The Newcomb Problem

by Kevin J. Lin

First off, I'd like to thank everyone who responded with their comments on the problem. Sorry I couldn't respond personally to each of you. It has been quite some time between when this puzzle was first posted and this solution page was ready. The two reasons for this were: A) I wanted as much data as possible so we all could see if there were any interesting patterns, and B) our researcher Mr. James wasn't ready (more on this later).

First, some numbers. The big number, of course, was the preference of "Box A" over both boxes. Out of the three hundred survey results from which we pulled our data, 183 favored A, and 117 favored both. This was surprising, because of how close they were. Only 61% of the people preferred Box A (this was the same percentage we had when we checked our data at 200 respondents).

While age seemed to have little impact on the results, this may have been caused by the fact that nearly half the respondents were under 25. A full 85% were less than 35, so we did not get accurate measurements of age groupings (the measured splits, in case you forgot, started at 20, and broke every five years up to 40).

When we first broke our data, females seemed to prefer A a higher percentage of the time than males, but his came closer to even as the result set grew.

So this completes the "survey says" portion of the solution.

The Newcomb Problem, or paradox, as it is sometimes called, has created enormous controversy over the years since William Newcomb posed it. Granted, not as much as gun control or gay marriage, but as far as math problems go, it's a real tempest.

The problem, in a variant form, can be found in the rec.puzzles archives. The phrasing as it exists there is somewhat ambiguous (it fails to mention, for instance, that the Newcomb being is likely to be correct!) but captures the spirit of the puzzle.

It leaves out a stipulation which is found in most other versions, which specifies in one way or other that A) You believe the Newcomb Being to have advanced (supernatural or otherwise) prescience in action prediction, and B) The Newcomb Being's success in prediction is not dependent upon your choice.

The second point is critical. Why? Imagine if the Newcomb Being was a normal human, who had managed to score a 90% success ratio over a hundred trial runs. The reason for his or her success might be due to fallibility! After all, if someone posed this problem to you without any supernatural credentials, what could possibly convince you or anyone else not to take both boxes? This person might score a full 100%, simply because they failed to convince anyone of their prediction skills. Worse yet, they could insure a 100% by advertising that, yes, it was highly unlikely that they would ever actually put the $1,000,000 in the first box.

So for the problem to remain interesting, we must add something to the effect that you have grounds to believe the Newcomb Being can predict future actions accurately.

How?

That's an interesting question. It is actually THE interesting question which many based their response on.

"R" wrote:

"...If somebody CLAIMED that the situation was as described and asked me to make a choice, I would take both boxes because I wouldn't believe that the predictor has the power described. The argument for taking only box A is invalid if the predictor does not have the claimed predictive ability. But the argument for taking both boxes IS valid."

Others hypothesized on how the Newcomb Being might derive its skills from statistical analysis of previous players.

"T" wrote:

"...Simply for the sake of stirring things up, a benevolent participant may conclude that this game is repeated many times with each outcome noted by the Newcomb Being, thus by opting to take only the "A" box, you are influencing the being's future decisions, making it more likely to believe that we humans are a bit dull and would skip on the $1 million dollar opportunity and thus make it more likely that the being will leave the $1 million in the box. Such an act of kindness by today's participant may line the pockets of tomorrow's player."

"T", incidentally, chose both boxes. So much for benevolence! This is an interesting model for reasons other than making fun of "T". For one, "T" guessed the operation of the program which determined what actual players in our "simulation" received. For another, "T" was taking advantage of the act of kindness by yesterday's participant to line his pockets. (At the expense of tomorrow's). To be kind, "T" did not know that his choice was going to have any future impact when he made it.

But if the Newcomb Being functioned like our newcomb-bin program, would this change the nature of the puzzle? It certainly would seem to- in fact it would change it into a variant of the prisoners dilemma. And I suspect it would be extremely difficult to convince anyone that taking just one box, while detrimental to themselves, was "for the good of humanity". And from a game theory standpoint, the correct solution becomes apparent: Maximize your personal gain.

Or does it?

After exhaustively combing (newcombing?) over the research done on the problem, The Grey Labyrinth discovered an exciting new fact. Someone else was also interested in learning the answer, and was even harder at work uncovering it.

This someone, or something, was The Newcomb Institute of Technology.

The U.S. government occasionally finances odd operations which have the interesting side effect of providing answers to historic philosophic problems. For example, the DOD's STUD project allowed Daniel Dennett to write his "Where Am I?" essay, and later David Sanford's "Where Was I?" follow-up.

It appears the non-profit N.I.T. has received enormous funding to solve the Newcomb Problem. The government has kept the project quite hush-hush because of the furor which would result if the anti-philosophical majority were catch wind of this "pork-barrel" enterprise.

However, because of certain favors performed by The Grey Labyrinth for the government, we were allowed to send an interviewer to the N.I.T. and report their progress to the general public. I doubt we would have ever learned of the existence of this project if it were not on the verge of a major breakthrough.

Naturally, everyone at the Grey Labyrinth was eager to investigate the N.I.T's findings. The prospect of actually participating in such an experiment (though at the time we could not imagine how) was quite enticing. The philosophic implications of such a test dwarfed the mere potential for walking away with a million dollars. At least for me it did.

Unfortunately, I was not selected to visit the Newcomb Institute. One of our senior researchers, Eric James, was chosen by lot for that honor. Following his visit, he prepared the following report:

October 1, 1996

I arrived at the Newcomb Institute of Technology in A______ (editor's note: At the request of the N.I.T., the location and real names of the employees are being withheld for security reasons) early this morning. I was met at the door by Dr. Smith who took me for a brief tour of the facilities. Equipped with state-of-the-art technology from all scientific disciplines, I saw nothing which suggested research on the newcomb boxes. Admittedly, I didn't know what I was looking for- psychics in the lotus position bending spoons, I suppose. There was none of that- rooms full of complicated machinery, computers, laboratories, and the like.

After the tour came an horrendously tedious exercise in signing legal forms and waivers. It was pretty clear I was relieving the Institute of any responsibility no matter what they did. While unapprehensive arriving, I was curious to know exactly how risky choosing between two boxes could actually be.

This process lasted several hours. At the conclusion, I was led to a grey vault, containing a single cylindrical capsule, about the size of a small car. Dr. Smith told me that this was a specially prepared sleep capsule in which I was to spend the night. The capsule contained sophisticated electronic equipment with which he said they would "measure my brainwaves."

Suspicious, but doubting any malevolence, I settled into the compact sepulcher and was quickly lulled to sleep by a wonderful symphony of new age music.

October 2, 1996

I awoke the next morning fully refreshed, and was quickly escorted to the office of Dr. Smith, who explained the circumstances of the strange experiment I had become a part of.

"May I assume that prior to your arrival here you had a chance to study the literature surrounding the Newcomb Problem?"

I nodded.

"One of the principle reasons, and there are others, for the Newcomb Institute's existence, was of course to study the implications of advanced predictions on human choice. Particularly in scenarios where an individual's knowlege of the predictor's capabilities will have a direct impact on his or her choice. The Newcomb Problem itself is the epitome of such a scenario: you are presented with a choice where what is normally the correct and obvious answer becomes flawed if it is accurately predicted by your 'opponent'. There are numerous strategic applications for such studies, even now that the cold war has drawn to a close."

Before I had a chance to ask him to elaborate on this open-ended comment, he continued:

"But the newcomb problem, and others like it, are special because the events which determine the optimal strategy are completed prior to commitment to a particular strategy. Or so it would seem. And as it turns out, most proponents in favor of the "two box" selection argue that no entity could be both accurate in its prediction and provide a demonstration to the subject, without damaging the validity of its prediction. And so it is for this reason we are pleased to announce that we have created a scenario in which the Newcomb Problem can be demonstrated experimentally."

"So you have some prophet holed away here who is reading tea leaves and will reveal my actions to you before I've even decided what they are?" I asked skeptically.

"We're a non-prophet organization Mr. James."

"Sock it to me. What's the game?"

"We built you."

"Uh huh."

"To be more precise, we built nine of you. The "sleeper capsule" you spent last night in did not read your brainwaves, as you probably already guessed. Rather, it performed an extremely low-level scan of your entire body, right down to the cellular level. Using technologies I am not at liberty to discuss, we reconstructed nine identical copies. The ten 'Eric James's are having meetings in nine seperate rooms, being provided exactly the same information. One is of course the original, but he, or perhaps you, has no way of knowing."

"And you expect me to believe this?"

"On the contrary, I expect you to disbelieve this. The heart of the newcomb problem relies on the subject believing in the validity of the predictor. Until I can convince you what I am saying is true, the experiment is meaningless."

"How is this going to happen?"

"What would it take to convince you?"

I thought for a moment, "Well, seeing them wouldn't be enough. A visual reproduction would be far simpler than a clone, and not accurate for predictions. I imagine a quick conversation with one would be sufficient."

"Regrattably, while we could do that, it would influence your future actions. Our prior studies have shown that behavior among replicas remains remarkably similiar over a short period of time, say several hours, provided that the environments and stimulus are held constant. Meeting yourself would cause rapid divergence in your actions to the point that even a few minutes of exposure would be sufficient to destroy the experiment."

"Okay, I'll buy that, I don't have to meet myself in person, a simple knowlege test will suffice, provided I am the only one who could possibly know the answer."

"Exactly what I had in mind. Mr. James, would you mind thinking of two unrelated nine-digit numbers?"

I thought for a moment, "Why two?"

"I will ask for either the first or second number, and give you the other. The number you tell me will be used as a proof for another you. Obviously we pre-arranged this experiment so that five of you will be asked for the first, and five for the second. If I can tell you the other nine-digit number you were thinking of, this would be a convincing demonstration, no?"

"It seems unlikely you could guess it, if I intended to make it a hard number, and I do. So yes, if you can give me the other number, I will be thoroughly convinced, surprised, and impressed."

"Agreed. Please think of the two numbers now, and in your mind specify one to be the first. You may take up to five minutes to decide."

He turned to a lap-top on his desk and began typing as I thought. It was trickier than I first imagined, because it is so hard to hold eighteen digits in your head at once. For the first I decided on the last seven digits of an old flame's phone number backwards, followed by the third three numbers which popped into my head. For the second I chose my high school locker combination, the last two digits of pi I could remember, and my father's age.

"Ready."

Looking at his laptop he said, "Please give me... the second number you thought of."

"315287965."

He typed these into his lap top as I rattled them off, and then immediate said, "9035738228?"

I was understandably dumbstruck. He was exactly right.

"Impressive," I said.

"Are you convinced?"

"I'm still a little skeptical that there are nine exact duplicates of me somewhere in this building. This could be one of those mentalist tricks... somehow I was subconsciously 'forced' into choosing those numbers. Let's try again, but this time I'll name the game. If what you say is true, the other nine will pick the same game."

He nodded, "What will it be then?"

"I'm thinking of two things... will call them 'A' and 'B'. You can ask for one or the other, and I'll give it to you. You then tell me what the other was. And this time, it can really be anything, a person, a number, a phrase... anything."

"Very good, I will ask for," he began typing away, pausing to look at the screen, "... Choice B".

"And that would be the theme from 'Phantom of the Opera', that little organ bit which sounds like Pink Floyd."

He duly entered this into his laptop and seconds later resounded, "Choice A would have been... Pierre Menard's toothbrush."

"Wow."

"Now are you convinced?"

"Let's say that you may or may not have nine duplicates of me feeding you these answers. Regardless, you have successfully demonstrated 'superior predictive powers'."

"That's all we need. Shall we begin?"

I nodded. He stood up and led me out of the room, down a hall, through a large steel airlock, into a small anti-climactic office with a chair. I was instructed to sit there. My counterparts were either doing the same, or facing the Newcomb Challenge. I was told that even the first to choose had to face a certain amount of "buffer time" to prevent us from knowing our place in line.

Two and half hours later it was my turn.

I stood in the center of large conference room. The only trappings were a large clock counting down the minutes until I had to make my decision, a glass table, and two boxes.

Without a second thought, I chose...

Box A, alone.

Probably not a lot of suspense there. The ten Eric Jameses returned to the Grey Labyrinth, each now independently wealthy, although a million dollars isn't what it used to be. After drawing lots, one of them wrote up his logs, and the rest went off to live on various remote islands in the Caribbean. We haven't heard from them recently.

Epilogue

We hope you found this little narrative entertaining, if not informative. You probably don't believe a word of it, which the N.I.T. thinks is just fine. The notion of anyone being able to build exact duplicates of people is still in the realm of science fiction, and will fortunately remain there for the foreseeable future.

However, it does simplify the Newcomb Problem from an arm chair philosopher's standpoint. It meets the vital criteria of "superior predictive powers", without resorting to magic or time-travel.

In Eric James's case, the solution became quite obvious. His choice would have been predicted accurately- by himself. Does this mean that he, or they, had lost "free will"?

We'll leave it for you to choose.

Back to the Puzzle