Newcomb

[packbat]

Reposted from my Facebook:

Imagine the following scenario (a variation on the classic dilemma known as Newcomb's Problem):

About six months ago, a crack team of psychologists came up with a brilliant new device, and decided to run a curious experiment to test it. The experiment takes the following form:

1. Each subject, chosen by lottery, is provided with the money to purchase two identical plain manilla envelopes.
   
2. They and their envelopes are given free transportation to the lab, where they (but not the envelopes) fill out a survey.
   
3. They wait approximately one hour, and then are ushered into the experiment room.
   
4. In that room, they are permitted to examine three stacks - one containing twenty U.S. fifty-dollar bills, one containing twenty fifty-dollar-bill-sized pieces of blank U.S. fifty-dollar-bill stock, and one containing one thousand U.S. one-thousand-dollar bills.
   
5. An attendant removes the stack of thousand-dollar bills. They are instructed to privately place one of the remaining stacks in each of their manilla envelopes, so that they would have two apparently-identical envelopes, and then signal.
   
6. On the signal, the attendant returns with a case, which either does or does not contain the million dollars. The subject then gives either of their two envelopes in return for the case.

There is only one catch in this procedure: the case either contains blank bills or the million, as follows. If the psychologists predict the subject would return the envelope with the thousand dollars, the case contains the million. But if the psychologists predict that the subject will return the envelope with the blank paper, the case contains blank paper. And in each of the one hundred trials so far, the psychologists have always gotten it right. Everyone has either left with the thousand or left with the million.

(Edit: Well, not quite. A few clever people thought to randomize the envelopes so that they didn't know whether they lost the thousand or not. About half of them walked away with a thousand, the other half with nothing.)

The experiment is valid - it has been tested by dozens of experts in experimental protocol, sleight of hand, hypnotism, and every other relevant field. They neither coerce your choice nor switch out the million if you choose to keep the thousand.

You are in the room, with your two envelopes, and the attendant is before you with his case.

Do you give him the thousand dollars or the blank paper?

Comments

[goblinpaladin.livejournal.com]

Given that you just told us how it worked, does anyone answer 'blank paper'?

[packbat.livejournal.com]

Yes (http://www.overcomingbias.com/2008/01/newcombs-proble.html). Bearing in mind that my setup is unusual, the following two paragraphs explain:

There is a large literature on the topic of Newcomblike problems - especially if you consider the Prisoner's Dilemma as a special case, which it is generally held to be.  "Paradoxes of Rationality and Cooperation" is an edited volume that includes Newcomb's original essay.  For those who read only online material, this PhD thesis (http://w3.ub.uni-konstanz.de/v13/volltexte/2000/524//pdf/ledwig.pdf) summarizes the major standard positions.

I'm not going to go into the whole literature, but the dominant consensus in modern decision theory is that one should two-box [corresponding in my version to returning the blank paper], and Omega is just rewarding agents with irrational dispositions.  This dominant view goes by the name of "causal decision theory".

[goblinpaladin.livejournal.com]

Argh long. And well and truly outside of my fields. My confusion may have been related to the way you phrased it- it seemd to me that it was a scientific experiment that was examining the ethics of the people involved and that altruistic/honest types (returning the money) get rewarded, while selfish types don't.

In a case like Omega, the question is phrased such that the box could be empty or full and it matters nought either way. You are being neither honest nor dishonest- and it is always better to take both, because hey! rational.

Of course, in saying that, I'm sure that my instinctive answer would have still been 'take box B.' It just feels right.

Which is, of course, why I should have taken more logic and philosophy.

[packbat.livejournal.com]

Well, you can draw up a diagram mathematically:

contents of case:
    |$1 000 000 | $0
----|-----------|-------
keep|$1 001 000 | $1 000
----|-----------|-------
give|$1 000 000 | $0
    |           |

...and the game-theorists point out that the first row always returns more cash than the second, because you are always either in the first column (and your choice doesn't change things) or in the second (and your choice doesn't change things).

[goblinpaladin.livejournal.com]

That's right- where your choice doesn't change things.

But in your thought experiment, it seemed to be testing the subject's ethics and there a choice WOULD change things. KNOWING what the experiment was (and that honesty is rewarded with a million bucks) would surely mean that all subjects would return the money.

It was a misunderstanding on my part, because I didn't know what Newcomb was.

[packbat.livejournal.com]

Hm - I don't know that it's that deep a misunderstanding. If you consider it, giving away the thousand - or clamming up in the Prisoner's Dilemma (http://en.wikipedia.org/wiki/Prisoner's_dilemma), same thing - is a trust-based move, rather than the "rational" one. Remember, if you give away the thousand and they thought you wouldn't, you're left out in the cold. If you didn't have any reason to trust the predictor - if they did no better than chance - you'd have no reason not to keep the thousand.

[goblinpaladin.livejournal.com]

It sure is, but trust is a better (maybe? ethically?) response in society than a rational one. Also bear in mind that given the parameters of the question, the predictor was correct 100% of the time. Better to play it safe, given those odds.

[packbat.livejournal.com]

In society, however, the situation is different in many ways - people develop reputations, for one. As for the predictor being right ... well, for some reason, two-boxers aren't convinced. Don't ask me why.

[goblinpaladin.livejournal.com]

The thought experiment states that the predictor is always right, though. Well. 100% of demonstrations are correct, which is more than good enough for the scientific method.

[packbat.livejournal.com]

Technically, it could be that the predictors have merely been lucky one hundred times in a row. I gather that part of the resistance to giving away the thousand is that people believe luck is the more credible explanation than reliable prediction in this case - for example, due to a confidence in libertarian free will (http://plato.stanford.edu/entries/incompatibilism-theories/).

[goblinpaladin.livejournal.com]

True. I got the impression that it was more than just 100 lucky coin tosses in a row, though.

[packbat.livejournal.com]

(Oddly, I did not consider that ethical considerations might enter into it. I have heard of no study suggesting people who keep - or take - the thousand are less moral than those who don't.)

[goblinpaladin.livejournal.com]

(Well, it seemed that giving blank money in return for potential real money is dishonest. Maybe I'm a bit odd.)

[packbat.livejournal.com]

(No, it makes sense, it just didn't occur to me that I might be playing up that particular frame, so to speak.)

[active-apathy.livejournal.com]

For a subject who knows how the experiment works, and who wants to maximise their returns, I'd expect the answer would always be 'blank paper' - and to beforehand fill out the survey in such a way that the experimenter will expect to be given the thousand.

The test isn't the decision itself; it's the predicted decision. Manipulate the prediction, and the possible outcomes are $1,001,000 if you succeed, or $1000 if you fail.

[packbat.livejournal.com]

According to causal decision theory, that is the optimal strategy. Of course, no individual so far has successfully carried it out.

[goblinpaladin.livejournal.com]

Hmm. I didn't consider that, probably because a 100% success rate (including tests which alter the subject's perception) imply that the test is not manipulatable like that.

Do these psychologists have some kind of crazy mind-reading powers?

[the-zaniak.livejournal.com]

Hang on, I don't understand. Is this legitimate, the psychologists have been right 100% of the time? Or is this all just theoretical?

"Crazy mind-reading powers" is among the leading candidates, yes...

[packbat.livejournal.com]

It's not actually happening, of course - it's just a philosophy exercise. But in the hypothetical, you have the fullest confidence that the test is legitimate and the psychologists have predicted correctly one hundred times out of one hundred - the only question that remains is what you will choose.

I was thoroughly confused as to which bits were real! I prefer the example with aliens in it.

[the-zaniak.livejournal.com]

Oh! Okay. I do understand. So doesn't it come down to "pick the blank paper, get $1000000, don't pick it, get considerably less"?

I'm a little bit lost as to the exact mechanics.

Sorry, sorry! I'll be more careful next time!

[packbat.livejournal.com]

Step 1: You take a test.
Step 2: They decide if you'll return the $1000. If they think you will, they put $1 000 000 in the case. If they think you won't, or they think you'll pull some shenanigans, they put blank paper in the case.
Step 3: The attendant walks in with the case, hands it to you, and leaves with whatever envelope you give him.

Thus, you get whatever was in the case plus whatever was in the envelope you kept. Simple as that.

(As for the prediction step, I don't know how they do it - all I know is that they've been right one hundred times out of a hundred.)

Re: Sorry, sorry! I'll be more careful next time!

[the-zaniak.livejournal.com]

So return the $1000, be guaranteed the $1 000 000?

Ah, but it can't be that easy, can it? :P

[packbat.livejournal.com]

Technically, convince the psychologists you will return the $1000, be guaranteed the $1 000 000. Thus far, no-one has convinced the psychologists that they would return the $1000 except the people who actually do, however.

Or am I still missing something?

[the-zaniak.livejournal.com]

Yes, but if you're aware of the results, then you'd be aware that returning the $1000 garners you the million, right? So convincing the psychologists would be easy; if you're aware of the system, then they'd be aware that you're guaranteed to return the $1000, so they would know that you were going to, and put the $1 000 000 in the box.

Not anything that'd get you in trouble during the game...

[packbat.livejournal.com]

Some people would reason the way you do about the problem - they would return the $1000 and leave with the $1 000 000.

That said, some people argue that by the time they have to decide whether to return the envelope, the million will either be there or not, and therefore they don't have to return the $1000 to have a chance at the million - they claim their odds of getting the million cannot be affected by which envelope they do, in fact, return, because the million is either already there or already not there. Such a person may then choose to keep the thousand, being as keeping the thousand doesn't change what's in their case. And, so far, every person reasoning that way has opened the case and found it with blank paper.

And they deserve to lose the $1000000!

[the-zaniak.livejournal.com]

Those people are idiots!

Well, "idiot" is a strong term...

[packbat.livejournal.com]

As far as I am aware, their position is actually pretty popular (see the link replying to goblinpaladin). In fact, the split is verifiably strange (http://en.wikipedia.org/wiki/Newcomb's_paradox):

In his 1969 article, Nozick noted that "To almost everyone, it is perfectly clear and obvious what should be done. The difficulty is that these people seem to divide almost evenly on the problem, with large numbers thinking that the opposing half is just being silly."

I think you can read the beginning of Nozick's essay here. (http://books.google.com/books?hl=en&lr=&id=gjA-OLUWiSUC&oi=fnd&pg=PA207&dq=%22Nozick%22+%229.+Newcomb%27s+problem+and+two+principles+of+choice%22+&ots=Fy51ZWvvM3&sig=pm1WNxRic_wiswB3ibGW8zy9zq0#PPA209,M1)

Well, $1 000 000 is a lot of money!

[the-zaniak.livejournal.com]

If there was a bit of doubt somewhere, then yes, I'd be able to see the argument of the other side. But one of the conditions is that the psychologists have 100% accuracy. With that in mind, I can't possibly see any justification for the other argument. If it were a real-life issue, then sure, free will and all that, but given that the box-givers have essentially already seen what you're going to do, there's absolutely no grey area.

I'm not saying they aren't <em>losers</em>...

[packbat.livejournal.com]

Like the guy said - both sides find their decisions perfectly obvious. I can't tell you why.

HTML does not work in subjects, good fellow!

[the-zaniak.livejournal.com]

My sister and I will frequently have long conversation threads on livejournal, holding two conversations simultaneously; one in the "message", and another in the subject.

Occasionally the conversation in "message" will reach a natural end, while the "subject" conversation will keep going, leaving awkward half-hearted messages in the comments.

The opposite is never a problem; subjects are completely optional, so low-effort subjects are fine. They're a step up from "no" subjects, even.

Curse you, Red Baron! Must I be reduced to mere *asterisks* for emphasis?

[packbat.livejournal.com]

Ha! I was wondering where the subject-line thing came from!

I also intend to clear out my "memories" and redo them with my best entries. Not my actual memories.

[the-zaniak.livejournal.com]

Yes, I decided a long time ago to try to use as much of the system as was available to me. I always include subjects in comments and entries, and I always fill out music, location, and mood.

At the party I had tonight, someone mentioned how annoying it was that I don't use tags, so I'll have to add that to the list.

I sometimes leave the "re:" in subjects, too, but I never leave them blank.

[the-zaniak.livejournal.com]

Oh, and icons.

Re: Ah, but it can't be that easy, can it? :P

[the-zaniak.livejournal.com]

On a completely unrelated note, you don't know off-hand when the second game of Nomicide started, do you? I'm not particularly interested in going through the game that you played between the two games.

From a "person interested in reading the archives" point of view, by the way, the first game's ending is utterly bewildering. All the links point to the rule "The gostak distims the doshes flutzly.", but since the definition of each word changes all the time, I have no idea what actually happened, what rule everyone broke that gave you one hundred million points.

I could piece it together from the archives, but it's a daunting task, and not very reader-friendly.

Re: Ah, but it can't be that easy, can it? :P

[packbat.livejournal.com]

November 10th, 2007. (http://community.livejournal.com/nomicide/2007/11/10/)

And you've got a really good point with the readability, there - it must make it hard to catch up, too. I'm not sure how one can fix it, except by having a Historian or something...

Re: Ah, but it can't be that easy, can it? :P

[the-zaniak.livejournal.com]

It's an interesting read, just frustrating at times. Surely you could edit those few entries that don't make sense out of context? Or would that infuriate the community?

You could use your NomicWiki page for a history of the game. It would take about 10 man-hours to do, but it would be worth it. I'm not suggesting you do it, perhaps you could delegate.

Not to mention I'll have a job on Monday...

[packbat.livejournal.com]

Eh, it's a lot of volunteer work - I'd probably want to make it pay off in-game first. ;)

The idea is that the slate is wiped clean each game, right?

[the-zaniak.livejournal.com]

It doesn't seem to be explicitly stated, so I'm just checking quickly before I get too far through the archives: did Game 2 start with just the basic rules, with the exception of the two that you changed?

Mostly - many Nomics persist after victory. Nomicide would have, if the winner had chose otherwise.

[packbat.livejournal.com]

It started with the Initial Ruleset, Game 2 (http://community.livejournal.com/nomicide/39030.html) - there was actually some pretty big changes, particularly the sponsorship deal.

I mean, it might grow on me, but it's not doing so thus far.

[the-zaniak.livejournal.com]

Blech. I'm going to be honest, I hate it. I really liked the format of the first one. Which are we using for Game 3?

Maybe it just needs better fertilizer?

[packbat.livejournal.com]

We haven't decided. I bet if you wrote a ruleset people liked, you could get in as Head and enact it, though!

Nifty icon!

[the-zaniak.livejournal.com]

Remind me what's wrong with the original ruleset?

Swiped it off DevArt - http://Mrcrapinson.deviantart.com/art/Diablo-Suelto-71385814

[packbat.livejournal.com]

The original ruleset is very general - it's not optimized for Internet play, and indeed it works very badly for Internet play, judging by almost every other LJ nomic that was attempted.

As far as the critical differences go, I think the main thing is the deadlines and the loosening of the everyone-must-vote criterion. If I were going back towards the original version, those are the changes I'd ask to keep.

[active-apathy.livejournal.com]

That all the LJ nomics to try it died quickly and horribly; using default Nomic on LJ, your nomic dies the moment someone either doesn't propose, or doesn't vote. This is a Bad Thing - so our base ruleset was designed around post-mortems of the other LJ nomics we could find, and I think we can be fairly confident that it worked.

On the other hand, if by 'original ruleset' you mean the one for the first game: there's nothing at all wrong with it, and I'd happily start with it again.

I didn't realise that Packbat was referring to a different one, in fact.

[the-zaniak.livejournal.com]

That is indeed the one I meant!

Ah, I should have made that clear!

[packbat.livejournal.com]

Incidentally, if you're curious as to the 'default Nomic' i.e. Peter Suber's original game (http://www.earlham.edu/~peters/writing/nomic.htm), it's online.

*nodnod* Thought that might've been the case

[active-apathy.livejournal.com]

Shiny! Well, in that case, I'm all for the way we played the first game - i.e., slowly adding in complexity rather than having rules that were moderately tricky upfront.