packbat: A bat wearing a big asexual-flag (black-gray-white-purple) backpack. (darwin has a posse)
packbat ([personal profile] packbat) wrote2008-05-30 09:11 pm

Newcomb

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?

[identity profile] packbat.livejournal.com 2008-05-31 02:31 am (UTC)(link)
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".

[identity profile] goblinpaladin.livejournal.com 2008-05-31 02:38 am (UTC)(link)
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.

[identity profile] packbat.livejournal.com 2008-05-31 02:39 am (UTC)(link)
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).

[identity profile] goblinpaladin.livejournal.com 2008-05-31 02:43 am (UTC)(link)
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.

[identity profile] packbat.livejournal.com 2008-05-31 03:12 am (UTC)(link)
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.

[identity profile] goblinpaladin.livejournal.com 2008-05-31 03:22 am (UTC)(link)
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.

[identity profile] packbat.livejournal.com 2008-05-31 03:34 am (UTC)(link)
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.

[identity profile] goblinpaladin.livejournal.com 2008-05-31 03:37 am (UTC)(link)
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.

[identity profile] packbat.livejournal.com 2008-05-31 04:12 pm (UTC)(link)
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/).

[identity profile] goblinpaladin.livejournal.com 2008-06-01 03:05 am (UTC)(link)
True. I got the impression that it was more than just 100 lucky coin tosses in a row, though.

[identity profile] packbat.livejournal.com 2008-05-31 02:41 am (UTC)(link)
(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.)

[identity profile] goblinpaladin.livejournal.com 2008-05-31 02:44 am (UTC)(link)
(Well, it seemed that giving blank money in return for potential real money is dishonest. Maybe I'm a bit odd.)

[identity profile] packbat.livejournal.com 2008-05-31 02:58 am (UTC)(link)
(No, it makes sense, it just didn't occur to me that I might be playing up that particular frame, so to speak.)