superior being from another part of the galaxy presents you with two boxes, one open and one closed. In the open box there is a thousand-dollar bill. In the closed box there is either one million dollars or there is nothing. You are to choose between taking both boxes or taking the closed box only. But there's a catch.

The being claims that he is able to predict what any human being will decide to do. If he predicted you would take only the closed box, then he placed a million dollars in it. But if he predicted you would take both boxes, he left the closed box empty. Furthermore, he has run this experiment with 999 people before, and has been right every time.

What do you do?

On the one hand, the evidence is fairly obvious that if you choose to take only the closed box you will get one million dollars, whereas if you take both boxes you get only a measly thousand. You'd be stupid to take both boxes.

On the other hand, at the time you make your decision, the closed box already is empty or else contains a million dollars. Either way, if you take both boxes you get a thousand dollars more than if you take the closed box only.<br clear="all">

What would you do? Please read the rest of Kiekeben's essay before offering your reasoning.