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Newcomb's paradox

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Re: Newcomb's paradox

#51

Post by SilasX »

baddox wrote: post #50
SilasX wrote: post #43

Earlier quoted context omitted.

But then if people only care about the benefits to them, then they'll be overtaken by "lizards" who exploit them but never get voted out because no one thinks voting passes a CBA. Populations who vote "despite" its wastefulness systematically win against those who don't. Arguably, the only reason any population isn't overrun by lizards is because it's people are mostly "wasteful" in this sense. One intermediate solut…

But I don't think people are wasteful in that sense. Voter participation and voter awareness tends to be low, at least in the USA. Besides, if your government only works if people act in a specific irrational manner, I don't have high hopes for it, especially considering that one usually cited fundamental role of government is to fix problems where individual rationality does not lead to group rationality. Forcing pe…

Voter participation is very high, and voter decisions very wise, relative to the lizard scenario; and it's not clear that "not being overlorded by lizards" is a kind of irrationality.

Remember, the lizard scenario is something like "500 lizards outvote 300 million and put in 99% tax rates on non-lizards, to be spent entirely on lizards, all because none of the 300 million want to vote, reasoning that their vote doesn't affect the outcome."

Mandatory voting would definitely be an improvement over that for much the same reasons I gave before.

Re: Newcomb's paradox

#52

Post by samatman »

connerbrooks wrote: post #26
samatman wrote: post #21

Via Turing, we know that the Predictor would be able to decide programs, and since it can't, it can't be a Predictor. The isomorphism between the program which defeats decidability and the two-box Newcomb problem is left as an exercise.

I think this may be the proof. Start by assuming that the predictor is a decider P for a computational model of a human M in a situation encoded by w. We can then construct a Turing Machine S that decides A_TM. S { 1. Run P on w. 2. If P halts, run M on w; if M accepts, accept, if it rejects reject. } Since S decides A_TM we must have made a mistake somewhere in our proof, our only mistake could be that the predictor…

Full marks!

Re: Newcomb's paradox

#53

Post by samatman »

jcoffland wrote: post #32
samatman wrote: post #21

Via Turing, we know that the Predictor would be able to decide programs, and since it can't, it can't be a Predictor. The isomorphism between the program which defeats decidability and the two-box Newcomb problem is left as an exercise.

You assume that a human cannot be described with something less powerful than a Turing machine. There is no reason to believe that knowing what a human will do in this instance is equal to decidability of computer programs.

I assume nothing of the sort. I merely assume that humans, like computers, are capable of evaluating the truth of something and then deliberately reporting the opposite. That is all that is required.

Re: Newcomb's paradox

#54

Post by empthought »

SilasX wrote: post #16
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…

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…

That generalization is no longer a paradox; it's just a situation. The paradox is about choice theory and you have eliminated any element of choice.

People who choose (or act, if you don't care for free will) to take only one box are always leaving money on the table, full stop. The point of the game is to maximize winnings.

The alternative approach is that people who have chosen one box have always received more money than those who chose both. Explanations about how or why are distractions and are inconsequential; the paradox is about these two -- both generally considered to be valid -- approaches yielding such different results.

In my opinion, the resolution of the paradox is that's an impossible situation. Either someone is lying about the mechanisms (in which case take one box like everyone else because it's a magic trick of some kind) or not (in which case the "predictor" can be wrong and the boxes are already set, so take both boxes to eliminate the risk of receiving nothing and to maximize your winnings).

Re: Newcomb's paradox

#55

Post by Retric »

empthought wrote: post #36
Strilanc wrote: post #19

Earlier quoted context omitted.

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-aro…

How do "the ahead-of-time simulations invalidate the idea that your decision can't affect the outcome, despite the final decision ultimately occurring afterwards?" They're only simulations. The predictor is defined as being very likely to have correct predictions; it's not defined as God or a time traveler or an omniscient computer with knowledge of the universe's intricate workings. The fact that to an observer who…

But that's the thing you assume there something different about you and simulated you where in theory there might not be.

In other words if your hard coding something then hard coding pick B gets you 1,000,000 but hard coding pick AB gets you 1,000 assuming the predictor looks at your source code.

As to the game show you would gave a series of people where people who pick B get 1,000,000 and people who pick AB get 1,000 now which group looks like idiots?

Edit: Depending on the accuracy of the predictions, it's less about information traveling into the past as it is being the type of person that chooses B.

Re: Newcomb's paradox

#56

Post by empthought »

greggyb wrote: post #49
empthought wrote: post #37

Earlier quoted context omitted.

It's not a rule of the game that the predictor is infallible, only that it's very likely to be correct.

It seems there are multiple versions of the paradox. It does seem reasonable that you can find someone to take the bet for <$999K if it is known that The Predictor is "very likely to be correct". Any bet amount <$999K is qualitatively the same as my original $500K suggestion, you increase your guaranteed minimum by decreasing your potential maximum without having to resolve the paradox.

I think any version of the paradox that defines the predictor as infallible misses the whole point of the paradox. That's just defining the outcome of the game as the will of God. "Has always been observed to be correct" is the appropriate construction.

However, I think someone could resuscitate the original intent of the paradox by having the Predictor's actions also hinge on whether or not it predicts that you would make such a bet, and leave box B empty if it does predict that. Essentially defining itself to be correct in the situation where, without this addendum, it would have been incorrect and you would have won the bet.

Re: Newcomb's paradox

#57

Post by greggyb »

empthought wrote: post #56
greggyb wrote: post #49

Earlier quoted context omitted.

It seems there are multiple versions of the paradox. It does seem reasonable that you can find someone to take the bet for <$999K if it is known that The Predictor is "very likely to be correct". Any bet amount <$999K is qualitatively the same as my original $500K suggestion, you increase your guaranteed minimum by decreasing your potential maximum without having to resolve the paradox.

I think any version of the paradox that defines the predictor as infallible misses the whole point of the paradox. That's just defining the outcome of the game as the will of God. "Has always been observed to be correct" is the appropriate construction. However, I think someone could resuscitate the original intent of the paradox by having the Predictor's actions also hinge on whether or not it predicts that you woul…

I mean, now you're just creating a moving target.

I think you are intent upon maintaining the paradox, whereas I was just pointing out a loophole that allows a better outcome without resolving it. Gordian knot and all.

Re: Newcomb's paradox

#58

Post by SilasX »

empthought wrote: post #54
SilasX wrote: post #16

Earlier quoted context omitted.

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…

That generalization is no longer a paradox; it's just a situation. The paradox is about choice theory and you have eliminated any element of choice. People who choose (or act, if you don't care for free will) to take only one box are always leaving money on the table , full stop. The point of the game is to maximize winnings. The alternative approach is that people who have chosen one box have always received more mo…

>That generalization is no longer a paradox; it's just a situation. The paradox is about choice theory and you have eliminated any element of choice.

You're still choosing whether to use a decision procedure that results in how many boxes to take when offered this choice, which then determines whether you get this offer at all.

And I don't know what you're trying to say with the paradox/situation distinction; "Newcomb's problem with transparent boxes" is a paradox and a situation, just like the original: how are people ending up better off by "leaving money on the table"? (whatever that would mean)

>People who choose (or act, if you don't care for free will) to take only one box are always leaving money on the table, full stop. The point of the game is to maximize winnings.

But once you pin down what "leaving money on the table" means, it's not at all clear that the concept coincides with something you want to avoid. If the people "leaving money on the table" have more money, then "I don't want to be right", as the saying goes.

>In my opinion, the resolution of the paradox is that's an impossible situation.

I disagree. At the very least, you can play as omega against an algorithm, with varying degrees of scrutability. How should that kind of algorithm be written so that it gets more money (in transparent boxes, how to get omegas to offer you filled boxes in the first place)? Your answer would require addressing the same issues that arise here for humans in that situation.

There are also statistical versions of the paradox, like merchants vs shoplifters. Obviously, they aren't perfect predictors, but they do well enough for the sort of "acausal" effects in the paradox to happen, ie people not shoplifting, even when they could get away with it. Here are some more real life examples:

http://lesswrong.com/lw/4yn/realworld_newcomblike_problems/

To be sure, people aren't predictable enough now to get the kind of scenario described in the problem. But they are predictable enough for the uncomfortable implications: even an accuracy slightly better than chance gets you situations were one-boxing is statistically superior.

(I do agree that in pracitce, whenever you see this kind of situation, you should assume there's some trick until overwhelming evidence comes in to the contrary.)

Re: Newcomb's paradox

#59

Post by empthought »

SilasX wrote: post #58
empthought wrote: post #54

Earlier quoted context omitted.

That generalization is no longer a paradox; it's just a situation. The paradox is about choice theory and you have eliminated any element of choice. People who choose (or act, if you don't care for free will) to take only one box are always leaving money on the table , full stop. The point of the game is to maximize winnings. The alternative approach is that people who have chosen one box have always received more mo…

>That generalization is no longer a paradox; it's just a situation. The paradox is about choice theory and you have eliminated any element of choice. You're still choosing whether to use a decision procedure that results in how many boxes to take when offered this choice, which then determines whether you get this offer at all. And I don't know what you're trying to say with the paradox/situation distinction; "Newcom…

> But once you pin down what "leaving money on the table" means, it's not at all clear that the concept coincides with something you want to avoid.

In this case (which I have to imagine is deliberate on the part of Nozick or Newcomb), "leaving money on the table" means literally leaving money on the table. Taking one box always, always results in less money than the total amount of money available in the boxes to people who take both boxes. (Of course, the evidence to date is that people who choose both boxes always have less money available to them in the first place.)

But the equally justifiable decision-making method is to perform the action that has yielded the best observed results in the past for others, despite there being no way that one's actions now can possibly have affected the past (choice or determinism doesn't matter).

The nature-of-the-predictor stuff is just irrelevant nonsense in either approach to the problem, which is a happy coincidence because it is, in fact, irrelevant and impossible nonsense. :)

Edit: "there's no way that one's actions now can possibly have affected the past" is given in the original problem. Wikipedia's article quotes it as "what you actually decide to do is not part of the explanation of why he made the prediction he made."

Re: Newcomb's paradox

#60

Post by empthought »

Retric wrote: post #55
empthought wrote: post #36

Earlier quoted context omitted.

How do "the ahead-of-time simulations invalidate the idea that your decision can't affect the outcome, despite the final decision ultimately occurring afterwards?" They're only simulations. The predictor is defined as being very likely to have correct predictions; it's not defined as God or a time traveler or an omniscient computer with knowledge of the universe's intricate workings. The fact that to an observer who…

But that's the thing you assume there something different about you and simulated you where in theory there might not be. In other words if your hard coding something then hard coding pick B gets you 1,000,000 but hard coding pick AB gets you 1,000 assuming the predictor looks at your source code. As to the game show you would gave a series of people where people who pick B get 1,000,000 and people who pick AB get 1,…

I don't know why you're talking about hard-coding and simulation and whatnot. The mechanism that the predictor uses is completely irrelevant and specifically defined to be unknown in the thought experiment description, aside from it disallowing backwards causality and things like time travel.

Every single person who picked only box B left $1000 on the table. That's a bare fact. You don't even need to know or care what the prediction is to know that.

In general when someone leaves $1000 that they could have had, no strings attached, that's a less desirable outcome than the one where they had the extra $1000.

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