T|S One Box or Two Boxes (Newcomb's Paradox)

guys

just take box A and then hope that Bob gives you some of the $100,000 out of the goodness of his own heart

Another thing that bothers me about this is it starts out with "Bob can predict your actions almost perfectly," and then shares his predictions about the box contents. The question actually never says he can predict accurately the contents of a box.

He's not predicting the contents of the box. He's the one stocking the box.

This is making me feel illiterate, and I know I'm not. -_-

Read the wiki page? I might not have explained the question well.

Btw, I think you have to take both boxes. Whatever he predicts, he isn't predicting anything at the moment that you're choosing a box. There's no reverse causality.

Hang on, if you only take one box, it's a random choice.

I should have clarified in the poll options. The only two options are a) Take Box A and Box B, or b) Take Box B.

Oh, that affects what I selected/voted for.

Has somebody defined 'almost perfectly' at this juncture? Is the dude 90%, or 99.9%?

I think the 'almost' exists so that you aren't dealing with a question of determinism.

xp to Mark: I don't see why you would pick something else, like only take Box A. That's 100% a losing strategy.

Got it.

Right, here is the paradox explained.

Bob knows you are only going to take one box. (i.e. box b) so that's his prediction. So, box B gets big money.

You take the box, and get £100,000.
Or, you take both boxes and get £101,000

However, suppose Bob thinks "Here's a daft lad, he's going to take both, innee?"
You take box B, proving Bob wrong, and get nowt for your trouble.
Or take both, proving him right, and get £1,000

So, the only way you are guaranteed the money is if Bob sees you're a smart lad (or lady, obv), and guesses one box. Bob needs to be infallible.

Therefore Bob is the pope.

xp to Mark: I don't see why you would pick something else, like only take Box A. That's 100% a losing strategy.

No it isn't, it's a "always get £1,000" strategy, Bob's prediction then doesn't affect the outcome, see my previous post.

a grand in the hand is worth a paradox in the box

The only mechanism we know of that yields consistently *almost perfect* predictions are based on physical or mathematical laws, and those are reliable enough to be treated as certainties.

The mechanism by which Bob is able to make such accurate predictions is where the fairy dust enters the equation. We need to know more about this guy.

Does Bob work purely through inspired guesswork? Magical incantations? Or does he have system where he inputs known values which yield his results? How many predictions has he made already, and what were they in relation to? If his accuracy at predicting has been measured, what was his exact percentage of success, to the third decimal place? If that information is not available, why not?

Inquiring minds and all that.

No it isn't, it's a "always get £1,000" strategy, Bob's prediction then doesn't affect the outcome, see my previous post.

Super wrong. You get the $1,000 whether you take just A or both A + B (even if B is empty) and if B isn't empty, you hit the jackpot. There's NEVER a reason to just take A.

Oh true enough.

I hadn't considered the "only take box a" option seriously anyway.

Maybe Bob is running a perfect simulation of our universe - on hardware a little quicker than that which ours runs on.

Or even if he's just a reeeeeeeaaallly good reader of people, it doesn't really matter - the premiss that he is accurate in all his predictions isn't prima facie 100% ridiculously implausible and can be taken at face value.

This is a pure thought exercise that has nothing to do with real life.

The amount of money is in flux until you've made your choice; it is determined by whether the number of boxes you chose matches Bob's prediction. It's like Schroedinger's Cat.

― Marni and Louboutin: coming to Tuesdays this fall on FOX (HI DERE), Tuesday, 25 May 2010 20:57 (Yesterday) Bookmark Suggest Ban Permalink

I'm afraid Dan is wrong here - the whole point of the paradox is that the money is NOT in flux, Bob makes his prediction, then puts the money in the boxes, THEN you get to pick. So the money is already in the boxes (or not) when you make your choice. Hence the paradox - Bob's predictions are reliable so you should choose only one box; but at the time of your choice the contents of the boxes are already in place so you should take them both to maximise your return.

Except really the only way to actually maximize your return is to take box B alone.

ledge's strategy only works if you assume you can trick Bob into making a false prediction.

the premiss that he is accurate in all his predictions isn't prima facie 100% ridiculously implausible

yes, yes it is.

OK, imagine you are Bob.

You predict.

ledge's strategy only works if you assume you can trick Bob into making a false prediction

Bob's prediction doesn't make a jot of difference when you're standing there trying to make up your mind, with the money already in the box/es. Or so a two-boxer would argue.

here's a nice argument:

One can imagine that the Predictor, who is also a truth-teller it turns out, tells your buddy whether or not the million is in the box. What would your buddy, who has all the information about the potential payoffs, recommend that you do? If he had your financial interests at heart, he would always, no matter what the Predictor did, recommend you take two boxes. It would seem completely irrational to go against the advice of your well-informed buddy.

Bluddy ell, now Chris Tarrant is in the room!

also, fwiw

it is a logic puzzle, or at best really watered down game theory

it was apparently orgininally formulated to point out problems with bayesian decision theory, and some people have argued that it's identical with the prisoner's dilemma. iow rather than a fun game for all to play it is more of a thing for philosophers to puzzle over and write lots of papers containing lines like "v(b1) = v(m).p(m/b1)+v(n).p(n/b1) = 990,000".

it's not nearly well defined enough to be that, if we're free to assume that bob is this, that or t'other

All that matters is that Bob is a reliable predictor, it doesn't matter how he does it - it could even be pure luck. That's really the point, in fact - the result is probabilistically dependent on what you pick (because of Bob's history of reliable predictions) - but causally independent (because Bob is only predicting, not affecting the outcome: the money is already in the boxes).

the real question here is, is Bob Newcomb a viking at sleep

Seems strange to give figures for the cash involved, and not for the reliability of Bob's predictions.

I suppose it'd just be a probability equation then, but without it it's just a question akin to 'How long is a piece of string, Bob'?

If the predictor isn't 100% accurate, then this isn't about free will. If the predictor is 100% accurate, then the problem of free will is implied, but not demonstrated by the problem itself. At best, this problem seems to be a good way to stimulate discussion about why the population is split on their decision-making strategies.

yeah it's nothing to do with free will really.

Btw, I think you have to take both boxes. Whatever he predicts, he isn't predicting anything at the moment that you're choosing a box. There's no reverse causality.

― Mordy, Tuesday, May 25, 2010 10:15 PM (Yesterday)

going to disagree with this, the whole question hinges on the idea that your choice creates the status of the boxes. this would be more clear if bob was 100% accurate, but even with the slight margin of error in your formulation, theres no point in taking the super long shot.

still say this isnt a paradox, but rather an uncomfortable counterfactual situation that irritates people because we are wired to be really defensive about free will, and reject reverse causation out of hand. within the structure of bob world, free will (in this case) is suspended, and reverse causation is possible by definition, which removes the paradox.

xposts

going to disagree with this, the whole question hinges on the idea that your choice creates the status of the boxes.

exactly

very happy that my bros with philosophy degrees are backing me up on this, makes me feel like I don't fail at thinking after all

xp only on ilx could you read a post like that from a username like that. i love it.

the whole question hinges on the idea that your choice creates the status of the boxes.

it really doesn't, the problem (as originally formulated) is nothing to do with free will or reverse causality, but about decision theory.

as counterintuitive as it seems on the surface, HI DERE is right about the flux aspect of the money because standard temporal rules are suspended in this case (again, this is even more obvious in the case of the 100% accurate bob). the money in the boxes is indeterminate until you make your choice, which again, i realize is a punch in the directional time part of the brain, but infallible predictors dont exist either so you get what you get.

xpostststsss

Bob (almost) always predicts what you are going to do correctly, regardless of the mental contortions you go through in making your decision. If you decide to take both boxes, he will have predicted that you will take both boxes. If you take one, he will have predicted you will take one. You're betting on him being wrong, something he rarely is based on the setup, ergo by taking both boxes you are betting on the long odds that he has made a mistake, whereas if you take one, you are betting against the log odds that he has made a mistake.

what about your pal who knows what's in the boxes, and always tells you to take both?

going to disagree with this, the whole question hinges on the idea that your choice creates the status of the boxes.

exactly

very happy that my bros with philosophy degrees are backing me up on this, makes me feel like I don't fail at thinking after all

― Marni and Louboutin: coming to Tuesdays this fall on FOX (HI DERE), Wednesday, May 26, 2010 3:31 PM (4 minutes ago) Bookmark

If the predictor is less than 100% accurate, does your choice create the status of the boxes? The prediction creates the status of the boxes, but the predictor could be wrong about your choice. If the predictor is wrong, then your choice had nothing to do with the causality of the status of the boxes.

Here's a more realistic version of the problem, where the answer seems fairly clear (and it's the equivalent of two-boxing). (And it's nothing to do with free will.)

Though it is well established that there is a strong statistical correlation between smoking and lung cancer, it doesn't follow that smoking is a cause of cancer. The statistical association might be due to a common cause (a certain genetic pre-disposition say) of which smoking and lung cancer are independent probable effects. (This is sometimes referred to as "Fisher's smoking hypothesis"). If you have the bad gene you are more likely to get lung cancer than if you don't, and you are also more likely to find that you prefer smoking to abstaining. Suppose you are convinced of the truth of this common cause hypothesis and like to smoke. Does the fact that smoking increases the probability of lung cancer give you a reason not to smoke?

what about your pal who knows what's in the boxes, and always tells you to take both?

he's a dick who has already palmed $99K for himself

I don't think this problem has anything to do with free will. Probability is different than causality, right? The problem seems to be that the probability changes depending on your choice, given a reliable predictor.

If you were Bob, would you predict that the dude "will take 2 boxes"? Or no?

Whatever is the selection, it would always be the same, right?

In which case, Bob is lacking in free will. Just as much as if both boxes were transparent.

For 'selection' read 'prediction' obv.

If Bob was a perfect predictor, then this would be a problem about free will and causality, but he's not, he's a highly reliable predictor, which makes this a problem about probability.

Bob chooses first, and chooses on the basis of the scenario, which never changes, so his prediction never changes.