Newcomb's Paradox

Logic & Philosophy of Mathematics
442

I don’t talk about irrelevant scenarios unfortunately. Would you take the test or not?

443

It’s the exact problem we’ve been discussing, except instead of saying either “I choose to share” or “I choose to take it all” we push either a red or a blue button.

If you think that these are two different scenarios then you are very mistaken.

I don’t understand what you’re asking. The problem is ill-explained, unlike this very simple case of pushing a button and winning one of three possible monetary rewards.

444

It’s the exact problem we’ve been discussing, except instead of saying either “I choose to share” or “I choose to take it all” we push either a red or a blue button.

Fo-shur, fo-shur. We already did this song and dance, I told you the exact assumption you need and asked you if your scenario had the assumption and you created Game 1.5

So I’ll ask again, maybe this time you’ll be able to read it:

Is the process determining whether you can win at least $500 influenced causally by your choice or not? Just like in the Newcomb problem, the process determining whether you can win at least $1,000,000, i.e. the prediction isn’t influenced causally by your choice.

The problem is ill-explained

What’s unclear?

445

I have what might be a novel take. The paradox presumes determinism. After all there could be no predictor if determinism were not true. Moreover if we grant real choice, you get the absurd situation of there being a million dollars in box 2 if the player chooses OB and 0 if they choose TB.

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

446

Well that’s just not true. I predict that Team A will beat Team B at football because Team A are professional adults and Team B are children.

Does this require determinism? Does this deny free will?

447

If you are talking about the perfect predictor case then yes, there is somewhat of a contradiction. If the predictor is always correct and says X will happen then X will happen, so the player doesn’t have any choice so it’s a weird question to ask the player to choose. (But that’s not a novel take)

If the predictor isn’t perfect, then no. You can have (very good) predictors even in the real world.

448

It’s still not clear what you’re asking.

In the button-pushing case, does the clone going first or second determine whether or not my choice “causally influences” the reward?

If it did, does it matter? Would you argue that it is rational to push the red button if I go first, else it’s rational to push the blue button if I go second?

449

No.

In this case, but not in the football case, anyone may trivially change their mind and make a different choice.

450

It’s still not clear what you’re asking.

It’s your problem that isn’t clear. I want the equivalent of the prediction and the predictor putting the million in the box or not.

451

Okay, then I give $500 to a drug addict and $500 to a nun.

I predict that the drug addict will use it to buy drugs and that the nun will donate it to a charitable cause.

452

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.

453

it doesn’t matter. There is no logical or physical impossibility.

454

Then the two games are:

Game 1

  1. If my clone pushes the red button then $1,000 is placed in a blue box and $1,000,000 is placed in a red box
  2. If my clone pushes 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 my clone and I both push the red button then $1,000,000 is donated to charity
  2. If my clone and I both push the blue button then $1,000 is donated to charity
  3. If I push the red button and my clone pushes the blue button then $0 is donated to charity
  4. If I push the blue button and my clone pushes the red button 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
455

I commend you for the elaborate OP! Let me share some of thoughts I had.

You are thinking about it from a universal standpoint; but the critical factors of which box to choose is up to the particular nuances of the person’s knowledge, beliefs, and habits that the predictor is predicting.

For example, in 2.2, wouldn’t one’s knowledge of their own habits affect whether they should choose OB or TB despite them not knowing about the thought experiment during phrase 1? Viz., if:

  1. P is the prediction of a 99% perfect predictor about your choice given your past;
  2. You know that you constantly in the past choose to gamble on high volumes of money (even if it was irrational according to your standards); and
  3. According to your logic, it is irrational to gamble on the OB but offers an analogous payout to your past questionable gambling decisions;

Then:

  1. It is highly probable that you are a OB and that choosing TB will result in $1000 whereas OB will result in $1,000,000.

TB is not always the most decision with the highest probability of maximizing the money payout. Remember, P is the probability of the predictor guessing correctly, which is ~99% in both versions of your thought experiment; which means your prediction of yourself is the predictor, in effect, of which choice you should make. So your knowledge of yourself is what you gauge to determine in probability what such an agent would accurately predict about you.

Likewise, e.g., in version 2, the idea of being a OB during phase 1 but switching to a TB in phase 2 is not rational according to your own definition of rationality as having to do with maximizing outcomes; because a 99% accurate prediction of your choice would have an extremely high probability of predicting that you are posing as an OB and will choose TB, so you would end up getting $1000 in all probability by trying to trick the predictor into giving you $1,001,000.

Also crucially, we have to know what about a person a predictor would use to calculate which decision they will make. Presumably, these are the three main aspects of such a prediction: habits, beliefs, and desires.

For example, in version 2, if I go in fervently believing that I am a OB despite it being false; that would most likely result in the predictor predicting I will choose OB because strongly formed beliefs, even if they are utterly false, strongly predict how we will behave as humans. Each person’s most rational decision to make here depends heavily on what they are currently convinced by and not how they can try to manipulate the scenario to the best of their benefit. Paradoxically, the very act of trying to maximize the outcome in the way you described betrays the entire project; because it doesn’t maximize it from the viewpoint of totality. Going back to my example of the OB poser, this tactic actually is factored into the prediction of the predictor; so this kind of plan sabotages the whole project.

I would say which decision is more rational depends on those three aforesaid factors of the given person; and, for me, I would be a OB because I know that:

  1. Posing as a OB and then switching is self-undermining;

  2. Picking TB results in a significantly worse payout;

  3. Picking OB results in a much higher payout; and

  4. All of this reasoning is probably known to the 99% accurate predictor, so there is a good chance they will think I will choose OB.

Cheers,
Eudemian

456

Right, Game 1 is equivalent to my IQ test game so I am waiting for whether you take the test or not. I can try to present it the same way:

  1. If you have psychological troubles then you have psychological troubles.
  2. If you don’t have psychological troubles then you don’t have psychological troubles.
  3. If you take the test, then you get $1.
  4. If you don’t take the test, then you get $0.

With additional info: 99% of people who took the test have psychological troubles and 99% of people who didn’t take the test don’t have psychological troubles.

Game 2 still doesn’t clarify whether it satisfies the assumption or not.

457

That game is not equivalent. Me having psychological troubles has nothing to do with either a) the prediction or b) my choice. It’s as irrelevant as my hair colour.

It’s a red herring, and it will always be a red herring. You need to move on from this IQ test rubbish.

If you can’t determine that answer from the rules as stated then neither can I. Based only on those rules as stated, should you push the red button or the blue button?

And what if you don’t know which of Game 1 or Game 2 you are playing?

458

That’s not true. If you are a OB (i.e. the predictor predicted you’ll OB) then choosing TB will result in $1,001,000.

Indeed whatever knowledge you have of yourself, TB is the best strategy.

Also crucially, we have to know what about a person a predictor would use to calculate which decision they will make. Presumably, these are the three main aspects of such a prediction: habits, beliefs, and desires.

We don’t. They could do whatever they want, it doesn’t matter for the rational strategy in version 1 at least.

459

Me having psychological troubles has nothing to do with either a) the prediction or b) my choice. It’s as irrelevant as my hair colour.

That’s clearly false. Read the additional information:
99% of people who took the test have psychological troubles and 99% of people who didn’t take the test don’t have psychological troubles.

How could you say that this has nothing to do with your choice? Do you not see that people who don’t take the test don’t have psychological troubles.

If you can’t determine that answer from the rules as stated then neither can I.

If the creator of a game is as clueless about the game as someone trying to understand it then of what use is the game?

In game 1, which I understand, I push the blue button obviously. But also I think you made a mistake, pushing the red button should donate the content of the blue box not the red one (the $1,000 one). I take it as you meant the blue one.

460

You’re getting your logic very wrong here, as explained before.

  1. Most people who a) took the test b) took the test because c) they have psychological problems
  2. Most people who a) chose to share b) won exactly $500 because c) they chose to share

Both of these are true, but note the dissimilarity in structure. In (1), (c) is unrelated to either (a) or (b), whereas in (2), (c) is directly related to (a).

For (1) to be comparable to my game, you would have to say:

  1. Most people who a) chose to share b) chose to share because c) they won $500, or
  2. Most people who a) took the test b) have psychological problems because c) they took the test

But both (3) and (4) are false.

So, once again, this IQ test example is a red herring.

I’m not clueless about the game. I know exactly how the game works; it’s as described in steps (1) - (4). What I don’t understand is either a) what you’re asking for or b) why it matters.

As I see it, the only thing that matters is to reliably donate as much money as possible to charity, and to do that we push the red button.

No, I meant what I said. In this case, pushing the blue button means “take both boxes”.

461
  1. Most people who a) took the test b) took the test because c) they have psychological problems

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

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.

(c) is directly related to (a).

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

I know exactly how the game works; it’s as described in steps (1) - (4). What I don’t understand is either a) what you’re asking for or b) why it matters.

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?”.

No, I meant what I said. In this case, pushing the blue button means “take both boxes”.

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