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The Newcomb Problem

Started by Densun Apr 21, 2004 at 3:30 PM 3 replies 200+ views

Original Post

Apr 21, 2004 at 3:30 PM

Here's an interesting question. I've already read discussions on this from experts or something, but I'd be interested in hearing what people here come up with. A being, who you believe to have superior predictive powers, makes you an offer. Before you are two boxes, identical in appearance. Within one box, let us call it 'Box A', there is either one million dollars or nothing. Within the other box, 'Box B', there is definitely one thousand dollars. The being, whom in deference to tradition we will call the Newcomb Being, will allow you to either take both boxes, or just Box A. Twenty-four hours ago, the Newcomb being made a prediction about what you would choose. At this point, it placed the money in the boxes. If the Newcomb Being predicted that you would take both boxes, it left nothing for you in Box A and the $1000 in Box B. If the Newcomb Being predicted that you would only take Box A, it would leave the million dollars in it, as well as the thousand dollars in Box B. If the being predicts you will base your choice on a random event (like flipping a coin), it will leave Box A empty. Now you have grounds to believe that in such matters, the Newcomb Being has a success rate on predictions of about 90%. Depending upon you choice and the being's anticipation of your choice, you could walk away with $1,000,000, $1,001,000, $1000, or nothing. If you choose both boxes, the least you could receive is $1000 and the most would be $1,001,000. This seems to be the decision which would maximize your return, while minimizing risk. On the other hand, if you pick both boxes, chances are that the Being would have predicted this and left you nothing in Box A. Giving up an almost certain one million for a certain one thousand seems awfully foolish. Working out the expected return, based on the Being's 90% success rate, you come up with following decision matrix: You Choose - Box A Contains: - Box B Contains: - Expected Value Only A - .9 x $1,000,000 - $1000 - $900,000 Both Boxes - .1 x $1,000,000 - $1000 - $101,000 It seems like choosing only Box A gives you a lot higher expected return on average, even if there is the risk of nothing. But there you stand, before the boxes, and the Being has already placed the money. There either is or is not $1,000,000 in Box A. There certainly is $1000 in Box B. Nothing you could do at this point will change what is in the boxes. Why shouldn't you just take both to be on the safe side? The being awaits your response. What do you do? (sorry for the botched table above. I'm not sure how to format it) [edited by - mtw on April 21, 2004 4:31:11 PM]

Densun

Apr 21, 2004 at 3:43 PM

Here''s some discussion that went on at the place where I got the problem from.

KevinG

Apr 21, 2004 at 3:43 PM

Take both BoxA and BoxB, and if BoxA doesnt contain anything, go back to the Newcomb being and punch it in its face (or faces)
repeatedly until it submits and gives you the $1,000,000 anyway.

That''s the smart way to do it, damnit.

griffenjam

Apr 21, 2004 at 5:06 PM

I don't get it, you would never select just box B, so you either select only box A or both. Either way the being would know that you would be getting box A; You don't need any predicting skills for that. With that knowledge it would never put anything in A, why would it?
With this in mind I would select both, at least I get the grand and maybe he would feel giving that day and slip in the million. HEck if he were really smart he would predict that if he slips me the mil I would give him $500,000 of it as a tip.

Edit:

Apon rereading this part

quote:

wenty-four hours ago, the Newcomb being made a prediction about what you would choose. At this point, it placed the money in the boxes. If the Newcomb Being predicted that you would take both boxes, it left nothing for you in Box A and the $1000 in Box B. If the Newcomb Being predicted that you would only take Box A, it would leave the million dollars in it, as well as the thousand dollars in Box B. If the being predicts you will base your choice on a random event (like flipping a coin), it will leave Box A empty.

It seems that if you select only box A the million will be there every time. In that case I take only box A, I can miss out on the extra thousand.

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[edited by - griffenjam on April 21, 2004 6:08:58 PM]

capn_midnight

Apr 21, 2004 at 5:45 PM

A) Any conclusion as to what you "should" do given this situation is meaningless, as this situation will never come up

B) basing your decisions in games of chance on statistical analysis only works if you can play an infinite number of times, and if money is required to play, an infinite amount of money. Try it, flip a coin, it''s a 50% chance to get heads. Say you get tails, does that mean it''s a 100% chance to get heads, to balance out the odds from recieving tails first? NO! It''s a 50% chance again. 50/50 chance of flipping heads does not mean that out of 100 flips you will land 50 heads and 50 tails exactly. It means out of an infinite number of flips, you will land 50% heads. You could very well flip 100 out of 100 as tails, all the while expecting heads because "it''s due". So many times I hear people saying "I''m due, I''m due, been on a month long bad streak, I''m due to win". Yeah right, you''re due to end up lying in a gutter in a pool of your own liver blood and someone elses urine.

C) If the Newborn being can predict the future, then it doesn''t matter, what will be is what was, you don''t need to worry about choosing which box to take as you will have already taken it. That 10% chance that he is wrong is meaningless, a complete illusion, considering B above.

D) There ARE games of chance, however, that DO happen, and that you CAN play any number of times (thereby minimizing the error of statistical analysis, though not completely). For example, craps. Craps is an amazing statistical system, and one would spend their time better studying craps than the Newborn being. You get the same returns as with studying the Newborn being (practice of statistics) and your findings are actually usable to actually win you money.

E) What''s the answer? Choose box A or B? Neither, don''t choose any box, and the time you save not choosing boxes can be used to study craps, where you can choose Pass or Don''t Pass.

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