Total Posts:14|Showing Posts:1-14
Jump to topic:

Newcomb's Paradox

dylancatlow
Posts: 12,242
Add as Friend
Challenge to a Debate
Send a Message
10/12/2016 8:13:39 PM
Posted: 1 month ago
Before one can talk about Newcomb's Paradox one must first talk about Newcomb's Problem, because Newcomb's Paradox is what results when one tries to answer Newcomb's Problem. Newcomb's Problem is a thought experiment in which one is asked to play a game for the chance to earn money. Upon agreeing to play one is presented with two opaque boxes, one of which either contains a million dollars or nothing (box A) and one which always contains a thousand dollars (box B). One has the option of either taking box A and forgoing the thousand dollars known to be inside of box B, or taking both boxes.

The person who decides whether or not box A contains a million dollars, let's call him the Predictor, makes up his mind in the following way: if he thinks you will only go for box A he will put a million dollars in box A, but if he thinks you will be greedy and go for both boxes he will leave box A empty. The predictor has a long and flawless track record of making accurate predictions; he has played this game with many others and never made a mistake. Although it's never specified how good of a track record he has, it's implied that his predictive ability could be put through any numbers of tests without error, so that the probability that he is merely a lucky guesser is arbitrarily small, or in other words as improbable as it could get without it being impossible. The problem you are asked to solve is: should you go for box A only, or go for both boxes? The paradox arises out of the fact that there seems to be sound arguments going in both directions. Logically, this shouldn't be. If it's rational to do one thing it's irrational to do the opposite.

The argument for taking only box A runs as follows: if I take box A the predictor has probably predicted this and has therefore left a million dollars in box A, in which case I will end up with a million dollars. But if I take both boxes the predictor has probably predicted this and has left box A empty, in which case I will only end up with a thousand dollars. Statically speaking, I will earn more money by going for box A only, so it's the better option.

The argument for taking both boxes runs as follows: when I make my decision either box A contains a million dollars or it contains nothing. If it contains a million dollars I can be greedy with no downside, so I should take the thousand dollars in box B, and if box A is empty, then the only way I will walk away with any money at all is by taking box B. Either way, I'm better off taking box B.

What I think the solution is:

If the universe evolves deterministically then there really is no paradox at all, as there's not even a choice to be made regarding which option to take. Instead of debating which option you ought to take, you can really only talk about which option you hope is made. Obviously, if one thinks the Predictor is the real deal, then one should hope that one only picks box A, because in that case the causal chain leading up to that decision would indicate to the Predictor that he should leave one million dollars in box A, whereas if you pick box B he can easily punish that decision. In other words, although at the time one makes one's decision the Predictor has "locked in" his decision and it can not change no matter what one does, one is not in fact free to deviate from the decision that was causally implied at the time the Predictor locked in his prediction, implying that the Predictor can punish you no matter what you do - indeed, you can only act in one way.

But let's say that the universe does not evolve deterministically. In that case, the Predictor can't base his decision on anything that has happened so far. The only way for him to reliably know what you will do is to look at what you do, implying that he can literally see the future as it unfolds. But in order for him to read the future so as to make his decision, he must know the prediction he makes, as it's part of the future. This implies that causality is running in both directions, and that what the Predictor is looking at is only a partial description of the future, which is retroactively filled in. The assumption that his decision is locked in at the time one exercises one's freedom is therefore false, so one should take box A only.
keithprosser
Posts: 1,895
Add as Friend
Challenge to a Debate
Send a Message
10/12/2016 10:16:10 PM
Posted: 1 month ago
The reason that a case can be made for both the one box and two box strategies is that there is a choice as to whether you imagine playing the game in 'Newcomb's world' or the 'real world'.

In Newcombs world there is such a thing as a (nearly) perfect predictor so you can rely on the prediction being correct implying the one-box strategy is best.

But in the real world perfect predictors do not exist so the two-box strategy is best.

If you imagine being transported to a parallel 'Newcombs world' of perfect predictors to play the game then you will go one way, if you imagine it more like a piece of this-world flim-flam you will go the other!

To summarise, I see this as a psychological curiosity rather than a logical one.
dylancatlow
Posts: 12,242
Add as Friend
Challenge to a Debate
Send a Message
10/12/2016 11:18:35 PM
Posted: 1 month ago
At 10/12/2016 10:16:10 PM, keithprosser wrote:
The reason that a case can be made for both the one box and two box strategies is that there is a choice as to whether you imagine playing the game in 'Newcomb's world' or the 'real world'.

In Newcombs world there is such a thing as a (nearly) perfect predictor so you can rely on the prediction being correct implying the one-box strategy is best.

But in the real world perfect predictors do not exist so the two-box strategy is best.

If you imagine being transported to a parallel 'Newcombs world' of perfect predictors to play the game then you will go one way, if you imagine it more like a piece of this-world flim-flam you will go the other!

To summarise, I see this as a psychological curiosity rather than a logical one.

Most thought experiments are not realistic. But so long as the situations they describe are logically possible, they can tell us something about the world we do live in. The sort of reasoning we use when thinking about thought experiments is really no different than the reasoning we use when thinking about the real world, and occasionally what's true in thought experiments reveals something about the abstract, rational structure by which we evaluate concrete affairs, and sometimes it takes unlikely and implausible arrangements to illuminate some aspect or principle of that structure.
keithprosser
Posts: 1,895
Add as Friend
Challenge to a Debate
Send a Message
10/12/2016 11:59:24 PM
Posted: 1 month ago
I don't disagree. From what I have read about Newcombs paradox the intresting thing is that people are split into one-boxer and two-boxer camps, despite having the same information and your OP correctly states the apparently sound arguments that appeal to one group and is rejected by the other.

As I see it, if rational people can draw different conclusion from a set of premises then there must be a hidden factor, and I think in this case it is that some people 'unconsciously' accept the notion of an nearly infallible predictor and some don't.

I think that there are other puzzles that are more to do with pure logic - the surprise exam puzzle for instance.
Furyan5
Posts: 1,228
Add as Friend
Challenge to a Debate
Send a Message
10/13/2016 3:21:59 PM
Posted: 1 month ago
At 10/12/2016 11:59:24 PM, keithprosser wrote:
I don't disagree. From what I have read about Newcombs paradox the intresting thing is that people are split into one-boxer and two-boxer camps, despite having the same information and your OP correctly states the apparently sound arguments that appeal to one group and is rejected by the other.

As I see it, if rational people can draw different conclusion from a set of premises then there must be a hidden factor, and I think in this case it is that some people 'unconsciously' accept the notion of an nearly infallible predictor and some don't.

I think that there are other puzzles that are more to do with pure logic - the surprise exam puzzle for instance.

I'd be interested to see how many one boxer's believe in free will.
keithprosser
Posts: 1,895
Add as Friend
Challenge to a Debate
Send a Message
10/13/2016 4:15:59 PM
Posted: 1 month ago
At 10/13/2016 3:21:59 PM, Furyan5 wrote:
At 10/12/2016 11:59:24 PM, keithprosser wrote:
I don't disagree. From what I have read about Newcombs paradox the intresting thing is that people are split into one-boxer and two-boxer camps, despite having the same information and your OP correctly states the apparently sound arguments that appeal to one group and is rejected by the other.

As I see it, if rational people can draw different conclusion from a set of premises then there must be a hidden factor, and I think in this case it is that some people 'unconsciously' accept the notion of an nearly infallible predictor and some don't.

I think that there are other puzzles that are more to do with pure logic - the surprise exam puzzle for instance.

I'd be interested to see how many one boxer's believe in free will.

Presumably very few.... but that might be by assuming people are rational which is not always a safe thing to do!
Furyan5
Posts: 1,228
Add as Friend
Challenge to a Debate
Send a Message
10/13/2016 4:23:21 PM
Posted: 1 month ago
At 10/13/2016 4:15:59 PM, keithprosser wrote:
At 10/13/2016 3:21:59 PM, Furyan5 wrote:
At 10/12/2016 11:59:24 PM, keithprosser wrote:
I don't disagree. From what I have read about Newcombs paradox the intresting thing is that people are split into one-boxer and two-boxer camps, despite having the same information and your OP correctly states the apparently sound arguments that appeal to one group and is rejected by the other.

As I see it, if rational people can draw different conclusion from a set of premises then there must be a hidden factor, and I think in this case it is that some people 'unconsciously' accept the notion of an nearly infallible predictor and some don't.

I think that there are other puzzles that are more to do with pure logic - the surprise exam puzzle for instance.

I'd be interested to see how many one boxer's believe in free will.

Presumably very few.... but that might be by assuming people are rational which is not always a safe thing to do!

That's my point. If predominantly determinist are one boxer's and free willer's are two boxer's then logic is not a determining factor. Unless we assume one of the two groups is illogical.
skipsaweirdo
Posts: 1,861
Add as Friend
Challenge to a Debate
Send a Message
10/16/2016 12:29:50 PM
Posted: 1 month ago
At 10/12/2016 10:16:10 PM, keithprosser wrote:
The reason that a case can be made for both the one box and two box strategies is that there is a choice as to whether you imagine playing the game in 'Newcomb's world' or the 'real world'.

In Newcombs world there is such a thing as a (nearly) perfect predictor so you can rely on the prediction being correct implying the one-box strategy is best.

But in the real world perfect predictors do not exist so the two-box strategy is best.

If you imagine being transported to a parallel 'Newcombs world' of perfect predictors to play the game then you will go one way, if you imagine it more like a piece of this-world flim-flam you will go the other!

To summarise, I see this as a psychological curiosity rather than a logical one.
Agreed. It is a reflection of who is or isn't a materialist, not who is logical.
dylancatlow
Posts: 12,242
Add as Friend
Challenge to a Debate
Send a Message
10/20/2016 7:18:50 PM
Posted: 1 month ago
At 10/19/2016 3:22:57 AM, Raisor wrote:
I'd flip a coin.

If the predictor can predict something as complex as the behavior of a human, don't you think he could predict (1) the fact that you would flip a coin to decide and (2) the outcome of the coin toss? The only advantage to flipping a coin would be if for some reason you had an innate bias towards picking the worse option.
Raisor
Posts: 4,458
Add as Friend
Challenge to a Debate
Send a Message
10/21/2016 1:44:03 AM
Posted: 1 month ago
At 10/20/2016 7:18:50 PM, dylancatlow wrote:
At 10/19/2016 3:22:57 AM, Raisor wrote:
I'd flip a coin.

If the predictor can predict something as complex as the behavior of a human, don't you think he could predict (1) the fact that you would flip a coin to decide and (2) the outcome of the coin toss? The only advantage to flipping a coin would be if for some reason you had an innate bias towards picking the worse option.

Haha true.

I think I agree with your analysis. If the predictor is legit, which seems baked into the premise, then it is just a matter of fulfilling your fate.

It reminds me of Calvinism, wherein only those predestined will go to heaven, but everyone strives to act righteous in hopes they are fulfilling their saintly fate. The conclusion may be foregone, box A may already be predicted, but you still need to act out the choice, since only by acting out the choice do you bear out the conclusion that you are the type of person to choose box A.

I see why the argument for choosing both boxes is compelling, but I really don't think it works if the predictor is as good as the premise makes it.
keithprosser
Posts: 1,895
Add as Friend
Challenge to a Debate
Send a Message
10/21/2016 4:50:49 AM
Posted: 1 month ago
One problem is the premises are a bit ambiguous about the predictor. If the predictor is 'magically' always right then one-box is the logical choice, but the premises allow for some doubt about the predictor being always right. In the real world a 'predictor' would do no better than chance, so two-box is the logical choice.

I think if you enter into the 'world' of the puzzle you should accept the predictor is genuine and go one-box. But if you found yourself on an actual TV show in this world you should possibly go two-box to be guarantee some prize, but I'd probably go one-box anyway because that gives you a fair chance of a big money big payoff at the risk of losing out on a much smaller prize.
dylancatlow
Posts: 12,242
Add as Friend
Challenge to a Debate
Send a Message
10/21/2016 6:13:27 PM
Posted: 1 month ago
At 10/21/2016 4:50:49 AM, keithprosser wrote:
One problem is the premises are a bit ambiguous about the predictor. If the predictor is 'magically' always right then one-box is the logical choice, but the premises allow for some doubt about the predictor being always right. In the real world a 'predictor' would do no better than chance, so two-box is the logical choice.

I think if you enter into the 'world' of the puzzle you should accept the predictor is genuine and go one-box. But if you found yourself on an actual TV show in this world you should possibly go two-box to be guarantee some prize, but I'd probably go one-box anyway because that gives you a fair chance of a big money big payoff at the risk of losing out on a much smaller prize.

It comes down to whether you think the ability to read the future is logically possible, which is to say higher than zero probability. If you think the chance is higher than zero, then it seems like at some point you would be forced to conclude that it's more likely that the predictor is the real deal rather than merely lucky, since the improbability of his "being lucky" can be made arbitrary small. It's effectively infinitely small.
Amoranemix
Posts: 520
Add as Friend
Challenge to a Debate
Send a Message
10/21/2016 6:35:59 PM
Posted: 1 month ago
- dylancatlow 1
But let's say that the universe does not evolve deterministically. In that case, the Predictor can't base his decision on anything that has happened so far. The only way for him to reliably know what you will do is to look at what you do, implying that he can literally see the future as it unfolds.
Why does it imply that ?

There are two similar questions associated with the paradox :
1. What decision would be the most in your interest ?
2. Which decision would be the wisest ?

The two questions are the the same. The first asks for a best decision independent of what you know. The second asks for a decision based on what you know, i.e. based on evidence. The two are not the same, as evidence may point in the wrong direction.

What the answers to those two questions are depends. I follow keithprosser in that a distinction should be made between the real world and the hypothetical scenario. In the real world you would have information that is missing in the hypothetical scenario (e.g. where you are, how much time you have, how the predictor communicates) and in the real world you may lack information that is given in the scenario.

Let's try to answer the questions for the hypothetical scenario.

The first question cannot be answered as it would require to know what is in the boxes, which cannot be deduced from the information provided. The main problem is that the nature and reliability is unknown. Nothing is said on its nature and only opinions are offered on its reliability. In addition, it is not clear whether the laws of nature in the scenario are the same as in the real world.

The second question cannot be answered. You find yourself in a situation where you are presented with overwhelming statistical evidence that either your decision will influence the past or that your behaviour is predictable where it shouldn't be. The latter almost impossible and I think the former is impossible. However, if it is possible, then for a good enough track record, it would be more likely the predictor is able to make such a prediction than that it would have guessed luckily. It is however not feasible to work out how good that track record needs to be.

For the real scenario :

For the first question there is no significant difference between the two scenarios.

The second question can also not be answered as in the real world there are plenty of other possibilities besides an extreme stroke of luck and a clairvoyant predictor : you are on candid camera, box A contains a million dollars and box B a bomb, you memory has been altered, you are dreaming, etc.

- dylancatlow 13 to keithprosser
It comes down to whether you think the ability to read the future is logically possible, which is to say higher than zero probability. If you think the chance is higher than zero, then it seems like at some point you would be forced to conclude that it's more likely that the predictor is the real deal rather than merely lucky, since the improbability of his "being lucky" can be made arbitrary small. It's effectively infinitely small.
Predicting the future is possible, but is a lot more difficult than 'predicting' the past. However, according to quantum physics one cannot predict the future without influencing that future. The predictor would therefore have to influence you, but not necessarily to the extent of changing your choice.
The earth does not belong to man; man belongs to the earth.