The Newcomb Problem

I still can't see what here is called "paradox".
Here is an alternative formulation, that doesn't involve seeing the future.
You are offered to play one of two games:
Game A:
You pay $1000, and get a 90% chance to win a million dollars.
Game B:
You don't have to pay anything, and still have a 10% chance to win a million.

There is also a third possibility (equivalent to only being able to pick a single box B, not both boxes): you don't pay anything, and don't get any shot at a million bucks.

I don't see anything paradoxical in any of this.

weaselman, I think the really big difference between the choices in your alternative formulation and in the original problem is that you suggest the player has complete control over whether there is a 90% or 10% chance of getting the big money. In the original problem, the substantive event was the being's actual prediction, which is not something that the player can choose -- the player only chooses between one box or both after the being has made the prediction and secretly stocked the box(es) with money.

The summary is that, in the original problem, the being makes the $1,000,000 decision while the player makes the $1,000 decision -- possibly affecting the being's prediction, but only if you accept the notion that better-than-normal predictive ability means that changes in choices of present actions can change the predictions that were made about them in the past. I prefer to think instead that changes in the present only affect whether past predictions were correct or incorrect, rather than changing what prediction was made.

How do you figure the player doesn't have any control over the prediction? The being isn't just making up its predictions - to be 90% accurate, they have to be based on the actual player's actions. The only thing "fishy" about this is that the prediction has already happened before the player makes his choice, so it can't be affected by it, but that's usual with time travel and seeing the future, once you assume those things are possible, you have to also affect that future events can affect the past. If that's what you mean by "paradox", I agree, that there is a contradiction with the causality principle here, but causality principle is not mentioned in the conditions of the problem, so the problem itself as formulated is self-consistent, and does not contain any paradoxes.

Quote: weaselman

... The only thing "fishy" about this is that the prediction has already happened before the player makes his choice, so it can't be affected by it, but that's usual with time travel and seeing the future, once you assume those things are possible, you have to also affect that future events can affect the past. ...

That, indeed, is the part that I have not accepted, other than that for this problem I have allowed the idea of the being seeing a blurry image of the future from which he makes a prediction that may or may not be correct, but which is unusually accurate. I do not accept, as a part of reality to be used in analyzing my choices, the notion of my decision/action changing the past.

I don't think I used the word "paradox" myself, and I didn't mean for my previous post to be a claim or explanation that there is or is not a paradox. Sorry about not being clear on that.

What I do consider a bit of a quirk, is that while I think that logic (based on belief in the future not being able to change the past) would lead one to choose both boxes (getting an extra $1k no matter what the being had predicted in the past), exhibiting that kind of sound logic should tend to influence the being's opinion of the player, so that the being would be less likely to add the big bucks to box A. This means that exhibiting the ability for solid logic leads one to a less-desirable outcome, while consistently-illogical behavior likely brings fortuitous outcomes due to the decisions of another (the being). To be clever enough to "win" the maximum theoretically possible, a player whose thinking actually embodies logic must act in a way to deceive the 90%-accurate being about what the player will choose in the future -- be smart but very-effectively play dumb. Is that convoluted enough to qualify as a quirk, if not a paradox?

Quote:

What I do consider a bit of a quirk, is that while I think that logic (based on belief in the future not being able to change the past) would lead one to choose both boxes (getting an extra $1k no matter what the being had predicted in the past), exhibiting that kind of sound logic should tend to influence the being's opinion of the player

This begs the question.
If the "logic based on belief in the future not being able to change the past" is correct, than there cannot be any being making predictions about the future, and the whole problem is nonsense. If (for the purposes of this particular problem) we assume that it is possible for future evens to influence past at least to an extent (btw, contemporary quantum physics kinda agrees with such a possibility), then you can't apply the above logic to this particular problem, because it is not compatible with the core assumption.

And I also don't think you can be "clever enough to deceive ...", at least, not if predicting the future works the way I imagine - it is not a kind of psychological analysis of the player's past actions (that could be used to deceive), but a direct insight into the actual future event. The Newcomb being sees the actual choice you are going to make, not just comes up with an intelligent guess, based on interviewing you or something like that.

BTW. If our poll results can be extrapolated on the entire population of players, the Newcomb being doesn't need to be clairvoyant. It could just always predict that the player will pick box A, and be right 60% of time. It doesn't change the problem qualitatively (the accuracy is less than 90%, but box A is still a logically/mathematically optimal choice), but takes away the weirdness of influencing the past events.
Or, to make things more interesting, it could flip a coin, and achieve 50% accuracy.
Note, that this doesn't change the original problem at all (except for the actual numerical value, that doesn't matter) - I just checked, and it only says that you believe that Newcomb being has supernatural powers, not that it actually does have them, and, even if it did, there is no mention of a specific power to foresee the future. The being's predictions could therefore be based on some poll results or a large set of data from past experiments.

What I am saying is, I think, in the context of this problem it does not (should not) matter how the prediction is made, just what the accuracy of it is. As long as it is greater than 0.1%, picking box A is mathematically optimal strategy.

I would pick both.

Reading the formulas and thoughts previously posted resulted in my own thought process, which wavered from a reasonable understanding to an indiscernible static of numbers and concepts I couldn't digest. As a result, I came to this conclusion.

Picking only one box gives a pretty good, maybe even great chance of striking it big. However, 'great' isn't 'absolute'. A 90% chance of success still yields a 10% chance of failure. And although that is/was his current record, you couldn't assume it would remain his record. .300 hitters sometimes go o-for. Coin flips that are 50-50 sometime yield the same result 5-6-10 times in a row. Also, since you can't know what criteria the Newcomb Being uses for predictions, you couldn't assume it would pick one box over another and thus you could have no advantage.

Picking both boxes guarantee's you $1,000. I like $1,000. If there were 20 of us partaking in this little game, I might have $1,000 and have to watch 19 other jump up and down with $1,000,000. That would not change the fact that I still have $1,000 I didn't previously have. It could also be possible to have my $1,000 and watch 19 others pout around with $0. But regardless of others joy or misery, I would have $1,000, no matter what. And as previously stated, I like $1,000.

Basically, when faced with possibilities and probabilities I can't understand, I revert to being as simple as possible. The single box - chance of happy with chance of regret vs. Both boxes - guaranteed happy.

As Grandpappy always said, one in the hand is worth two in the bush.

Quote: Face

I would pick both.
.

Hey Face, great screen name. I've been on forums for 19 years and have never seen it. I'm stealing it ASAP.

Quote: EvenBob

Hey Face, great screen name. I've been on forums for 19 years and have never seen it. I'm stealing it ASAP.

Thanks, EvenBob. The creator always enjoys compliments to the creation, be it of painting, classical score, or the changing of an oft used common noun to proper though use of capitalization. You have my unneeded permission to use it in any way you see fit. Unless you really wanted to STEAL it, in which case I rescind my entirely required permission and have already notified the proper authorities. ;)

Quote: Face

Unless you really wanted to STEAL it, in which case I rescind my entirely required permission and have already notified the proper authorities. ;)

Oops, too late. Sue me..

There have been a lot of posts lately about time travel and clairvoyance. I said this many posts back that we don't need to assume either for this problem. The original question said that Newcomb has "superior predictive powers." It could be that Newcomb is just good at reading people, like Mike Caro is good at reading players at the poker table. In this case, I still say that picking both is the correct answer.

Sorry for repeating myself.

Quote: Wizard

There have been a lot of posts lately about time travel and clairvoyance. I said this many posts back that we don't need to assume either for this problem. The original question said that Newcomb has "superior predictive powers." It could be that Newcomb is just good at reading people, like Mike Caro is good at reading players at the poker table. In this case, I still say that picking both is the correct answer.

Sorry for repeating myself.

The underlying point is that it doesn't state how the Newcomb achieves "superior predictive powers' - we are reading this 'normally' by assuming that the Newcomb is using current trends etc to provide a prediction. This, in my opinion, is where the differences in opinions arise - the premise is not totally clear in that it can always be read the same way.

Taking this further, why not allow the player to flip a coin ? You can add that the Newcomb can still predict with 90% accuracy and not change the dynamics (except that we 'may' think that the Newcomb is time traveling to some degree). If the premise states that the Newcomb can predict with 90% accuracy then there is no reason to forbid anything a player can do unless you are underlining the fact that the Newcomb uses some unknown power (which, of course, he may do to foresee a flip of the coin if we extend the premise).

So, it's the wording of the question itself that causes some people to interpret a viewpoint different to others.

Again, taking things further (by starting with a false premise) - imagine that the Newcomb can divide by 0 by using some unknown, superior mathematics (that we have to assume). So, 1 x 0 = 2 x 0 and dividing both sides by 0 we get 1 = 2. Using this premise can now lead us to all sorts of paradoxical situations BUT some people will not accept the premise at face value.

If the question had been worded:-

You have 10 balls of which 9 are marked with 'A' and 1 is marked with 'A/B'. You pick either Box A or Boxes A + B then you draw a ball out. If the ball matches your selection then you win ...etc...etc...etc. So, by picking A + B you will be guaranteed $1,000 regardless of which ball you draw HOWEVER just picking Box A will give you a greater chance of winning $1,000,000.

The above premise is far more easily understood and accepted by people and will result in Box A as the choice. The only reason that the Newcomb problem gives diverse results is that people do not accept the premise (and the not allowing of the coin flip enforces something that does not exist i.e. it could easily have stated that the Newcomb still retains 90% without affecting the problem).

I'm off to find Box C to see what that's got in it :-) :-) :-)

Quote: Wizard

In this case, I still say that picking both is the correct answer.

"Correct" in what sense? Obviously, it has a lower EV ... Are you suggesting some kind of a utility function, or a different criteria of correctness altogether?

Quote: weaselman

"Correct" in what sense? Obviously, it has a lower EV ...

It only has "lower EV" if you calculate that EV using an assumption that your choice NOW has the potential to determine what the being predicted in the past. The Wizard and I have both rejected that notion.

(I personally find it to be a favorable position to be in agreement with the Wizard on such matters.)

And yes, I stated before that consistently exhibiting logical analysis in the past could impact the being's opinion of you and encourage a prediction/action that would mean less money being placed in box A. Is that what you mean by "lower EV"? But we are talking about a choice made NOW, not a pattern of behavior in the past. And I think you rejected the idea that the being was basing the prediction on my past behavior, so I have no idea how you come up with an EV.

Yes, Wizard, I too am repeating myself.

Quote: Doc

It only has "lower EV" if you calculate that EV using an assumption that your choice NOW has the potential to determine what the being predicted in the past. The Wizard and I have both rejected that notion.

But, like I said earlier, I don't think that notion has anything to do with the methodology of determining the EV.

If you are placing a roulette bet after the dealer has released the ball, the outcome is already fixed, but as far as you are concerned, your odds are 1/38th. Consider a roulette wheel, with no zeroes, paying 36 (not 35) units for a win.
You can expect your $100 bet to win $2.77, but by your logic, you would only make that bet before the ball is released, because after the outcome is set you somehow reason that it is better to settle for the "sure thing" and just keep your $100. That doesn't really make sense to you, does it?

Same thing happens here. Yes, you are making your choice after the outcome has been determined, but that has no effect on your EV. You still have a 90% to find a million bucks in box A.

Quote: weaselman

"Correct" in what sense? Obviously, it has a lower EV ... Are you suggesting some kind of a utility function, or a different criteria of correctness altogether?

I say both is the right answer because A+1000>A. Now some others might say that the A in A+1000 in different than the A by itself. However, my interpretation is that Newcomb is NOT clairvoyant, just a good reader of tells.

I think most of us would agree that the correct answer has to do with HOW Newcomb is able to have "superior predictive powers." Let me run this up the flagpole to see if anyone salutes. If we assume that Newcomb is psychic/clairvoyant then picking A only is the right answer. If Newcomb is just a very good reader of people, by picking up on their tells, then both A and B is the right answer.

Quote:

Now some others might say that the A in A+1000 in different than the A by itself.

Exactly.

Quote: Wizard

I think most of us would agree that the correct answer has to do with HOW Newcomb is able to have "superior predictive powers."

He could for example, base his decision on our poll, and always stuff box A, to be correct 60% of time.
Or he could flip a coin, and be right 50% of time.
Or he could only predict that you'll choose box A once out of every 100 trials (and only be right 40% of the time) ...

In each of these scenarios, you'd be better off choosing box A.

Quote:

If Newcomb is just a very good reader of people, by picking up on their tells, then both A and B is the right answer.

As long as he predicts A more often then 0.11..% of time, provided that he really is right 90% of time, it is better in terms of EV to pick A. I think, it is reasonable to assume the first part of the above condition to be true provided that the second one is true (because whatever the real proportion is, there's gotta be more than 0.11% of people who believes in choosing A).
And I don't think the exact method he uses to come up with his predictions is any more relevant here than the exact principle of a shuffling machine mechanism is relevant to determining a BJ strategy.

Quote: weaselman

As long as he predicts A more often then 0.11..% of time, provided that he really is right 90% of time, it is better in terms of EV to pick A. I think, it is reasonable to assume the first part of the above condition to be true provided that the second one is true (because whatever the real proportion is, there's gotta be more than 0.11% of people who believes in choosing A).
And I don't think the exact method he uses to come up with his predictions is any more relevant here than the exact principle of a shuffling machine mechanism is relevant to determining a BJ strategy.

The question says that Newcomb's accuracy rate is 90%. I assume that to mean that he is 90% right for both A pickers and both pickers.

If Newcomb were psychic then I would say picking A only would be the obvious correct answer. Newcomb would have seen you pick A, and thus put the million in box A with 90% probability. I know it sounds ridiculous that picking box A would cause something to happen in the past, but it is a logical conclusion to an illogical premise. So I stand by what I wrote in my last post.

I'm going to try to reply to multiple posts here. Hope I don't mess up the formatting. ;-)

Quote: Wizard

.... If we assume that Newcomb is psychic/clairvoyant then picking A only is the right answer. ...

I'm not really certain of the meaning of "clairvoyant". Does that mean seeing the future clearly? If so, why would the predictions only be 90% correct? Earlier, I stated, "... I have allowed the idea of the being seeing a blurry image of the future from which he makes a prediction that may or may not be correct..." Would that be a clairvoyant? I still reject the idea that my changing my mind and my choice when the time came could change the being's earlier prediction and actions.

Quote: weaselman

He could for example, base his decision on our poll, and always stuff box A, to be correct 60% of time. ...

In each of these scenarios, you'd be better off choosing box A.

I didn't follow that -- if he were always to stuff box A, why wouldn't I be $1k better off by choosing both boxes?

I guess, weaselman, our differing view of this problem may come down to this question: When I am actually faced with making the choice, (a) do I really have free choice of whether to take one or both, and (b) does the choice I make at that time potentially change how much money is actually in box A? What is your opinion on those two items?

Quote: Doc

I guess, weaselman, our differing view of this problem may come down to this question: When I am actually faced with making the choice, (a) do I really have free choice of whether to take one or both, and (b) does the choice I make at that time potentially change how much money is actually in box A? What is your opinion on those two items?

(a) Yes, but free choice (or free will) isn't at issue here. The issue is whether your choice can be foretold by others. There'd be no paradox if the NB acted *after* you made your choice -- he'd say "look, if you pick just box A, I'm going to scoop up this big pile of money and put it in box A just before you open it. If you pick both boxes, I'm not." And then you'd pick box A only, because you like money.

(b) Not exactly - it changes the potential money in box A. I've said this a few ways before, but I look at it like this: if you believe the premise that the NB can determine what your choice will be and act accordingly, it's a no-brainer to just pick box A. I don't look at it like you:

Quote: Doc

I still reject the idea that my changing my mind and my choice when the time came could change the being's earlier prediction and actions.

See, I think that's exactly the point of departure. That is the *premise* of the problem. If you can accept the premise, to me the answer is easy. But accepting the premise is difficult (edit: see the Wizard's earlier post, where he says he could accept it if the NB were psychic, but maybe not otherwise). But I accept that going through all of the mind-changing that you'd do at the point of decision is part of the NB's earlier prediction, and that he's right 90% of the time *regardless of how*. In other words, he's going to take all of your thought processes into account and decide accordingly, even if you'd think "hey, my decision now can't affect what the NB did yesterday, so I'm picking both boxes". In that case, the NB knows that and you get $1000.

Quote: MathExtremist

...(b) Not exactly - it changes the potential money in box A. I've said this a few ways before, but I look at it like this: if you believe the premise that the NB can determine what your choice will be and act accordingly, it's a no-brainer to just pick box A. I don't look at it like you:

Quote: Doc

I still reject the idea that my changing my mind and my choice when the time came could change the being's earlier prediction and actions.

See, I think that's exactly the point of departure. That is the *premise* of the problem. If you can accept the premise, to me the answer is easy. But accepting the premise is difficult ....

First, perhaps I don't understand "potential money" -- to me, real money is either in box A or it isn't.

Second, I don't read it as being the "premise" of the problem that my later actions can change the earlier predictions. I consider the premise as being that the being is very good at predicting the future, though not so good that I would claim that he actually sees the future event and knows what will occur.

I pick A, and I'd like any Newcomb being reading this to know I will always pick box A in this situation if it ever arises.

By stating you'd pick A+B, it's clear that any being that can read tells and behaviour will know this, and not put any money in Box A for the A+B-ers. Thus you'll get the $1000, and A is empty. The more you argue A+B, the more it's clear that picking A+B is your best bet. The more you argue A-only, the more it's clear pikcing A-only is your best bet... the being is likely to be correct, so you'll get what you expect.

Quote: Doc

I didn't follow that -- if he were always to stuff box A, why wouldn't I be $1k better off by choosing both boxes?

I messed up. If he always picks A, then yes, it is better for the player to pick both.
But if he favors the "both" decision more often than once in a thousand trials, then you are better off choosing A.

Quote:

I guess, weaselman, our differing view of this problem may come down to this question: When I am actually faced with making the choice, (a) do I really have free choice of whether to take one or both,

Yes, I think, it is clear from the problem statement that you do.

Quote:

and (b) does the choice I make at that time potentially change how much money is actually in box A? What is your opinion on those two items?

My whole point is that I don't think it matters.

If the being really has supernatural powers, the problem is equivalent to the one I formulated earlier - you either play for free for a 10% chance of winning, or pay $1000 to increase your chances to 90%.

If it doesn't, you can, for instance, hope to fool it into believing that you are picking A, when your real intent is to choose both, but still you have only 10% chance of succeeding.

Either way, if you pick A, your chance of becoming a millionaire is 90%, and if you also take B, the chance drops to 10%.

I suppose we have all reached the point that we have opinions, while none of us has an argument/explanation that convinces the others. Even so, I thought I would express my thoughts on probability and random events related to this problem, just to see whether this (or rebuttal comments) helps any of us see a different viewpoint. Sorry that I couldn't figure out a more concise way to express these thoughts.

I associate probabilities with random events. For example, there is perhaps some probability that I will make a typographical error (or several) in this post, because such errors seem to occur randomly. In contrast, I do not think it is appropriate to talk about the probability that I will clap my hands twice before typing the next sentence, because that would be a deliberate decision and not a random event.

For the problem under discussion, I am willing to allow the notion of a sophisticated being that has a track record of 90% accuracy in prior predictions about the future, though we are not sure just how. Lacking further information, I think it is acceptable to use this 90% figure as an estimate of the average accuracy of all of the being’s predictions to come, though it is not meaningful to talk about being 90% accurate in any one particular prediction.

I interpret this to mean that given that the being has made a prediction about the future, there is a 90% probability that he will be correct: I treat the outcome of the prediction (right or wrong) as a random event with a probability estimated based on past experience.

I do not consider the money-placing decision by the being to be a random event. We do not know the being’s methods, but we do know that he makes a specific choice/decision.

I do not consider my choice of box or boxes to be a random event, even though you, your friends, the being itself, and even I don’t really know for certain in advance what I will do. That doesn’t make it a random event. It is a deliberate, perhaps-reasoned, perhaps-illogical choice I am free to make when the time comes.

You could perhaps anticipate with 90% accuracy that the being would be correct in his prediction. However, since my choice of box(es) is not a random event, I do not think it is proper to say that there is a 90% probability of what I will do, even if you somehow know the being’s prediction. The random event is whether the prediction is correct or not, not which choice I actually make.

Similarly, I do not think that it is reasonable to say that, given at the last minute I make my specific final decision, there is a 90% probability of a specific amount of money being in box A. The money in box A was a deliberate decision by the being, not a random event with a probability.

I think that the attempts to rationalize a decision based on a calculated expected value have all included somewhere along the line an assumption of a probability for actions that are not random events. I think this leads to failure to use EV calculations properly and decisions that are not optimal, given conditions that exist at the time the decisions are to be made.

I draw an equivalence between the NB predicting your choice, whatever it is, with 90% accuracy and the NB predicting your eye color, whatever it is, with 90% accuracy. In other words, the NB is right 90% of the time, regardless of whether the prediction is based on something you're actively free to change (your mind) or not (your eye color).

So suppose the NB guesses your eye color as brown/not-brown. It's right 90% of the time.

NB's guess	Actual eye color	Reward
Brown	Brown	$1,000,000
Brown	Not brown	$1,001,000
Not brown	Brown	$0
Not brown	Not brown	$1000

Given this, and factoring in the 90% prediction rate, would you rather be brown-eyed or not?

Quote: Wizard

There have been a lot of posts lately about time travel and clairvoyance. I said this many posts back that we don't need to assume either for this problem. The original question said that Newcomb has "superior predictive powers." It could be that Newcomb is just good at reading people, like Mike Caro is good at reading players at the poker table. In this case, I still say that picking both is the correct answer.

Sorry for repeating myself.

If that's the case, then picking A only is +EV as long as his predictive powers are >50%.

Quote: MathExtremist

I draw an equivalence between the NB predicting your choice, whatever it is, with 90% accuracy and the NB predicting your eye color, whatever it is, with 90% accuracy. In other words, the NB is right 90% of the time, regardless of whether the prediction is based on something you're actively free to change (your mind) or not (your eye color).

So suppose the NB guesses your eye color as brown/not-brown. It's right 90% of the time.

NB's guess	Actual eye color	Reward
Brown	Brown	$1,000,000
Brown	Not brown	$1,001,000
Not brown	Brown	$0
Not brown	Not brown	$1000

Given this, and factoring in the 90% prediction rate, would you rather be brown-eyed or not?

Part (a), the smart-ass answer:
Given that scenario, I'd rather be blue-eyed with the NB guessing that I am brown-eyed. Of course, I don't get to choose either of those, so my preferences for one are just as irrelevant at the other. It's all up to the NB and nature, not me.

Part (b), regaining my composure:
Does anything of this table have to do with computing expected value? The point of my previous post was that I felt people were improperly trying to calculate an expected value by using "probabilities" of non-random events.

Or were you suggesting that there is a probability that I will choose to change my eye color?

Quote: Doc

Part (a), the smart-ass answer:
Given that scenario, I'd rather be blue-eyed with the NB guessing that I am brown-eyed. Of course, I don't get to choose either of those, so my preferences for one are just as irrelevant at the other. It's all up to the NB and nature, not me.

But that wasn't the question. What the NB guesses is up to the NB. In this scenario, would you rather have been born with brown eyes or not?

Quote:

Does anything of this table have to do with computing expected value? The point of my previous post was that I felt people were improperly trying to calculate an expected value by using "probabilities" of non-random events.

I can non-randomly "flip" a coin by picking it up, examining it, and choosing to place it down either on heads or tails. If I tell you that in the past, I have chosen heads roughly 50% of the time, do you perceive a meaningful difference between a random coin-flip and my non-random process?

And, from my prior post, do you agree with the equivalence I drew between the NB's prediction rate based on a changeable trait vs. a non-changeable one?

Quote: MathExtremist

I can non-randomly "flip" a coin by picking it up, examining it, and choosing to place it down either on heads or tails. If I tell you that in the past, I have chosen heads roughly 50% of the time, do you perceive a meaningful difference between a random coin-flip and my non-random process?

Yes, indeed, I perceive a substantial difference. In one case there is a random event with a 50% probability. In the other, you can have any result you want on any particular decision. Even if you continue to choose heads 50% of the time on average, it is not a random event, and I would not consider the 50% figure to be a probability -- it is an occurrence of your choosing that you tend to chose one way 50% of the time, with the heads/tails times being when you want them. Would you ever wager on a coin flip if the other person got to choose the result? Even if you kept your guess secret from the other person, it could quite possibly become a game of strategy (rock, paper, scissors, or maybe something more complex) rather than random chance.

Quote: MathExtremist

And, from my prior post, do you agree with the equivalence I drew between the NB's prediction rate based on a changeable trait vs. a non-changeable one?

No, I don't think so. In one case, the result of the future "event" is set when the prediction is made, even before then. It is less a prediction than a (perhaps very good) guess about a fact. In the other case, there is an event which will have one value or another in the future, but that value is not determined until I explicitly choose it later. Neither of those cases involve a random event for which I feel expected values should be calculated.

Quote: mkl654321

If that's the case, then picking A only is +EV as long as his predictive powers are >50%.

So you're saying that even if we know that Newcomb has no psychic powers that A only is still the right answer? Can you explain to me how choosing A only now causes him to put the million dollars in the box 24 hours ago? Do you realize what you are advocating?

Quote: Wizard

So you're saying that even if we know that Newcomb has no psychic powers that A only is still the right answer? Can you explain to me how choosing A only now causes him to put the million dollars in the box 24 hours ago? Do you realize what you are advocating?

No big deal. Denying that he has psychic powers simply means that his predictive methodology, whatever it may be, is based on some real-world phenomenon of which he is perceptive to some degree (50.001%+). I don't need to know exactly what that mechanism is---only that it does work.

Given his 90% (let's say) success rate in predicting what I would do, I have a 9-1 chance in my favor that if I pick Box A only, that is what he predicted I would do, so I will get $Big. It isn't necessary to flip back and forth between past and future; in other words, no paradox exists, so none need be constructed. If we accept the premise as given (fully realizing that premise's real-life implausibility), then the decision is trivial.

Quote: mkl654321

...If we accept the premise as given (fully realizing that premise's real-life implausibility), then the decision is trivial.

There just might actually be agreement on this statement. The problem remains that people disagree on which direction the "trivial" decision should go.

Quote: mkl654321

I don't need to know exactly what that mechanism is---only that it does work.

Big disagreement from me. I just can't accept that an action now could change the past, unless we assume supernatural powers to begin with. I don't think I have anything further to add on this topic.

Quote: Wizard

Big disagreement from me. I just can't accept that an action now could change the past, unless we assume supernatural powers to begin with. I don't think I have anything further to add on this topic.

I think that what you're missing is that the action doesn't have to change the past; it merely has to VALIDATE it (i.e., the prediction). The timeline disconnect is that we can't change the success rate of the predictor no matter which option we choose--which would not, of course, be the case in the real world.

Quote: mkl654321

I think that what you're missing is that the action doesn't have to change the past; it merely has to VALIDATE it (i.e., the prediction). The timeline disconnect is that we can't change the success rate of the predictor no matter which option we choose--which would not, of course, be the case in the real world.

This has already been discussed before. Unless the being has already made an infinite number of predictions, which doesn't seem a reasonable assumption to me, then no matter what we do and no matter whether we do as predicted or not we change his prediction success rate. It goes higher each time a prediction is correct and drops each time a prediction is in error. That's why many pages back most (some?) of us seemed to agree to accept the idea that the prediction accuracy rate is approximately 90% but continues to fluctuate, though we allow that we expect it to continue to average about 90% into the future. This is why I have worded it that it is not meaningful to claim 90% accuracy on a single yes/no prediction.

I still go with the Wizard on this one. Or maybe he's still with me, can't remember who posted our choice first.

Quote: Wizard

Now you have grounds to believe that in such matters, the Newcomb Being has a success rate on predictions of about 90%.
Do you choose box A only, or both? .

Try it with:

The Newcomb Being has a success rate on predictions of 99%. Do you choose box A only, or both?

The Newcomb Being has a success rate on predictions of 1%. Do you choose box A only, or both?

Does this help?

Quote: MrCasinoGames

Quote: Wizard

Now you have grounds to believe that in such matters, the Newcomb Being has a success rate on predictions of about 90%.
Do you choose box A only, or both? .

Try it with:

The Newcomb Being has a success rate on predictions of 99%. Do you choose box A only, or both?

The Newcomb Being has a success rate on predictions of 1%. Do you choose box A only, or both?

Does this help?

Does it help? Well, it at least keeps my answer the same. So long as the being makes his prediction/decision in advance and has already placed the money in the boxes, I'll take both boxes and come out $1,000 better off than I would have by only taking box A. It might not be as much money as I would perhaps fantasize, but it's an extra $1,000 compared to the alternative actually available to me.

Quote: MrCasinoGames

Quote: Wizard

Now you have grounds to believe that in such matters, the Newcomb Being has a success rate on predictions of about 90%.
Do you choose box A only, or both? .

Try it with:

The Newcomb Being has a success rate on predictions of 99%. Do you choose box A only, or both?

The Newcomb Being has a success rate on predictions of 1%. Do you choose box A only, or both?

Does this help?

Now try with:
You believe, the Newcomb Being has a success rate on predictions of about 100%.
Do you choose box A only, or both?

Quote: MrCasinoGames

Now try with:
You believe, the Newcomb Being has a success rate on predictions of about 100%.
Do you choose box A only, or both?

As has already been discussed, if the being makes advanced predictions with a 100% accuracy rate and that rate is to continue, then the element of free will is destroyed -- the player cannot make any choice other than what has been predicted. My description of this has repeatedly been that I have no need to analyze my decision at all; I'll just watch and see what I do, because my action has already been predetermined.

The Wizard has asked me to throw in my two cents, so I will. Anyone who thinks long enough about Newcomb's Paradox should find it deeply disturbing. It is a paradox precisely because it takes two things which we understand to be true and suggests that they can't both be true. First, as several have mentioned, it makes a mockery of free will. If we have free will, then it must be the case that two boxes are better than one. After all, it's two boxes. That is the so-called dominance principle: that if there are two boxes that have positive or zero amounts in them, and you have a choice of one of them or both of them, you can't do worse by taking both of them. And we use the dominance principle all the time in making choices, so it's not like this is some obscure concept. Indeed, it is the dominance principle that underlies the one-shot solution to the Prisoner's Dilemma, for those of you who are familiar with it.

And if we don't have free will, well then, what's the question? "What should you do" isn't much of a question if you have no ability to choose.

Two decades or so of thinking about this problem have drawn me to the conclusion that it will never be answered until we really understand consciousness, free will and causality; and we've been thinking about these issues for several thousand years and we don't have any really good answers yet. When we get at the bottom of what the brain actually does and how it works, and when we understand why time only goes forward and not backward, or at least seems to, (both are entirely unanswered questions at the moment, although we have glimmerings of answers to each) only then will we have an answer to Newcomb's paradox that makes sense.

Our problem in trying to answer it today is like the problem of trying to answer Zeno's Paradox without a deep understanding of continuous functions which wasn't really completed until the 19th century by Weierstrass among others, although there are still some philosophers who don't think that one resolved. In any case, before Weierstrass (which I think resolves the issue) people simply didn't have the language or concepts to resolve the paradox, and their discussions about the paradox were just...confused. That's where I think we are with respect to our friend Newcomb. that's why i gave up thinking about it, FWIW.

Oh, and what would I do? Does it matter? Once I know the answer to that question, the paradox is resolved.

Good post, jfalk, thanks for contributing. I think you put in the wrong link. Here is a link about Zeno's Paradox.

To wrap this discussion up:

http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1381295

"Conclusion:
Our analysis shows that the resolution of Newcomb’s paradox is in fact quite simple. Newcomb’s paradox takes two incompatible interpretations of a question, with two different answers, and makes it seem as though they are the same interpretation. The lesson of Newcomb’s paradox is just the ancient verity that one must carefully define all one’s terms."

In the terms of this paper, I'm "Fearful". And yes, this paper was authored by the same Gregory Benford that won the Nebula award, and who (quite appropriately for this forum) penned the line:

"Passion is inversely proportional to the amount of real information available."

Quote: jfalk

Anyone who thinks long enough about Newcomb's Paradox should find it deeply disturbing. .

I disagree. Whats there to think about, take both choices and get on with it. You're guaranteed to win 1K and maybe a million, why give anymore thought to it than that? If somebody offers you a sure thing, take it. Unless you're greedy, then you usually get what you deserve.

See? How hard was that..

I disagree. Whats there to think about, take Box A and get on with it. You've a good chance of winning a million, why give anymore thought to it than that? If somebody offers you a 90% chance of a large reward, take it. Faint heart never won fair lady.

See? How hard was that...

Quote: thecesspit

I disagree. Whats there to think about, take Box A and get on with it. You've a good chance of winning a million, why give anymore thought to it than that? If somebody offers you a 90% chance of a large reward, take it. Faint heart never won fair lady.

See? How hard was that...

Either way, why give any thought to it at all? Pick one and get it over with.

Indeed my point, I was just trying to reinforce yours (but from the opposite view point).

While a 90% predictor is unlikely, we know that 56% predictors occurs in sports betting... so I fail to see why the Newcomb beast couldn't in actuality exist and score better than a coin flip.

Though the lower predictor, the more I like taking both boxes.

Thanks, MathExtremist. That article is quite interesting, but I'm afraid it doesn't quite resolve the issue for me. It parameterizes the game as a two person game and shows that the two ways of looking at the problem are not mutually consistent. The problem is that it gives a strategy to the Newcomb being. The consistenency requirement then imposes constraints on a joint probability distribution. But it's not clear to me this a two person game. If it's a one person game against a natural condition, in that case, all of the problems still follow through, and there is no guidance, or even potential guidance, as to which game you're playing. That, it seems to me is the problem. That said, the article is quite interesting and recommended to anybody well versed in game theory.

Quote: Doc

As has already been discussed, if the being makes advanced predictions with a 100% accuracy rate and that rate is to continue, then the element of free will is destroyed -- the player cannot make any choice other than what has been predicted. My description of this has repeatedly been that I have no need to analyze my decision at all; I'll just watch and see what I do, because my action has already been predetermined.

If You believe, the Newcomb Being has a success rate on predictions of about 100%.
Then the choice is:
(1) Choose box A only, get million dollars.
(2) Choose both Box and get $1000.

The free will is still there and The choice is still there (The choice is do you want million dollars or $1000).

Suppose , that after you have made the final decision (that cannot changed anymore), but before opening the box, you are offered to make another choice.
Guess what the actual prediction was. If you guess correctly, your winnings so far are doubled.
What would your guess be, and what do you think is the probability of win?
Will you agree it has to be the same as the probability of finding the million bucks in the first box if picked it alone (or not finding it if you picked both)?

Quote: MrCasinoGames

If You believe, the Newcomb Being has a success rate on predictions of about 100%.
Then the choice is:
(1) Choose box A only, get million dollars.
(2) Choose both Box and get $1000.

The free will is still there and The choice is still there (The choice is do you want million dollars or $1000).

Absurd. Your option (1) says that the million is definitely in box A which by definition says that the being predicted that you would choose only box A which (under your assumption in this particular post) assures there is 100% probability that you would choose box A. There is no free will involved -- your "choice" of box A is absolutely required of you. Similarly (but exactly the opposite) for your option (2). No free will available there either.

As I have mentioned before, the being makes the important decision as to whether to give you the $1 million or not, while (so long as there is neither a guaranteed accuracy of 100% or 0%) you have the choice of whether to take the extra $1,000. In those two extreme cases, you have no choice at all -- everything is determined by the being and by the rules. If you can actually make a free-will choice, what you choose will change the being's accuracy rate.

I don't understand how you can believe there is a free-will choice available when the being has previously made a 100%-accurate "prediction" of what you will do and definitely documented his advance prediction by placing a fixed amount of money in the boxes. How do you have the option to "choose" something other than what was predicted? The only answer I can see is if you believe that future actions change what happened in the past. If that is your genuine belief, we will never come to an agreement.

Quote: Doc

Absurd. Your option (1) says that the million is definitely in box A which by definition says that the being predicted that you would choose only box A which (under your assumption in this particular post) assures there is 100% probability that you would choose box A. There is no free will involved -- your "choice" of box A is absolutely required of you. Similarly (but exactly the opposite) for your option (2). No free will available there either.

As I have mentioned before, the being makes the important decision as to whether to give you the $1 million or not, while (so long as there is neither a guaranteed accuracy of 100% or 0%) you have the choice of whether to take the extra $1,000. In those two extreme cases, you have no choice at all -- everything is determined by the being and by the rules. If you can actually make a free-will choice, what you choose will change the being's accuracy rate.

I don't understand how you can believe there is a free-will choice available when the being has previously made a 100%-accurate "prediction" of what you will do and definitely documented his advance prediction by placing a fixed amount of money in the boxes. How do you have the option to "choose" something other than what was predicted? The only answer I can see is if you believe that future actions change what happened in the past. If that is your genuine belief, we will never come to an agreement.

Below is the difference:
Success rate on predictions of about 100% or 90%.

If You believe, the Newcomb Being has a success rate on predictions of about 100% (on your final(very last) choice, no the choice 24 hour ago).
Your choice is:
(1) Choose box A only = (million dollars 100% of the time) and (nothing 0% of the time).
(2) Choose both Box = (thousand dollars 100% of the time) and (million+$1000. 0% of the time).

If You believe, the Newcomb Being has a success rate on predictions of about 90% (on your final(very last) choice, no the choice 24 hour ago).
Your choice is:
(1) Choose box A only = (million dollars 90% of the time) and (nothing 10% of the time).
(2) Choose both Box = (thousand dollars 90% of the time) and (million+thousand dollars 10% of the time).

In both case, not much of a choice (free will).