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

Aimless OTM, the only paradox here is in this stupid hypothetical universe where Bob determines the contents of the boxes

x-post

While taking only one box is risky assuming that Bob might be wrong, the problem setup goes to great lengths to remove the accuracy of his predictions from the equation; he is basically a given.

Essentially, this boils down to take 1 if you think Bob is right, take 2 if you think Bob is wrong. It's still more advantageous to take 1 because, if you are wrong, you have left $1K on the table, whereas if you take 2 and you are wrong, you have lost $999K.

how can you have lost what was never there in the first place?

hate bob so much right now

because, according to the rules of the universe, it would have been there had you made the other choice

this universe doesn't make any fucking sense.

the money's either in the box or it isn't - if you take both, you haven't lost anything, because you have already taken all that was there to begin with

like what is this magical universe where, if you leave a box behind, $100k magically appears in it

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.

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

5. But if you're the type of person who would take Box B, you might as well take both boxes, since the amount in them is predetermined.
6. But if you're now the type of person who would take both boxes, then Box B is empty (ie: back to step 3)

this is the part that doesn't work for me as a paradox. i don't buy the psychological inference made in your point #5, and nothing in the setup implies that bob's predictions wouldn't take such a thing into account in the first place anyway. if you take box B, then box B is almost certainly going to contain $100,000. period. so you might as well take box B, accepting that you really are a box-B-taking kind of person.

i mean, if you go ahead and take both boxes knowing A) that the near-infallible bob has predicted your choice in advance -- and B) that IF bob has correctly predicted that you would choose both boxes, then box B will be empty -- then you're pretty much a moron. and you have to credit bob with knowing that you're not a moron, right?

Wrong. Because if you take both boxes there's no reverse-correlation. It might mean you are the kind of person who would take both boxes, but you haven't damned yourself to less money because you took them in the moment. You were damned from the moment Bob made the prediction. Any chooser should simultaneously want to be the kind of person who would only take Box B, and recognize the impossibility of being that kind of person (because at the moment of choice, you are totally free to take both boxes). A similar paradox that explains this problem is Kavka's toxin puzzle.

An eccentric billionaire places before you a vial of toxin that, if you drink it, will make you painfully ill for a day, but will not threaten your life or have any lasting effects. The billionaire will pay you one million dollars tomorrow morning if, at midnight tonight, you intend to drink the toxin tomorrow afternoon. He emphasizes that you need not drink the toxin to receive the money; in fact, the money will already be in your bank account hours before the time for drinking it arrives, if you succeed. All you have to do is. . . intend at midnight tonight to drink the stuff tomorrow afternoon. You are perfectly free to change your mind after receiving the money and not drink the toxin.

The problem is similar to the one here. In Kavka, you simultaneously want to have intended to drink the poison and realized that any practical person would not drink the poison. Similarly, you want to be the kind of person who would only pick Box B, but must grapple with the fact that at the moment of choice, you'll inevitably take both boxes.

Because if you take both boxes there's no reverse-correlation. It might mean you are the kind of person who would take both boxes, but you haven't damned yourself to less money because you took them in the moment. You were damned from the moment Bob made the prediction. Any chooser should simultaneously want to be the kind of person who would only take Box B, and recognize the impossibility of being that kind of person (because at the moment of choice, you are totally free to take both boxes).

but that assumes things that aren't stated in the puzzle's premises. nowhere is it said that bob's prediction is indirect, based on the kind of person you are, or the kind of person bob takes you to be. it's instead an "almost perfect" estimate of what you will actually do. it therefore can't be circumvented by speculating about the kind of person that bob envisions or the kind of person you actually might be. no matter what you choose or why, no many how much analysis you subject the choice to, bob's prediction remains "almost perfect." and it is therefore almost perfectly certain that box B will be empty if you take both boxes -- no matter what rationale you use to arrive at that choice.

kava's toxin seems similarly non-paradoxical. it's only when one begins to question whether or not one should actually drink the toxin that the attainment of the money comes to be in jeopardy. therefore, the real question is not the wormhole implied by the hidden paradox, it's a straightforward, "should i drink the toxin?" and the answer is a similarly straightforward, "yes, you should." if one puts aside all thought of what one might gain by NOT drinking the toxin and instead simply plans to do it, then one remains assured of gaining the money.

strike

"...no many how much analysis you subject the choice to..."

sub

"...no matter the analysis to which you subject the choice..."

working through the booze here

i mean, i get what you're saying: if you choose to take box B and really mean it, then bob very likely predicted that. okay, so having made that sincere choice, what's to prevent you from changing your mind and taking both boxes, thus somehow "fooling" the supposedly near-infallible bob?

two things:

1) if it's a truly sincere choice, then once made, it cannot be undone. i.e., sincere choice is irrevocable. i say this because any mental decision that IS revocable can be described as a part of the pattern of consideration that might eventually lead to a real and final choice, and that's not what bob seems to be predicting.

2) although reverse causation cannot be assumed, we must still act as though reverse causation is in effect. i say this because we do not understand the actual mechanism that governs bob's predictions. that's what i meant earlier. we only know that the act of taking both boxes seems to drastically reduce the likelihood that box B will contain anything, and given the absence of any other information, we might as well go with what we've been given.

There's certainly a correlation between taking both boxes and Box B not containing anything. Not a causation though. (The causation is that Bob predicted you'd take both boxes, that's why Box B doesn't contain anything. That you took both boxes is incidental.)

OT: 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?

There's certainly a correlation between taking both boxes and Box B not containing anything. Not a causation though. (The causation is that Bob predicted you'd take both boxes, that's why Box B doesn't contain anything. That you took both boxes is incidental.)

yeah, i get that. but as a chooser, you have to assume a quasi-causal relationship between the choice you make (the only part of this situation you can control) and the outcome you hope to receive. you cannot know how bob came to possess this almost perfect understanding, after all. nor can you know what bob has predicted. you only know that whatever choice you ultimately do make, it is very likely to have been correctly anticipated by bob. therefore, by making a choice, and only from your own perceptual standpoint, you more-or-less "cause" the outcome. this has to do with the nature of time. in the scenario described, bob has predicted the future existence of something that did not yet exist at the time of prediction. in other words and regardless of what bob has predicted, prior to your actually making a choice, your choice does not exist. since it asks you (dear reader) to render a decision, this puzzle assumes the existence of free will. therefore, in the act of choosing, you validate (or invalidate) bob's prediction, and your choice IS causal in that sense. the problem is that you cannot possibly know how to invalidate bob's prediction, which makes it prudent to assume that bob has predicted things correctly and to make the choice that will provide maximum benefit under that circumstance.

the problem is that you cannot possibly know how to invalidate bob's prediction, which makes it prudent to assume that bob has predicted things correctly and to make the choice that will provide maximum benefit under that circumstance.

This is my reasoning as well.

The only thing that violates this is the friend who can see into the boxes, and the interesting thing is that if you assume Bob is near-infallible, the odds that you will get $101K after your friend looks at the money goes down dramatically.

contenderizer otm

Automatic thread bump. This poll is closing tomorrow.

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.

Automatic thread bump. This poll's results are now in.