Newcomb's paradox • Hacker News Board

Re: Newcomb's paradox

#11

Post by empthought » Sat, Apr 04, 2015, 2:34 AM UTC

Retric wrote: post #10

empthought wrote: post #7

Earlier quoted context omitted.

It's not about changing your mind for the money, it's about the fact that causality doesn't (shouldn't) run backwards in time. Consider this: when you are faced with the choice, the allotted money is already under the boxes. How could what you choose now affect this outcome? It can't. You must always take both boxes to get the maximum amount of money possible. Either the $1,000,000 is under the single box, or it is n…

Your assuming something along the lines of free will. Remember the choice is made independent of what's in the boxes. So, let's consider a deterministic system. If I write a program that uses pure logic to make the choice and it's non random then it always makes the same choice. EX: hard coding chose (A+B). Then that choice has in effect already made based on the algorithm selection making the (A+B) prediction basica…

But that doesn't matter in the slightest. The money is either there or it is not there. It's not put in the boxes after you've made the choice. It's put into the boxes before you even know there's a game.

Whether or not there is free will or determinism, picking both boxes always nets the most money of what's on the table.

Re: Newcomb's paradox

#12

Post by empthought » Sat, Apr 04, 2015, 2:38 AM UTC

greggyb wrote: post #8

For the risk-averse: Make a bet with someone for $500,000.00 that you can prove The Predictor is fallible. Take only box B. If box B contains $1,000,000.00, then you have lost the bet and you are left with only $500,000.00. If box B contains no money, you have wone the bet and are left with $500,000.00.

Mmm credit default swap.

Re: Newcomb's paradox

#13

Post by altrego99 » Sat, Apr 04, 2015, 2:57 AM UTC

Not sure why it is a paradox - assuming the predictor is superintelligent, you don't try to fool it. By definition its intelligence can predict what you will do in the very last moment, so the fact that it doesn't get to change anything once prediction is made, is immaterial.

Re: Newcomb's paradox

#14

Post by mietek » Sat, Apr 04, 2015, 3:32 AM UTC

> When formulated using Bayesian networks, two standard decision algorithms (Evidential Decision Theory and Causal Decision Theory) can be shown to fail systematically when faced with aspects of the prisoner’s dilemma and so-called “Newcomblike” problems. We describe a new form of decision algorithm, called Timeless Decision Theory, which consistently wins on these problems.

— Alex Altair, MIRI, “A Comparison of Decision Algorithms on Newcomblike Problems”

https://intelligence.org/files/Comparison.pdf

Re: Newcomb's paradox

#15

Post by fiatmoney » Sat, Apr 04, 2015, 3:34 AM UTC

The standard "solution" (that isn't really a solution, but an explanation) is that the predictor has decided to reward the kind of person who one-boxes, and is extremely good at predicting whether you are that kind of person (perhaps even better than you yourself are).

So, if you can "decide to be the kind of person" who one-boxes (and perhaps by induction "decide to be the kind of person who decides to be a certain kind of person"), you can make out pretty well.

Re: Newcomb's paradox

#16

Post by SilasX » Sat, Apr 04, 2015, 3:39 AM UTC

empthought wrote: post #7

fitter wrote: post #3

I guess this boils down to whether you believe in determinism. If you do, then the predictor will always be right, and you have essentially zero chance of fooling it by "changing your mind" later for the extra money. If you don't believe in such a thing, then theoretically some nondeterministic volition of yours could allow you to change your mind in a way that the predictor could not have deterministically forseen.

It's not about changing your mind for the money, it's about the fact that causality doesn't (shouldn't) run backwards in time. Consider this: when you are faced with the choice, the allotted money is already under the boxes. How could what you choose now affect this outcome? It can't. You must always take both boxes to get the maximum amount of money possible. Either the $1,000,000 is under the single box, or it is n…

Under a generalization of this problem, you can do transparent boxes and get basically the same paradox: in that case, omega never even presents you with this choice while putting $1 million in a box unless you're "the type of person" who would one-box even then.

Still no causality violation: omega simulates everyone,[2] and only offers the filled box to one-boxers, but leaves it empty for two-boxers. [1]

But you don't even have to conser these esoteric, hypothetical situations to get a newcomblike paradox: even "merchants vs shoplifters" has a similar dynamic: you will only be in the position of being able to trivially shoplift merchandise if you're in a neighborhood that draws from the set of people who usually don't. Merchants (Omega) are accurate enough in their predictions to be profitable.

[1] See counterfactual mugging for a similar dynamic.

[2] With a thorough enough simulator, it may not be possible to tell whether "you" are in the simulator or doing the real thing.

Re: Newcomb's paradox

#17

Post by breuleux » Sat, Apr 04, 2015, 3:40 AM UTC

empthought wrote: post #7

fitter wrote: post #3

I guess this boils down to whether you believe in determinism. If you do, then the predictor will always be right, and you have essentially zero chance of fooling it by "changing your mind" later for the extra money. If you don't believe in such a thing, then theoretically some nondeterministic volition of yours could allow you to change your mind in a way that the predictor could not have deterministically forseen.

It's not about changing your mind for the money, it's about the fact that causality doesn't (shouldn't) run backwards in time. Consider this: when you are faced with the choice, the allotted money is already under the boxes. How could what you choose now affect this outcome? It can't. You must always take both boxes to get the maximum amount of money possible. Either the $1,000,000 is under the single box, or it is n…

Well, the idea is that in order to predict which box you will pick, the predictor is basically running a perfect simulation of you. Depending on what the simulated version of you does, then the predictor will either put nothing or a million dollars in the second box.

So the problem is this: you are given the choice to pick one or both boxes, but you don't know whether you are playing for real or whether you are a simulation who will unwittingly tell the predictor what the real "you" will do. If your mind is deterministic and the predictor is perfect then you will necessarily choose the same in both simulation and reality. Alas, you need your simulated self to "tell" the predictor to put a million in the box, which is why it is preferable to only pick up that one box. It's not that causality runs backwards, it's that unbeknownst to you, you're actually choosing twice.

Of course, that whole thought experiment is a bit silly. Even under determinism it would be borderline impossible to do this with a physical system, and agents generally have an incentive to be unpredictable when it benefits them, so I don't think it is massively important to decide correctly in such contrived scenarios.

Re: Newcomb's paradox

#18

Post by SilasX » Sat, Apr 04, 2015, 3:48 AM UTC

breuleux wrote: post #17

empthought wrote: post #7

Earlier quoted context omitted.

It's not about changing your mind for the money, it's about the fact that causality doesn't (shouldn't) run backwards in time. Consider this: when you are faced with the choice, the allotted money is already under the boxes. How could what you choose now affect this outcome? It can't. You must always take both boxes to get the maximum amount of money possible. Either the $1,000,000 is under the single box, or it is n…

Well, the idea is that in order to predict which box you will pick, the predictor is basically running a perfect simulation of you. Depending on what the simulated version of you does, then the predictor will either put nothing or a million dollars in the second box. So the problem is this: you are given the choice to pick one or both boxes, but you don't know whether you are playing for real or whether you are a sim…

>Of course, that whole thought experiment is a bit silly. Even under determinism it would be borderline impossible to do this with a physical system,

What about if you played as Omega against against a (physical instantiation of a) computer program that can play this game?

>and agents generally have an incentive to be unpredictable when it benefits them, so I don't think it is massively important to decide correctly in such contrived scenarios.

Under the original version of this problem, Omega stiffs agents who deliberately make themselves unpredictable eg by hooking their action to an unpredictable randomizer. But then, it's not even clear that agents would benefit from reducing Omega's confidence they'll one-box via deliberate unpredictability.

Re: Newcomb's paradox

#19

Post by Strilanc » Sat, Apr 04, 2015, 5:32 AM UTC

empthought wrote: post #11

Retric wrote: post #10

Earlier quoted context omitted.

Your assuming something along the lines of free will. Remember the choice is made independent of what's in the boxes. So, let's consider a deterministic system. If I write a program that uses pure logic to make the choice and it's non random then it always makes the same choice. EX: hard coding chose (A+B). Then that choice has in effect already made based on the algorithm selection making the (A+B) prediction basica…

But that doesn't matter in the slightest. The money is either there or it is not there. It's not put in the boxes after you've made the choice. It's put into the boxes before you even know there's a game. Whether or not there is free will or determinism, picking both boxes always nets the most money of what's on the table.

You're using a mathematical model that doesn't apply. The ahead-of-time simulations invalidate the idea that your decision can't affect the outcome, despite the final decision ultimately occurring afterwards.

An analogy would be asserting that you can't possibly shoot yourself in the back of the head when firing into the distance, and sticking to that position even after finding out you're in a pac-man-style loop-around world.

A much closer but more technical analogy is that you can't solve imperfect information games by recursively solving subtrees in isolation. Optimal play can involve purposefully losing in some subtrees, so that bluffs are more effective in other subtrees.

The fact that you are doing worse by two-boxing, leaving with a thousand dollars instead of a million, despite following logic that's supposed to maximize how well you do, should be a huge red flag.

Re: Newcomb's paradox

#20

Post by cwp » Sat, Apr 04, 2015, 5:43 AM UTC

I always find this kind of philosophical thought experiment unsatisfying.

Super-accurate predictions of human behaviour are just not possible. If I could do it, I'd be a gazillionaire philanthropist/playboy dating supermodels and advising heads of state because I can't be bothered to rule the world directly. As it is, I can't do better than a draw against a 5-year-old at rock-paper-scissors.

So this paradox tells us more about psychology than philosophy. Folks who think "A and B" is the right answer basically ignore the bit about the predictor never (or almost never) being wrong and go with a strategy that is great for fallible human predictors.

And well they should. The only thing more ridiculous than an infallible predictor is one that wastes his time playing shell games where the best he can do is break even.