NationStates Jolt Archive

I'd probably say "both, please", because I wouldn't know of this crazy oracle type before playing and wouldn't mind being $1,000 richer.

I've been thinking about Newcomb's Paradox recently, and, after some discussion with a few friends, I thought I'd take it to NSG to see what you think. For those who don't know, the problem is as follows: (forgive me if I do not explain it well; if somebody wishes to clarify it, then please, feel free.)


-There is an entity called the Predictor who has the able to predict people's actions. Depending on the version, it's a deity, psychic, an advanced alien, or whatever. The point is, the Predictor can infallibly (or nearly infallibly, depending on the telling) predict people's actions.

-The player, then, is presented with two boxes: Box A and Box B, and given the option to either open both Boxes A and B, or just Box B. (Opening only Box A is not an option.)

-Box A contains $1,000. Box B, however, can either contain $1,000,000 or $0. The amount B contains is determined by the prediction of the Predictor, who, before the start of the game, predicts whether the player will take both boxes or just B. If the Predictor predicts that the player will take both boxes, then B is empty. If it predicts that the player will take only B, then B has $1,000,000.

-Once the game starts, the Predictor cannot change the contents of B.

-The player is not told what the Predictor has predicted-- he is simply told the rules of the game. (That is, the contents of A, and the possibilities for contents of B and how they are chosen.)


So, what would you pick? I can understand the argument for either strategy, but I think I'd go with box B, though I feel that it's difficult to justify this view: the arguments for both sides seem valid to me. No matter what the Predictor predicts, you get $1,000 more by choosing A and B than you would just choosing B.

However, if you eliminate the two options where the predictor is wrong(which should be impossible, according to the premises of the question), then choosing B must be the best option, because you get $1,000,000 more than you would by choosing both.

EDIT:

Here's a Wiki (http://en.wikipedia.org/wiki/Newcomb's_paradox) article that may explain it better.

Ah, but because the Predictor cannot change the contents of the box after he has made his prediction, then no matter what, you get $1,000 more if you choose both A and B:

If both A and B is predicted, and you choose both, you get $1,000.
If both A and B is predicted, and you choose B only, you get $0.
If B only is predicted, and you choose Both, you get $1,001,000.
If B only is predicted, and you choose B only, you get $1,000,000.

So by choosing both, you get $1,000 more than you would otherwise get, because the contents of the box have already been chosen and cannot change. Choosing both strictly dominates choosing B only, to use game theory.

Do you know that the Predictor's role in the game?

If so, then Box B is the only sensible option. Anyone who knows that the Predictor will place $1,000,000 in Box B if the Predictor predicts that they will only pick Box B will pick Box B. The Predictor is infallible, so the Predictor has forseen this decision, and thus will place $1,000,000 in Box B.

Circular as (a circular) hell...

Sooooo wheres the paradox then? You would I hope pick box B.

Sorry I just don't get it.

Going by your explanation, I would choose B. Why would anyone choose both? You get more money by choosing B.

So by choosing both, you get $1,000 more than you would otherwise get, because the contents of the box have already been chosen and cannot change.
But choosing both lowers your net gain from $1,000,000 to $1,000.

If you pick Box B, the predictor forsees this and places $1,000,000 in Box B. If you pick both boxes, then the predictor places nothing in Box B. Thus, you should always pick Box B.

Assuming, as the question does, that the Predictor is infallible.

Do you know that the Predictor's role in the game?

If so, then Box B is the only sensible option. Anyone who knows that the Predictor will place $1,000,000 in Box B if the Predictor predicts that they will only pick Box B will pick Box B. The Predictor is infallible, so the Predictor has forseen this decision, and thus will place $1,000,000 in Box B.

Circular as (a circular) hell...

Ah, but when you make your choice, the Predictor has already predicted and cannot change his prediction.

If the Predictor has predicted both A and B, then you're choosing between $1,000 (by choosing both) and $0.(By choosing B)

If the Predictor, however, has predicted B, then you are choosing between $1,001,000 (both) and $1,000,000 (B).

Again, while I agree with you and lean towards B, the argument for choosing both seems rational too!

I've been thinking about Newcomb's Paradox recently, and, after some discussion with a few friends, I thought I'd take it to NSG to see what you think. For those who don't know, the problem is as follows: (forgive me if I do not explain it well; if somebody wishes to clarify it, then please, feel free.)


-There is an entity called the Predictor who has the able to predict people's actions. Depending on the version, it's a deity, psychic, an advanced alien, or whatever. The point is, the Predictor can infallibly (or nearly infallibly, depending on the telling) predict people's actions.

-The player, then, is presented with two boxes: Box A and Box B, and given the option to either open both Boxes A and B, or just Box B. (Opening only Box A is not an option.)

-Box A contains $1,000. Box B, however, can either contain $1,000,000 or $0. The amount B contains is determined by the prediction of the Predictor, who, before the start of the game, predicts whether the player will take both boxes or just B. If the Predictor predicts that the player will take both boxes, then B is empty. If it predicts that the player will take only B, then B has $1,000,000.

-Once the game starts, the Predictor cannot change the contents of B.

-The player is not told what the Predictor has predicted-- he is simply told the rules of the game. (That is, the contents of A, and the possibilities for contents of B and how they are chosen.)


So, what would you pick? I can understand the argument for either strategy, but I think I'd go with box B, though I feel that it's difficult to justify this view: the arguments for both sides seem valid to me. No matter what the Predictor predicts, you get $1,000 more by choosing A and B than you would just choosing B.

However, if you eliminate the two options where the predictor is wrong(which should be impossible, according to the premises of the question), then choosing B must be the best option, because you get $1,000,000 more than you would by choosing both.

First of all, to verify his legitimacy, I will kick the Predictor in the groin. If he is wearing a cup, he's the real deal. :)

Ah, but when you make your choice, the Predictor has already predicted and cannot change his prediction.
And the Predictor is infallible.

S/he always correctly predicts which box(es) you'll pick. So, by the mere fact of choosing Box B, there is a $1,000,000 in it.

The highlighted options are not possible, since the predictor is infallible.

My intuition is to agree, actually, but the problem is that when you're making the choice, the prediction has already been made and cannot be changed. If the prediction is both, your best bet is to choose both, and if the prediction is B, then your best bet is to choose both, which shouldn't be possible, but there is no compulsion to stop you.

So, what's paradoxical about this? It's more of a thought expierment of decision rather than a self-contradictory situation.

Anyway, what's the predictor's prediction based on? The whim of the predictor?

If both A and B is predicted, and you choose both, you get $1,000.
If both A and B is predicted, and you choose B only, you get $0.
If B only is predicted, and you choose Both, you get $1,001,000.
If B only is predicted, and you choose B only, you get $1,000,000.


The highlighted options are not possible, since the predictor is infallible.

So, what's paradoxical about this? It's more of a thought expierment of decision rather than a self-contradictory situation.

Anyway, what's the predictor's prediction based on? The whim of the predictor?

Searching through the wiki, I come across:

The problem is called a paradox because two strategies that both sound intuitively logical give conflicting answers to the question of what choice maximizes the player's payout. The first strategy argues that, regardless of what prediction the Predictor has made, taking both boxes yields more money. That is, if the prediction is for both A and B to be taken, then the player's decision becomes a matter of choosing between $1,000 (by taking A and B) and $0 (by taking just B), in which case taking both boxes is obviously preferable. But, even if the prediction is for the player to take only B, then taking both boxes yields $1,001,000, and taking only B yields only $1,000,000—the difference is comparatively slight in the latter case, but taking both boxes is still better, regardless of which prediction has been made.

The second strategy suggests taking only B. By this strategy, we can ignore the possibilities that return $0 and $1,001,000, as they both require that the Predictor has made an incorrect prediction, and the problem states that the Predictor cannot be wrong. Thus, the choice becomes whether to receive $1,000 (both boxes) or to receive $1,000,000 (only box B)—so taking only box B is better.

In his 1969 article, Nozick noted that "To almost everyone, it is perfectly clear and obvious what should be done. The difficulty is that these people seem to divide almost evenly on the problem, with large numbers thinking that the opposing half is just being silly."

Honestly, the term "paradox" has typically been used with all the tellings I've heard of it, so I used it out of habit, but according to the wiki, it's sometimes known as Newcomb's problem instead.

And the Predictor is infallible.

S/he always correctly predicts which box(es) you'll pick. So, by the mere fact of choosing Box B, there is a $1,000,000 in it.

But that violates the part where your choice cannot retroactively change the prediction. The problem as I understand it is that your choice cannot retroactively change the prediction, you are given a free choice, and the Predictor is infallible.

Ah, but because the Predictor cannot change the contents of the box after he has made his prediction, then no matter what, you get $1,000 more if you choose both A and B:

If both A and B is predicted, and you choose both, you get $1,000.
If both A and B is predicted, and you choose B only, you get $0.
If B only is predicted, and you choose Both, you get $1,001,000.
If B only is predicted, and you choose B only, you get $1,000,000.

So by choosing both, you get $1,000 more than you would otherwise get, because the contents of the box have already been chosen and cannot change. Choosing both strictly dominates choosing B only, to use game theory.


But you have stated that the predictor is infaliable. So any option stateing the predictor got it wrong is out.

But that violates the part where your choice cannot retroactively change the prediction.
How?

No matter if your choice is free or determined, the infallible Predictor correctly predicts your choice. Thus, if you choose Box B then the Predictor predicted this before-hand and placed $1,000,000 in Box B. If you choose Box A then the Predictor predicted this before-hand and didn't place anything in Box B.

And so on

The second strategy suggests taking only B. By this strategy, we can ignore the possibilities that return $0 and $1,001,000, as they both require that the Predictor has made an incorrect prediction, and the problem states that the Predictor cannot be wrong. Thus, the choice becomes whether to receive $1,000 (both boxes) or to receive $1,000,000 (only box B)—so taking only box B is better.
This, to me, is the clincher.

If the Predictor can predict incorrectly, then it's a whole different ball game.

Oh, and Corasairs: it's called Wikipedia. There are multiple wikis, only one Wikipedia. [/pedantry]

what I pick would depends on whether or not the predictor is a nice guy who wants to get a Christmas card

if hes a dick:

beat him up and take his money

if hes nice:

take both because he wants you to have more money so you can be friends :)

if those two are non I say B

But that violates the part where your choice cannot retroactively change the prediction. The problem as I understand it is that your choice cannot retroactively change the prediction, you are given a free choice, and the Predictor is infallible.

Well thats the point. If the preditor is infalliable then your choice cannot retroatvily change anything.

Now if the predictor was not infaliable, then it makes more sense to open both boxes.

This, to me, is the clincher.

If the Predictor can predict incorrectly, then it's a whole different ball game.

I'd like to note, again, that I actually agree with you. I'm just trying to defend the other side because nobody else is doing it, and because I can see where it's coming from-- it seems to me you either have to violate the infallibility of the Predictor or the inability for your decision to retroactively determine the prediction.

I'd like to note, again, that I actually agree with you. I'm just trying to defend the other side because nobody else is doing it, and because I can see where it's coming from-- it seems to me you either have to violate the infallibility of the Predictor or the inability for your decision to retroactively determine the prediction.

There is no other side. Those that choose the other side are logicaly wrong.

I'd like to note, again, that I actually agree with you. I'm just trying to defend the other side because nobody else is doing it, and because I can see where it's coming from-- it seems to me you either have to violate the infallibility of the Predictor or the inability for your decision to retroactively determine the prediction.

There is no other side. Those that choose the other side are logicaly wrong.

In this situation I would not believe that they have convinced God to participate in their petty games or that an alien civilization travelled all the way to earth just to start a lottery, even though I believe both of those exist. I would consider proving them wrong worth more than $1000 so the worst scenario is to pick both, prove them right and only get $1000. Picking B would either prove them right and give me a million or give me nothing but prove them wrong which is worth more than $1000.

In general I don't have a problem with humans being predictable though. If you sell a soda can for $1 and an identical soda can for $2 you can predict that the customer will take a cheaper one. With close friends you can predict their opinions pretty well. A being who is vastly more intelligent than us and knows everything about a human should logically be able to predict the actions of that human.

I know myself. As soon as the person explaining said that they would put 1,000,000$ in box b if I choose box B, I would immediately choose box B.

All the other stuff is tiresome, cumbersome, may lead to temporal paradoxes etc. This is a milllion bucks in my pocket . Guaranteed. I'd be opening box B before he even finished speaking.

The answer to this one is actually simpler than it might look, if you really think about it.

The problem is that the paradox asks us to simultaneously think two contradictory things, both of which, believed alone, provide opposite answers. First, we must assume free will: we are making a free, rational decision about which box to pick. Second, we must assume determinism: the Predictor can infallibly predict our actions.

These assumptions, however, are incompatible... and once you accept incompatibilism, the resolution of the paradox becomes clear.

If determinism is true and we have no free will, there is no question of "should": we are not making a decision, but are merely responding to stimuli. If we are the sort of people who would pick Box B, we are lucky, because we get the million. If we are the sort of people who would pick both boxes, we are unlucky, because we only get the thousand. Our decision is not independent of these facts about ourselves, and thus it is pointless to discuss "should": we are or we aren't, and the Predictor's prediction is in accordance with this.

If free will is true and our decisions are not determined, the answer is simple: we should pick both boxes. It doesn't matter what the Predictor predicted; we get better results this way regardless. Because our decisions are not determined, furthermore, the Predictor's prediction is not necessarily true: we can make it so happen that the Predictor's prediction fails.

The appeal of picking only Box B comes from the weirdness of forcing together two incompatible assumptions. If our actions can be predicted with perfection, then our decision must be dependent upon our state when the Predictor made her prediction. Thus, if we choose Box B, it seems that it must be the case that the Predictor predicted that we would choose Box B. But obviously we cannot choose to change the past. The past is over; the Predictor's choice has already been made. If we are really choosing, then we should choose both boxes.

The answer to this one is actually simpler than it might look, if you really think about it.

The problem is that the paradox asks us to simultaneously think two contradictory things, both of which, believed alone, provide opposite answers. First, we must assume free will: we are making a free, rational decision about which box to pick. Second, we must assume determinism: the Predictor can infallibly predict our actions.

These assumptions, however, are incompatible... and once you accept incompatibilism, the resolution of the paradox becomes clear.

If determinism is true and we have no free will, there is no question of "should": we are not making a decision, but are merely responding to stimuli. If we are the sort of people who would pick Box B, we are lucky, because we get the million. If we are the sort of people who would pick both boxes, we are unlucky, because we only get the thousand. Our decision is not independent of these facts about ourselves, and thus it is pointless to discuss "should": we are or we aren't, and the Predictor's prediction is in accordance with this.

If free will is true and our decisions are not determined, the answer is simple: we should pick both boxes. It doesn't matter what the Predictor predicted; we get better results this way regardless. Because our decisions are not determined, furthermore, the Predictor's prediction is not necessarily true: we can make it so happen that the Predictor's prediction fails.

The appeal of picking only Box B comes from the weirdness of forcing together two incompatible assumptions. If our actions can be predicted with perfection, then our decision must be dependent upon our state when the Predictor made her prediction. Thus, if we choose Box B, it seems that it must be the case that the Predictor predicted that we would choose Box B. But obviously we cannot choose to change the past. The past is over; the Predictor's choice has already been made. If we are really choosing, then we should choose both boxes.

Now that really is a paradox. Of coure there is a third alternative. Determinism does not negate free will.

Now that really is a paradox.

But a resolved one.

Of coure there is a third alternative. Determinism does not negate free will.

Actually, I think Newcomb's Paradox is an interesting illustration of why we should think it does.

But I'm not absolutely sure. If you have a compatibilist way to resolve the problem, I would love to hear it.

Now that really is a paradox.

See how much better other people are at explaining things than I am? :D

First, we must assume free will: we are making a free, rational decision about which box to pick. Second, we must assume determinism: the Predictor can infallibly predict our actions.
Could the Predictor not infallible predict a free choice?

We're not talking about real-life here...

But a resolved one.



Actually, I think Newcomb's Paradox is an interesting illustration of why we should think it does.

But I'm not absolutely sure. If you have a compatibilist way to resolve the problem, I would love to hear it.

Have you yet had a look at my sandwhich experiment?

These assumptions, however, are incompatible...
If free will is true and our decisions are not determined, the answer is simple: we should pick both boxes. It doesn't matter what the Predictor predicted; we get better results this way regardless. Because our decisions are not determined, furthermore, the Predictor's prediction is not necessarily true: we can make it so happen that the Predictor's prediction fails...
The past is over; the Predictor's choice has already been made.
You're working under an overly assumptive definition of free will; that is, that in order for there to be a choice, it must be nondeterministic. Decision making is never totally arbitrary because not only is cool, thoughtful rationalisation deliberate and mechanical, but so too is impulse and intuition. The mechanisms for impulse and intuition merely occur at a level below that of which we are consciously aware. That does not preclude the fact that it is the decision-making process of our mind that is responsible for the outcome of our choice, but it does render it deterministic.

The tricky thing with predicting the outcome of a "free choice" is in having a full understanding both of a person's inner mechanisms and of the exact nature of the problem posed to them. This is why it's a "paradox" - the predictor, if its prediction is to be entirely accurate all of the time, must be able to take your response to its prediction into account. There is a trans-temporal feedback loop going on, and finding a fixed point for which the prediction reflects its own intervention is probably computationally intractable. But we're assuming this is possible, and that your assertion that "we cannot change the past" is actually false - namely, that your current physical structure is causal to the past prediction.

In case you didn't guess, I'd pick B, assuming I've had a chance to analyse the algorithm first.

I would choose Box B only because it's the polite choice. Trying to squeeze an extra 1000 bucks out of the predictor, after he's already given you a million, just seems rude.

Could the Predictor not infallible predict a free choice?

No. Free choice, by its very nature, cannot be predicted perfectly. If it is perfectly predictable, even in theory, then it is by necessity tied to something else, and it is not free.

Decision making is never totally arbitrary

Who said anything about "arbitrary"?

That does not preclude the fact that it is the decision-making process of our mind that is responsible for the outcome of our choice, but it does render it deterministic.

Yes, that's compatibilism. Not only have I heard this argument, but I've made it myself, so I understand where you're coming from.

The problem--in short--is that if you really think about the way we perceive decision-making, we don't perceive it that way at all. Nothing about "the decision-making process of our mind", if by that you mean a causal chain, can be seen to bring about a certain decision, because then our will does not decide, something else does.

Any cause we perceive does not seem to us to be a reason for action: the mere fact that we want something, or that our physical brain has a certain attribute, is not enough to determine our choice. We can recognize any of those things, and then go against them. We don't perceive them as "causing" our action.

Now, it is possible that they cause our action without our knowledge, but then of course we are not free. If we are ignorant of what causes our actions, we have obviously not freely chosen them.

The tricky thing with predicting the outcome of a "free choice" is in having a full understanding both of a person's inner mechanisms and of the exact nature of the problem posed to them. This is why it's a "paradox" - the predictor, if its prediction is to be entirely accurate all of the time, must be able to take your response to its prediction into account.

Yes, prediction, even under deterministic assumptions, is impossible if the person has the capacity to respond to your prediction. But in Newcomb's Paradox, the person doesn't; the person has no idea what the Predictor has predicted. Everything except what is in the boxes could be exactly the same. Perfect prediction, assuming determinism, is perfectly possible.

But we're assuming this is possible, and that your assertion that "we cannot change the past" is actually false - namely, that your current physical structure is causal to the past prediction.

We are? I don't think so. Perhaps you are, but that changes the nature of the thought experiment quite considerably... prediction is not the same as time travel.

Have you yet had a look at my sandwhich experiment?

:confused:

Actually, I think Newcomb's Paradox is an interesting illustration of why we should think it does.

But I'm not absolutely sure. If you have a compatibilist way to resolve the problem, I would love to hear it.
Radioactive atoms are truly random in their decision on when to decay but that does not mean they have free will, it means they don't make informed decisions at all, they just act randomly. Anything that is truly random is not derived from anything, not from knowledge, personality or anything else so it's completely meaningless nonsense rather than an informed decision or 'will'. An informed decision or 'will' is a conclusion derived from knowledge through a coherent thought process, in order words it is deterministic rather than random. Free will could be defined as the ability to reach a conclusion based only on your own internal knowledge and thought process, then it is deterministic. But free will can not be non-deterministic as a truly random act is not a decision.

Radioactive atoms are truly random in their decision on when to decay but that does not mean they have free will,

Of course not. "Randomness" is not free.

Anything that is truly random is not derived from anything, not from knowledge, personality or anything else

Free will must certainly be independent of "knowledge, personality or anything else", because none of these are reasons to do anything. I have no reason to recognize them as holding rightful sovereignty over my will. Thus, they are an imposition: if they determine it, I am not free.

An informed decision or 'will' must be a conclusion derived from knowledge through a coherent thought process, thus it must be non-random or in other words deterministic.

No. Thus, it must obey certain rules. These rules need not be a matter of causation.

Free will could be defined as the ability to reach a conclusion based only on your own internal knowledge and thought process, then it is deterministic. But free will can not be non-deterministic as a truly random act is not a decision.

Yes, I've heard it all already. Thanks.

Now, do you have a way to resolve Newcomb's Paradox under those assumptions? We are getting somewhat off-base.

Free will must certainly be independent of "knowledge, personality or anything else", because none of these are reasons to do anything. I have no reason to recognize them as holding rightful sovereignty over my will. Thus, they are an imposition: if they determine it, I am not free.
If a decision is independent of your traits such as your knowledge and personality then it has nothing to do with who you are so it is not your decision. If it is independent of anything else too then it is meaningless nonsense, it has to be derived from something to be meaningful.
Now, do you have a way to resolve Newcomb's Paradox under those assumptions? We are getting somewhat off-base.
Since I assume humans are deterministic the predictor can predict the decision so the choice is between $1000 from both or $1000000 from B. Someone who makes the same assumptions and wants as much money as possible will pick B. I assume people who make different assumptions or just want to pick the bad choice to demonstrate that they can be random will only get $1000 because the predictor will predict that these persons will make that choice since they are deterministic.

If a decision is independent of your traits such as your knowledge and personality then it has nothing to do with who you are so it is not your decision.

Nonsense. It is your will. It is your decision.

It is my traits that are not me. The whole fallacy of compatibilism is that it assumes that I can have identity in the relevant sense with my inclinations and my physical mental attributes. I cannot. They may be "mine", but they are foreign to my will: they do not give me a reason to act. I have no reason to recognize them as binding. They are just there.

I can think "my personality is like this" and "my desires are lack that" all I want; I still must actually choose.

If it is independent of anything else too then it is meaningless nonsense, it has to be derived from something to be meaningful.

Why? What is it about independence that is meaningless?

Since I assume humans are deterministic the predictor can predict the decision so the choice is between $1000 from both or $1000000 from B. Someone who makes the same assumptions and wants as much money as possible will pick B. I assume people who make different assumptions or just want to pick the bad choice to demonstrate that they can be random will only get $1000 because the predictor will predict that these persons will make that choice since they are deterministic.

You're not resolving the paradox at all; you're just cutting off one end. You're ignoring the other, which is at least as convincing as the reasoning you have presented: regardless of what the Predictor has predicted, if you choose both boxes you will always get more.

So you have compelling, decisive reasons to choose two incompatible answers. Contradictions cannot exist. Either you must explain why the circumstances themselves are flawed (as I did), or you must explain why the reasoning behind one or the other answer is (as seems impossible.)

ive never understood the point of a "paradox" where part of the set up is that predictions are true.

if my taking B means that i get a million bucks because the predictor had knowledge of the future, and you are going to take both because its already set, im getting a million bucks and you are getting $1k.

the person who gets the most money is the most right.

Nonsense. It is your will. It is your decision.

It is my traits that are not me. The whole fallacy of compatibilism is that it assumes that I can have identity in the relevant sense with my inclinations and my physical mental attributes. I cannot. They may be "mine", but they are foreign to my will: they do not give me a reason to act. I have no reason to recognize them as binding. They are just there.

I can think "my personality is like this" and "my desires are lack that" all I want; I still must actually choose.
You can consider what you think your personality and desires are but those estimations don't have to be accurate. You are the sum of your traits and previous experiences. A 'will' that is not caused by any of your attributes has nothing to do with you and is not a part of you.
Why? What is it about independence that is meaningless?
Something that has no connection to other information can not be understood as information. The only thing that is not a result of previous information is randomness.
You're not resolving the paradox at all; you're just cutting off one end. You're ignoring the other, which is at least as convincing as the reasoning you have presented: regardless of what the Predictor has predicted, if you choose both boxes you will always get more.

So you have compelling, decisive reasons to choose two incompatible answers. Contradictions cannot exist. Either you must explain why the circumstances themselves are flawed (as I did), or you must explain why the reasoning behind one or the other answer is (as seems impossible.)
The two different conclusions are drawn from two different scenarios that appear to be the same scenario if you apply lazy game theory that ignores probabilities to the scenarios.

If the probability of a correct prediction is 0.5 or unknown:

A. I choose both, predictor is right. Gain $1,000 * probability 0.5 = value $500.
B. I choose both, predictor is wrong. Gain $1,001,000 * probability 0.5 = value $500,500.
C. I choose B, predictor is right. Gain $1,000,000 * probability 0.5 = value $500,000.
D. I choose B, predictor is wrong. Gain $0 * probability 0 = value $0.

The average value of choosing both $1,000 * 0.5 + $1,001,000 * 0.5 = $501,000 is more than the average value of choosing B $1,00,000 * 0.5 + $0 * 0.5 = $500,000 so choose both.

If the probability of a correct prediction is known to be 1:

A. I choose both, predictor is right. Gain $1,000 * probability 1 = value $1,000.
B. I choose both, predictor is wrong. Gain $1,001,000 * probability 0 = value 0.
C. I choose B, predictor is right. Gain $1,000,000 * probability 1 = value $1,000,000.
D. I choose B, predictor is wrong. Gain $0 * probability 0 = value 0.

The average value of choosing both $1,000 * 1 + $0 * 0 = $1,000 is less than the average value of choosing B $1,000,000 * 1 + $0 * 0 = $500,000 so choose B.

if my taking B means that i get a million bucks because the predictor had knowledge of the future, and you are going to take both because its already set, im getting a million bucks and you are getting $1k.

But you would have gotten $1,001,000 if you had chosen otherwise. And I would have gotten nothing if I had.

the person who gets the most money is the most right.

That's exactly right. The person. Not the choice. Because the determinist assumptions at the heart of the paradox make it all about the person.

If this Predicter guy has over a million in cash on him I'll just bring a gun and stick him up. Simple.

But you would have gotten $1,001,000 if you had chosen otherwise. And I would have gotten nothing if I had.



That's exactly right. The person. Not the choice. Because the determinist assumptions at the heart of the paradox make it all about the person.

no i woudlnt have

you are denying a premise of the game which is that the predictor knew the future.

You can consider what you think your personality and desires are but those estimations don't have to be accurate.

So when I choose to do what I think I do not want, the reason for my action is that I really wanted to do what I actually did? How is that "free" at all? My choices are caused by something I don't even understand.

For that matter, people who actually are mistaken about their desires go with their mistaken understanding all the time.

Regardless, you're still missing the point. I have no reason to recognize any connection between my choice and my personality and desires. My personality and desires do not, from the subjective perspective of choice, determine my will. The mere fact of their existence does not say to me "I must choose this." I cannot merely be my personality; I cannot simply experience my desires. I can do both, but I cannot stop there: I must actually choose.

If you assert that my personality and my desires determine my will, then I cannot be free. I cannot accept their sovereignty over my will; the mere fact that I desire something, the mere fact that I am a certain kind of person, is not enough for me to decide, is not enough for me to be able to say I should make a particular choice. If, regardless of this gap, I must go with them, my will is bound, and not free.

A 'will' that is not caused by any of your attributes has nothing to do with you and is not a part of you.

Nonsense. It is your decision-making capacity. It is intimately a part of you.

What you're saying is as absurd as saying that if the nature of your foot isn't somehow "caused" by your brain, your foot isn't a part of you. Of course not. They're both a part of you, they're just independent parts of you.

Something that has no connection to other information can not be understood as information.

You're equivocating on "connection." Things can be similar enough for comparison without being causally connected.

The two different conclusions are drawn from two different scenarios that appear to be the same scenario if you apply lazy game theory that ignores probabilities to the scenarios.

You realize that philosophers have been debating this one for decades? Do you really think the answer is so simple?

The average value of choosing both $1,000 * 0.5 + $1,001,000 * 0.5 = $501,000 is more than the average value of choosing B $1,00,000 * 0.5 + $0 * 0.5 = $500,000 so choose both.

That's a straw man.

The people who argue that you should choose both need not make any assumption about the accuracy of the Predictor's prediction. All they need say is that whatever the Predictor predicted, whatever the accuracy of her prediction, choosing both is always the better option. Whether there's one million or nothing in the second box--and that's already been decided--you still gain $1000 more than you otherwise would.

The average value of choosing both $1,000 * 1 + $0 * 0 = $1,000 is less than the average value of choosing B $1,000,000 * 1 + $0 * 0 = $500,000 so choose B.

That's a solid argument. There's no way to refute it, under the assumptions of the paradox.

The problem is that there is an equally solid argument on the other side. And there's no way to refute that one, either, under the assumptions of the paradox.

That's because the assumptions of the paradox are contradictory--incompatible.

no i woudlnt have

Then there couldn't have been one million dollars in the second box. Instead of getting a million, you got nothing.

Either there is one million in the second box, or there is nothing. If there is nothing, it is better to take both. If there is one million, it is better to take both. Regardless of the Predictor's prediction, it is better to take both. It doesn't matter.

you are denying a premise of the game which is that the predictor knew the future.

I'm not concerned with the accuracy of the Predictor's prediction; I don't need to know anything about the Predictor's prediction at all. Whether the Predictor is some random fool or a prescient prophet, my reasoning is still solid.

...you are given a free choice, and the Predictor is infallible.
Those two propositions are mutually exclusive.

No. Free choice, by its very nature, cannot be predicted perfectly. If it is perfectly predictable, even in theory, then it is by necessity tied to something else, and it is not free.

Perhaps you could elaborate. It seems that there are plenty of situations which can be predicted perfectly.
Take the two boxes, for example. Suppose instead of one, there are two Predictors, who each predict a different choice. At least one of them has to be right, even if they just decide by flipping a coin.

Then there couldn't have been one million dollars in the second box. Instead of getting a million, you got nothing.

Either there is one million in the second box, or there is nothing. If there is nothing, it is better to take both. If there is one million, it is better to take both. Regardless of the Predictor's prediction, it is better to take both. It doesn't matter.



I'm not concerned with the accuracy of the Predictor's prediction; I don't need to know anything about the Predictor's prediction at all. Whether the Predictor is some random fool or a prescient prophet, my reasoning is still solid.

you are denying the premise of the game.

in the real world, it doesnt make a difference and you are a fool to not take both boxes. in the game, the predictor only puts a million in the box if its the only one you will take. you are a fool to take both boxes.

Take the two boxes, for example. Suppose instead of one, there are two Predictors, who each predict a different choice. At least one of them has to be right, even if they just decide by flipping a coin.

That's two predictions, not one. "He will either do x or do y" is not a perfect prediction, because it presents two possibilities.

Edit: As for "elaborate"... read the thread. I say that in the nicest way possible. Seriously. :)

you are denying the premise of the game.

So are you, ultimately--either free choice or the nature of time and causality. But you are rationally deriving your conclusion from the other premises. Just like me, only the premises I have chosen to uphold are different.

This is exactly why I have argued that the premises are contradictory.

in the game, the predictor only puts a million in the box if its the only one you will take. you are a fool to take both boxes.

You're falling into a common pattern among people who argue about Newcomb's Paradox. They are--rightly--convinced of one of the arguments, and thus they conclude that the other cannot be right.

But the beauty and genius of the paradox is that both are.

If you assert that my personality and my desires determine my will, then I cannot be free. I cannot accept their sovereignty over my will; the mere fact that I desire something, the mere fact that I am a certain kind of person, is not enough for me to decide, is not enough for me to be able to say I should make a particular choice. If, regardless of this gap, I must go with them, my will is bound, and not free.

Nonsense. It is your decision-making capacity. It is intimately a part of you.

What you're saying is as absurd as saying that if the nature of your foot isn't somehow "caused" by your brain, your foot isn't a part of you. Of course not. They're both a part of you, they're just independent parts of you.
I failed to get my point across and will try from the start again.

Will (free or not) is the ability to make an informed decision. Any action is either random or deterministic. The outcome of randomness is not based on any previous information but you can't make an informed decision without basing it on any previous information so the outcome of randomness is not an informed decision. The outcomes of all informed decisions are deterministic since it wouldn't be an informed decision if the outcome was random. Whether will is free or not depends on the requirements for being free, if it is enough to be able to make a decision on your own without receiving further external input after being presented with a choice then it is free but if it has to be random then will is not free.
That's a straw man.

The people who argue that you should choose both need not make any assumption about the accuracy of the Predictor's prediction. All they need say is that whatever the Predictor predicted, whatever the accuracy of her prediction, choosing both is always the better option. Whether there's one million or nothing in the second box--and that's already been decided--you still gain $1000 more than you otherwise would.
That is not true, the probability of an accurate prediction does matter, if the prediction is always accurate then you always get $1,000 from both or $1,000,000 from B.

Besides the paradox of choosing strategy there is also the paradox of if the scenario can be true.

If you are random then it is impossible to predict your choice so it is indeed a paradox to claim that a predictor can predict it. The paradox can be simplified to "I can predict randomness", "No, now you're just contradicting yourself."

If you are deterministic then your choice is caused by the contents of your mind (including how your decision making capability works). The prediction is caused by the predictor's knowledge about your mind so if the predictor's knowledge about you is accurate enough then the prediction can indeed arrive at the same conclusion as your choice despite being made before your choice because both are derived from the same knowledge. In this case it's not a paradox.

Any action is either random or deterministic.

Any decision (better word than "action", I think) is either part of the deterministic chain or independent of it.

Independence does not necessitate "randomness" in the sense you mean. The decision we make is "caused" in a sense--it is not arbitrary, it involves an act of volition--but it is not predicated on any material cause. You could perhaps call it "self-causing", which is a weird concept to wrap your head around... but not one we can logically rule out.

The outcome of randomness is not based on any previous information but you can't make an informed decision without basing it on any previous information so the outcome of randomness is not an informed decision.

You're confusing different things. I can choose to do something on some basis without that basis "causing" my action. It's the difference between choosing to sit down in a chair and having the chair somehow drag me into it: I choose to adopt that basis for my action, rather than having that basis cause my choice.

That is not true, the probability of an accurate prediction does matter, if the prediction is always accurate then you always get $1,000 from both or $1,000,000 from B.

That's right. The accuracy of the prediction matters for your argument. And, like I said, your argument is solid.

But it does not matter for the person who insists that you should choose both. That argument has nothing to do with accuracy. It simply notes that you have two boxes in front of you whose content has already been set. Will you get more by choosing only one, or by choosing both? Obviously, since we know that neither box contains negative money, you should choose both.

See the paradox? That reasoning is solid, too.

If you are deterministic then your choice is caused by the contents of your mind (including how your decision making capability works). The prediction is caused by the predictor's knowledge about your mind so if the predictor's knowledge about you is accurate enough then the prediction can indeed arrive at the same conclusion as your choice despite being made before your choice because both are derived from the same knowledge. In this case it's not a paradox.

That's right. If determinism is true, there is no paradox. But only because there is no meaningful "choice", in which case it is pointless to ask "Which should you choose?" anyway.

The problem, as I have insisted, is that the paradox demands that we assume both determinism and free will. They're incompatible. So the answers we get from solid reasoning are contradictory.

Any decision (better word than "action", I think) is either part of the deterministic chain or independent of it.

Independence does not necessitate "randomness" in the sense you mean. The decision we make is "caused" in a sense--it is not arbitrary, it involves an act of volition--but it is not predicated on any material cause. You could perhaps call it "self-causing", which is a weird concept to wrap your head around... but not one we can logically rule out.
I can accept that a decision is based on previous information (including the mechanics of the decision making process) instead of being caused by it but then a prediction of the choice can accurately reach the same conclusion as the choice if it is based on the same knowledge as the choice.

I can't prove that non-predictable non-random choices don't exist but I think the definition of this concept contradicts itself. It's either possible to predict a choice or it isn't. I think we'll just keep disagreeing on whether or not a third alternative exists.

The experience of non-predictable non-random events does exist though. When we don't have enough information to predict something we experience it as a non-predictable even if it is clearly non-random but in these cases the events could in theory be predictable if we had more information.

I can accept that a decision is based on previous information (including the mechanics of the decision making process) instead of being caused by it but then a prediction of the choice can accurately reach the same conclusion as the choice if it is based on the same knowledge as the choice.

No. You forget: if our choice is "based" on previous information, then we choose to make it on the basis. We could always choose otherwise.

We may have a general tendency to choose one way or another; desires are precisely that kind of tendency. We feel "pulled" in one direction or another. But there is never certainty, because we can always choose otherwise. Desires do not "cause" our actions. We can feel a desire all we want; we still must choose.

Again, take the example of the chair. Yes, I can choose to sit down there on the basis that there is a chair... and if I am exhausted, I'm very likely to do exactly that. But I can do otherwise. I can choose to leave the chair and run a mile instead. Not likely... but possible.

It's either possible to predict a choice or it isn't.

Right. But "impossible to predict perfectly" is not the same thing as "random." Randomness implies an arbitrariness that isn't present in free choice insofar as my own choice is the determining factor.

That's two predictions, not one. "He will either do x or do y" is not a perfect prediction, because it presents two possibilities.

Edit: As for "elaborate"... read the thread. I say that in the nicest way possible. Seriously. :)



So are you, ultimately--either free choice or the nature of time and causality. But you are rationally deriving your conclusion from the other premises. Just like me, only the premises I have chosen to uphold are different.

This is exactly why I have argued that the premises are contradictory.



You're falling into a common pattern among people who argue about Newcomb's Paradox. They are--rightly--convinced of one of the arguments, and thus they conclude that the other cannot be right.

But the beauty and genius of the paradox is that both are.

and yet *I* get $1,000,000 and YOU get $1,000

its not the end-all and be-all but it does indicate that you have left something out of your considerations.

We are? I don't think so. Perhaps you are, but that changes the nature of the thought experiment quite considerably... prediction is not the same as time travel.
If the prediction is to be assumed to be perfect, then we can assert that information can flow backwards through time. After all, any change in the state in future time is reflected in the past prediction; that's what it means to be a perfect predictor.

By viewing the problem of prediction in this way (as reverse causality, in a sense) the compatibilist approach makes sense, since it is the future choice that drives the past prediction, rather than the past prediction setting the future action in stone.

and yet *I* get $1,000,000 and YOU get $1,000

But you would have gotten $1,001,000 if you had made the other choice, since the boxes don't retroactively change their contents. And I would have gotten nothing if I had, for the same reason.

Not that I don't understand what you're saying. I do. Your argument is compelling. But so is mine. That's why it's a paradox.

its not the end-all and be-all but it does indicate that you have left something out of your considerations.

Yes, it does. So have you, as I have tried to show by presenting the other argument. That's part of the character of the thought experiment: we cannot make all the parts fit, because ultimately they are not reconcilable.

If the Predictor is actually infallible, box B is the only choice that makes sense. If not, then both boxes.

However, what do you do, with the same set of given circumstances, but instead of knowing which box is which, you have to randomly pick one to open? Do you open one or both? Does not knowing which is which change the game at all? And does it change if in that case the Predictor is actually infallible or not?

If the prediction is to be assumed to be perfect, then we can assert that information can flow backwards through time. After all, any change in the state in future time is reflected in the past prediction; that's what it means to be a perfect predictor.

No, it isn't.

Imagine that I throw a football at a certain angle with a certain velocity. Ignoring air resistance, I can use Newtonian equations to predict the path and ultimate position of the football (almost) exactly.

Does the path of the football cause my prediction? Of course not. But my prediction is still perfect: it still comes true every time (assuming other factors don't interfere.) My prediction of the football's path does not come from information flowing backwards, but from my knowledge of the physical laws that determine the relationship between past and future states of the universe.

Determinism asserts that human decision-making is ultimately like that football (though far more complicated): it is determined by physical laws of causation in the same sense that the football's path is, and thus a truly exceptional being like the Predictor would be able to predict its results just as I can predict the path of a football.

By viewing the problem of prediction in this way (as reverse causality, in a sense) the compatibilist approach makes sense, since it is the future choice that drives the past prediction, rather than the past prediction setting the future action in stone.

Hmm. Yes, that is one way to "solve" the paradox while keeping the perfect predictability. But I think it eliminates a crucial implicit element: conventional rules of time and causality.

(I don't mean to say that in a dismissive way. It is an interesting solution to the problem of free will.)

But you would have gotten $1,001,000 if you had made the other choice, since the boxes don't retroactively change their contents. And I would have gotten nothing if I had, for the same reason.

Not that I don't understand what you're saying. I do. Your argument is compelling. But so is mine. That's why it's a paradox.



Yes, it does. So have you, as I have tried to show by presenting the other argument. That's part of the character of the thought experiment: we cannot make all the parts fit, because ultimately they are not reconcilable.


you have (again) denied the premise of the game.

if i had chosen both i would have gotten what you got.

either the man is a predictor or he isnt. in this game he IS. if you dont take that into consideration you cant be right.

you are limiting your answers to what works in the real world. the game ISNT the real world. to deny the predictor is to change the game.

No, it isn't.

Imagine that I throw a football at a certain angle with a certain velocity. Ignoring air resistance, I can use Newtonian equations to predict the path and ultimate position of the football (almost) exactly.

Does the path of the football cause my prediction? Of course not. But my prediction is still perfect: it still comes true every time (assuming other factors don't interfere.) My prediction of the football's path does not come from information flowing backwards, but from my knowledge of the physical laws that determine the relationship between past and future states of the universe.

Determinism asserts that human decision-making is ultimately like that football (though far more complicated): it is determined by physical laws of causation in the same sense that the football's path is, and thus a truly exceptional being like the Predictor would be able to predict its results just as I can predict the path of a football.


That theory makes a really really good Predictor. However, the original premise required an infallible one. The key difference here is what you say, "assuming other factors don't interfere". If one of those other factors DID interfere (an alien from space was annoyed by your predictions and zapped the ball with a space ray that you had never heard of, for instance, and turned it into an elephant) then you would NOT be a perfect predictor, since your prediction would be wrong.

However, if a predictor is infallible, then, by definition, he is never wrong. Thus other factors could not interfere, because the predictor would have known they would. There are only two ways I can think of that this would be possible. Either the knowledge travels back to the predictor from the future, or the predictor is omniscient and knows absolutely everything about everything ever, which in my book ranks that guy pretty close to a god.

you have (again) denied the premise of the game.

This grows tiresome. You are repeatedly missing my point.

Yes, the Predictor is supposed to be infallible. But I don't care about that. Why should I? There are three things that matter to me. One, I can choose one box or both boxes. Two, neither box contains negative money. Three, the money in the boxes is already set--the fact of my choice will not change it. (The Predictor made a prediction, however perfect. Her prediction, her action, is in the past. It is already done.) If my aim is to maximize my monetary gain, it seems obvious that I should take both boxes: more is always better. Nothing about the Predictor's choice matters.

I cannot "choose" to change the past: the past is set. Just as my reasoning ignores the element of infallibility, your reasoning ignores the impossibility (usually explicit in the thought experiment, sometimes only implicit) of backwards causation.

Your reasoning is, of course, still solid--it is the logical and necessary conclusion from the recognition of the Predictor's infallibility. It is better to have $1,000,000 than $1,000. But mine is equally solid. It just springs from different premises of the thought experiment.

The problem, at heart, is that the premises are contradictory. That is why we arrive at opposite answers. Not because I am stubbornly refusing to abide by the rules.

or the predictor is omniscient and knows absolutely everything about everything ever, which in my book ranks that guy pretty close to a god.

He need not know everything. Just everything relevant to people's choices regarding the boxes.

About everything else, the only thing he need know is that it won't interfere.