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

The issue isn't about free will etc, it's about understanding the rules of this hypothetical universe and what the best strategy for success in them is. Since Bob can accurately predict your decisions, you make the choice where his prediction of your behavior gives you the largest amount of money, which means only taking box B.

he can predict your decisions *almost* perfectly

yeah what's with the "almost" - sometimes the laws of this universe don't work? what's that about?

Right, so if you look at the probabilities, it is more likely he is right than wrong:

(UNLIKELY) he predicts 1, you take 2: $101,000 payout
(LIKELY) he predicts 1, you take 1: $100,000 payout
(LIKELY) he predicts 2, you take 2: $1000 payout
(UNLIKELY) he predicts 2, you take 1: $0 payout

You guarantee yourself $1000 by always taking 2; you give yourself the most chance for a large payout by taking 1.

Also, if you take 1 when you should have taken 2 (ie, his prediction was wrong), you are missing out on $1000 extra dollars. However, if you take 2 when he should have taken 1 (ie, his prediction was right), you miss out on $99,000.

this is by definition not a paradox, sorry

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

^^^

watered down game theory

yep

I kind of like the definition of "paradox" as "annoying thought experiment" though

I think the problem is that lack of free will is being considered paradoxical, but within the structure there cant be actual free will (in fact it's kind of a decisive example of reverse causation, in other words, the choice made in the present causes the choice made by bob in the past).

both variants (100% accurate bob vs. almost always accurate bob) seem to fail as well - 100% relies completely on the free will paradox fallacy i just mentioned, and almost always becomes a really strange betting against the odds gambling problem indicator.

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.

contenderizer otm

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I kinda want to run a bunch of other polls in a similar vein (A priori knowledge: Yes/No, Abstract Objects: Platonism/Nominalism, etc). Peeps be interested?

yeah, there ain't enough philosophy in this place.

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