Newcomb's Paradox

[Michael]

@Suny

Who said this? Me? Where did you get this?

You are clearly trying to argue this:

1. It is true that 99% of people who take the test have psychological problems
2. It is not true that if I take the test then there is a 99% chance that I have psychological problems
3. Therefore (1) does not justify not taking the test

I am explaining that (1) is not the same as it being true that 99% of people who choose to share win $500. The connection between choosing to share and winning $500 is very different to the connection between taking the test and having psychological problems.

Hence your IQ test example is a red herring that does not refute my argument.

@Suny

Your (2) is also new. Was that always the setup? Why did some people who shared didn’t get exactly $500? Cause if people got $500 because they chose to share then they should also get $500.

Choosing to share is a necessary even if not sufficient condition to win exactly $500. Whereas choosing to take the test is neither a necessary nor a sufficient condition to have psychological problems.

Hence your IQ test example is a red herring that does not refute my argument.

@Suny

What does that mean? do you mean causally related, i.e. a) causally influences c) or the other way around?

I mean that in (2), (a) and (c) are the exact same thing: “chose to share”. This is unlike (1), where taking the test and having psychological problems are completely different things.

Hence your IQ test example is a red herring that does not refute my argument.

@Suny

I am testing if your game is equivalent to the Newcomb problem, how would it not matter? What do you not understand in what I am asking? I talked about causal influence and I said the simple version of “what’s the equivalent of the prediction?”.

The clone’s choice is the prediction. I’ll rephrase both games to replace the clones with the prediction if it’s confusing you.

Game 1

1. If I am predicted to push the red button then $1,000 is placed in a blue box and $1,000,000 is placed in a red box
2. If I am predicted to push the blue button then $1,000 is placed in a blue box and $0 is placed in a red box
3. If I push the red button then the contents of the red box are donated to charity
4. If I push the blue button then the contents of both boxes are donated to charity

Game 2

1. If I push the red button as predicted then $1,000,000 is donated to charity
2. If I push the blue button as predicted then $1,000 is donated to charity
3. If I push the red button as not predicted then $0 is donated to charity
4. If I push the blue button as not predicted then $1,001,000 is donated to charity

I say that:

1. If I know I’m playing Game 1 then it is rational to push the red button
2. If I know I’m playing Game 2 then it is rational to push the red button
3. If I don’t know which game I’m playing then it is rational to push the red button

There is no difference between these games. It doesn’t matter if the monies are put in boxes before I make my choice or if a lump sum is just donated after my choice.

@Suny

In what you wrote, pushing the red button gives $1,000 to charity whether the blue box is filled or not.

That’s not what I wrote? I can only recommend you read it again.

[Suny]

The connection between choosing to share and winning $500 is very different to the connection between taking the test and having psychological problems.

I am waiting for the great difference.

Choosing to share is a necessary even if not sufficient condition to win exactly $500. Whereas choosing to take the test is neither a necessary nor a sufficient condition to have psychological problems.

Right so the equivalent claim would be:

2. Most people who didn’t take the test don’t have psychological troubles and win $0 because they don’t take the test.

I see no problem with that.

I mean that in (2), (a) and (c) are the exact same thing: “chose to share”. This is unlike (1), where taking the test and having psychological problems are completely different things.

I made the actual equivalent claim and it works.

There is no difference between these games.

Now there isn’t indeed. So blue button it is.

That’s not what I wrote? I can only recommend you read it again.

I checked and yeah it seems I misread. I am sorry.

[Michael]

@Suny

Now there isn’t indeed. So blue button it is.

You’re flip-flopping.

These were the original four games. You accepted that in Game 3 it is rational to choose the red box, but denied that Game 1 is equivalent to Game 3.

This new Game 1 and Game 2 is equivalent to the original Game 1 and Game 3.

@Suny

I am waiting for the great difference.

I have explained it several times, very clearly here.

[Suny]

You accepted that in Game 3 it is rational to choose the red box, but denied that Game 1 is equivalent to Game 3.

Nope, I never discussed the Game 3 from the post you linked:

@Michael

Game 3

1. There is an empty red box and an empty blue box
2. You are asked to choose between either a) the red box or b) the blue box
3. If you chose (a) and were predicted to choose (a) then you win $1,000,000
4. If you chose (b) and were predicted to choose (b) then you win $1,000
5. If you chose (a) and were predicted to choose (b) then you win $0
6. If you chose (b) and were predicted to choose (a) then you win $1,001,000

What I said were different games (in this comment) were the games from this comment, Game 3 was:

@Michael

Game 3

1. There is an empty red box and an empty blue box
2. You are cloned
3. You are asked to choose between either a) the red box or b) the blue box
4. The clone is asked to choose between either a) the red box or b) the blue box
5. The clone is destroyed
6. If you both chose (a) then you win $1,000,000
7. If you both chose (b) then you win $1,000
8. If you chose (a) and your clone chose (b) then you win $0
9. If you chose (b) and your clone chose (a) then you win $1,001,000

So you’re getting confused with your thousands of Game 1/2/3. These new Game 1 and Game 2 are indeed equivalent to Game 1 and Game 3 from the comment you posted though.

I have explained it several times, very clearly here.

You said this and I replied with the equivalent statement in my version which was also true so you haven’t pointed to any difference.

[noAxioms]

@hypericin

The paradox presumes determinism. After all there could be no predictor if determinism were not true.

I contest this. Determinism is phenomenally not true (nobody will ever be able to predict when the nucleus will decay), but predictions can nevertheless be made. A computer program designed to compute the first 100 digits of pi will produce the same digits each time. It’s incredibly predictable despite probably utilizing quantum weirdness to implement the function. Some system are simply not particularly sensitive to fundamental uncertainty, and others are. Humans, in the short term, are like the computer, made of all components that are designed to minimize that uncertainty, so given full knowledge of a human state, that state will evolve over the short term quite predictably. That assumption I do admit is being made. It has nothing to do with determinism.

Moreover if we grant real choice

I think you mean ‘free choice’. I have real choice (not being compelled to make a particular decision). I doubt that I have most people’s definition of free choice, and I don’t know yours.
If we didn’t have real choice, we’d not have evolved brains at all to make better ones, instead letting fate choose what we had no control over in the first place.

So I’m wondering if the paradox could be worked into an argument for free will?

I invite you to describe how free will can be successfully leveraged in such a way that preserves the premises of the Newcomb scenario, and improves on the outcome over utilization of deterministic (rational) methods.

Remember, the alternative to determinism is randomness. That’s pretty much the only tool available to you without violation of physics, and certainly without violation of the Newcomb description.

@hypericin

anyone may trivially change their mind and make a different choice.

Actually they can’t. Change mind, sure, but as discussed, that’s just part of deliberation, and the box contents are not in any way a function of the deliberation. One cannot make a different choice since only one choice can be made. The rules don’t allow take-backs, which would be akin to peeking inside the opaque box before making your choice to add the other box to it or not.

The OP is actually pretty vague about how one is allowed to go about taking both boxes. It should be “if you want both, take the transparent one first”. This is a nit. We know what the rules mean.

@hypericin

especially when people might intentionally act against their own impulse to fool the predictor.

We presumed a goal of maximizing utility. Yes, I’ve brought up a different goal of messing with the predictor, which is quite easy to do, but it gets you less money. But if everybody does this, his 99% prediction record is going to tank.

@Suny

@noAxioms

You cannot be predisposed to OB and then choose TB

Why do you (and Pierre too) add your own assumptions to the problem

I will alter my statement then. 99% of the time (or whatever reliability we’ve assigned to the predictor), one cannot be predisposed to OB and then choose TB.

This seems to follow directly from the statement of the Newcomb scenario. If you disagree with this, then tell me a different assumption that is still consistent with the wording.

@Suny

[Why do you (and Pierre too)] change the fundamental question we try to answer

This question leaves unspecified what you think the fundamental question is, which, per the OP, seems to be “Given that the goal is to maximize your payout, which choice should be made?”. I cannot answer if you think the question is something other than that. You’d need to tell me the actual question and justify why you think it’s more fundamental.

You clearly don’t believe there is any choice to have at this point, everything has been determined by the predisposition.

There is very much choice, as there are two options and I’ve not been forbidden to take either of them. The contents of the opaque box is indeed determined by the predisposition.
So you got at least one belief wrong, and one of them only half right, since no mention of the box contents was made.

My conclusion is that based on what you’ve posted you simply don’t comprehend what was spelled out by either of us. Maybe you did, but chose to post as if you hadn’t.

@TheEudemian

your prediction of yourself is the predictor, in effect, of which choice you should make.

I must disagree, per my comments above. It is the choice made, and not any self-prediction of my choice, that the predictor is interested in. Hence knowledge of self is irrelevant, since if you know you’ll OB and then you choose otherwise, you just don’t really know yourself, do you?

@TheEudemian

Also crucially, we have to know what about a person a predictor would use to calculate which decision they will make.

Various methods have been suggested as to how this might work, but in the end, the only thing that seems to matter is that however the predictor does its thing, it works. So I again contest ‘crucially’.

Posing as a OB and then switching is self-undermining

Not to mention self contradictory. The predictor, if nothing else, can easily detect is intent to deceive, something a true OB type would not do.

@TheEudemian

Picking TB results in a significantly worse payout;
Picking OB results in a much higher payout

This wording has strong connotations of retrocausality. The choice does not determine the payout. Something before the prediction is made does.

Do the initials E.S. mean anything to you? Just a hunch.

[Pierre-Normand]

@hypericin

I have serious doubts that in the real world prediction could get anywhere close to perfect, especially when people might intentionally act against their own impulse to fool the predictor. And people change their mind about all sorts of things, let alone paradoxical puzzles.

The Newcomb problem remains paradoxical (or, at least, controversial) even in an indeterministic world where the predictor is necessarily fallible. That’s because the agent isn’t being asked to defeat the predictor’s prediction. Rather, they’re being asked how to maximise their expected reward. An agent who somehow managed to maximally falsify the prediction by being unpredictable (whether through randomisation or the exercise of contra-causal “free will” in the libertarian sense) could do no better than choosing randomly and winning $1,000,000 half the time.

A one-boxer would deem it clearly preferable to act predictably and secure $1,000,000 most of the time (or, at least, slightly more than 50% of the time) assuming a linear relationship between monetary gain and utility. And a two-boxer would still deem the agent who one-boxes irrational each time they do so, since the dominance argument doesn’t depend on the predictor being accurate at all. It applies even against a coin-flipping predictor. So neither side’s analysis turns on whether determinism is true. What generates the paradox is a disagreement about the scope of the agent’s causal efficacy: specifically, whether the agent’s rational grounds bear causally on the box contents or not, and that disagreement survives any amount of indeterminism.

That said, I think you’re onto something important in sensing a connection between the Newcomb problem and questions about free will and determinism albeit just not quite in the way you’ve framed it. The paradox doesn’t presuppose determinism, but the correct analysis of it does require getting clear about the relationship between the predictability of rational agency and its genuine causal efficacy, which is precisely the territory that debates about free will and determinism occupy. I plan to say more about this in my forthcoming reply to @Suny.

[Michael]

Both Game 3s are the same.

Game 3a

1. There is an empty red box and an empty blue box
2. You are asked to choose between either a) the red box or b) the blue box
3. If you chose (a) and were predicted to choose (a) then you win $1,000,000
4. If you chose (b) and were predicted to choose (b) then you win $1,000
5. If you chose (a) and were predicted to choose (b) then you win $0
6. If you chose (b) and were predicted to choose (a) then you win $1,001,000

Game 3b

1. There is an empty red box and an empty blue box
2. You are asked to choose between either a) the red box or b) the blue box
3. Your clone is asked to choose between either a) the red box or b) the blue box
4. If you chose (a) and your clone chose (a) then you win $1,000,000
5. If you chose (b) and your clone chose (b) then you win $1,000
6. If you chose (a) and your clone chose (b) then you win $0
7. If you chose (b) and your clone chose (a) then you win $1,001,000

The clone is just the tool used to make the prediction in Game 3b. It may in fact be the tool used to make the prediction in Game 3a, which is left unspecified.

In Game 3b it is most rational to choose the red box and so in Game 3a it is most rational to choose the red box.

[Suny]

@Michael, let’s make the analogy more formal. Here’s the Newcomb problem:

	Prediction OB	Prediction TB
OB	$1,000,000	$0
TB	$1,001,000	$1,000

Here’s the IQ test problem:

	Have psy troubles	Don’t have psy troubles
Avoid IQ test	$0 + psy troubles	$0
Take IQ test	$1 + psy troubles	$1

Again 99% of people avoiding the test don’t have psy troubles and 99% of people taking the test have psy troubles.

Do you avoid or take the test? I claim Avoid = OB, take = TB.

[Michael]

I take the test to earn the $1.

This is a red herring. The comparison you keep trying to draw between the two games doesn’t hold, as I keep explaining.

If I know I’m playing Game 3a then I take the red box. If I know I’m playing Game 3b then I take the red box. If I don’t know which of Game 3a or 3b I’m playing then I take the red box. The games are equivalent, and it’s irrational to take the blue box in Game 3b.

[Suny]

99% of the time (or whatever reliability we’ve assigned to the predictor), one cannot be predisposed to OB and then choose TB.

This isn’t part of any formulation of the Newcomb problem and makes little sense. You would need to clarify this.

This question leaves unspecified what you think the fundamental question is, which, per the OP, seems to be “Given that the goal is to maximize your payout, which choice should be made?”. I cannot answer if you think the question is something other than that. You’d need to tell me the actual question and justify why you think it’s more fundamental.

The (fundamental) question is what box to pick… obviously.

There is very much choice, as there are two options and I’ve not been forbidden to take either of them.

Ridiculous backtracking, it’s too late unfortunately.

[Suny]

The clone is just the tool used to make the prediction in Game 3b. It may in fact be the tool used to make the prediction in Game 3a, which is left unspecified.

In 3a, it’s clear the prediction was made before your choice (and therefore isn’t causally influenced by the choice), not in 3b so no both are not equivalent without further assumptions on 3b.

[Suny]

The comparison you keep trying to draw between the two games doesn’t hold, as I keep explaining.

Explain why. What’s the difference?

[Michael]

@Suny

In 3a, it’s clear the prediction was made before your choice, not in 3b so no both are not equivalent without further assumptions on 3b.

In 3b it doesn’t matter if the clone makes the choice before or after me. It is still always rational to take the red box. If it takes it before then it is used as the prediction. In fact, even if it takes it after it can be used to make the prediction, so long as the person who makes the prediction hasn’t seen the choice I made.

[Suny]

I am just saying both aren’t equivalent without further assumptions. Yes or no?

[Michael]

They are equivalent.

If the clone makes the choice after me then I ought take the red box.

If the clone makes the choice before me then I ought take the red box.

If the clone makes the choice before me and if his choice is used to predict my choice then I ought take the red box.

If a super-intelligent computer is used to predict my choice then I ought take the red box.

If the money is placed in the boxes before I make my choice then I ought take the red box.

If the money is placed in the boxes after I make my choice then I ought take the red box.

If the money isn’t placed in the boxes but just given as a lump sump then I ought take the red box.

It is always going to be the red box. You are being deceived into thinking any of the above are different.

[Suny]

I am not asking whether you have the same opinion on the problems. I am asking whether they are equivalent. But it’s fine you won’t admit it, it doesn’t matter.

[Michael]

@Suny

I am asking whether they are equivalent.

And I am answering: YES.

It’s irrational to say that if the clone makes the first choice then you ought take the blue box, else if you make the first choice then you ought take the red box, and you’d be paralyzed by indecision if you don’t know which of you and the clone makes the first choice.

Whereas I can clearly say that I will always choose the red box — and I will almost certainly win $1,000,000.

[Suny]

Is there anything written in the game 3b description that implies that your choice doesn’t influence causally your clone’s choice and that the choice of your clone doesn’t influence causally your choice?

[Michael]

It’s implied. The clone is a separate person with free will (assuming that you have free will). You are in one room and your clone is in another room. There’s no communication or magic or psychic connection.

It’s just game theory. Your choice ought consider how you suspect the other player is most likely to reason, and you have every reason to suspect that the other player will make the same choice as you, given that he has the same knowledge, beliefs, desires, dispositions, and reasoning skills — and trying to do the opposite of what you suspect that he will do is self-defeating, given that he is almost certainly trying to do the same.

A rational person just ought accept that you are almost certainly going to make the same choice, so you ought make sure that this will result in the biggest reward.

[Suny]

It’s implied

And yet you weren’t able to tell me that at the time.

There’s no communication or magic or psychic connection.

Is this written in the description?