Newcomb's Paradox

Logic & Philosophy of Mathematics
522

Yes but as you say the premises aren’t true so why consider the scenario? Why does it matter that rational agents all get $1,000 in your scenario?

523

Because it establishes the most rational action. If two-boxing is the most rational action then the agent would two-box even if (1) and (2) are true. The agent wouldn’t two-box if (1) and (2) are true. Therefore two-boxing isn’t the most rational action.

524

No one agrees with the premise “If TB is the rational choice then TB is also the rational choice when (1) and (2) are true”

The perfect predictor case is problematic as I have explained and if we ignore the problems then sure OB is the rational choice.

525

The prediction is only imperfect if either:

  1. An agent can take the least rational action
  2. The predictor can predict that the agent will take the least rational action

The fact that if both (1) and (2) are false then one-boxing is the most rational action is proof that two-boxing is the least rational action. As such we can rephrase the above:

The prediction is only imperfect if either:

  1. An agent can two-box
  2. The predictor can predict that the agent will two-box
526

Sure the predictor can only fail if everyone doesn’t act the same way or if the predictor can fail. This does not say anything about the best strategy in the Newcomb problem.

527

You’re ignoring the important point, which is that if a) everyone takes the most rational action and if b) everyone is predicted to take the most rational action then c) everyone will (and be predicted to) one-box. Therefore, one-boxing is the most rational action.

It is only possible for people to make different choices if it’s possible for people to irrationally two-box, and it is only possible for people to be predicted to make different choices if it’s possible for people to be predicted to irrationally two-box.

Introducing this imperfection in the prediction doesn’t switch the most rational action. You’ve just allowed for people to be irrational and two-box.

528

You’re equivocating on “least rational”, TB is the least rational “choice” in the perfect predictor case. So you haven’t shown what’s the least rational choice in the non-perfect case

Introducing the imperfection does change everything, first the problem becomes coherent.

529

So, we allegedly have two scenarios:

Perfect predictor

  1. The agent will take the most rational action (one-boxing)
  2. The predictor is always correct that the agent will take the most rational action (one-boxing)

Imperfect predictor

  1. The agent will take the most rational action (two-boxing)
  2. The predictor is almost always correct that the agent will take the most rational action (two-boxing)

Is this correct?

530

That’s good enough for me.

531

Then do you not accept that (3) follows?

  1. The agent will take the most rational action (two-boxing)
  2. The predictor is almost always correct that the agent will take the most rational action (two-boxing)
  3. Therefore, the agent will almost always win $1,000

Or to phrase this in the first person:

  1. I will take the most rational action (two-boxing)
  2. The predictor is almost always correct that I will take the most rational action (two-boxing)
  3. Therefore, I will almost always win $1,000

And as a parallel:

  1. I will take the least rational action (one-boxing)
  2. The predictor is almost always correct that I will take the least rational action (one-boxing)
  3. Therefore, I will almost always win $1,000,000
532

Sure. Just like you will take the IQ test and almost always have psy troubles.

And keep in mind the parallel is changing the fact that the agent was rational (i.e. was predicted to TB).

533

Then you’ve agreed with my second post, which you originally disagreed with.

And this is why one-boxing is the most rational choice and two-boxing the least rational choice.

It’s not just like it. In the above the arguments are valid; the conclusion is true because the premises are true. My reward is a direct consequence of both (a) choosing to one/two-box and (b) being predicted to one/two-box. Even your reasoning requires this to be true.

This is unlike your IQ test because having psychological troubles is not a consequence of taking the test.

534

Yes I agreed because as I said, you’re changing the situation in the parallel. I took it as two different “I”. If I wasn’t supposed to then yeah it’s not true just like I replied the first time.

The million isn’t a consequence of your choice of boxes. I hope you realize this.

535

I haven’t changed anything. It’s very simple. All of these are valid arguments:

Argument A

  1. I will one-box
  2. I will almost certainly be predicted to one-box
  3. Therefore, I will almost certainly win exactly $1,000,000

Argument B

  1. I will two-box
  2. I will almost certainly be predicted to two-box
  3. Therefore, I will almost certainly win exactly $1,000

Argument C

  1. I will one-box
  2. I will almost certainly be predicted to two-box
  3. Therefore, I will almost certainly win exactly $0

Argument D

  1. I will two-box
  2. I will almost certainly be predicted to one-box
  3. Therefore, I will almost certainly win exactly $1,001,000

But, as per the premise of the experiment, if “I will one-box” is true then “I will almost certainly be predicted to one-box” is true, and if “I will two-box” is true then “I will almost certainly be predicted to two-box“ is true, and so only Arguments A and B are applicable to the problem.

Therefore, we are left with:

  1. If I will one-box then I will almost certainly win exactly $1,000,000
  2. If I will two-box then I will almost certainly win exactly $1,000

This is the proof that it is most rational to one-box.

536

The (3) of the arguments don’t even get you to conclude that OB is the rational choice. To see if you are genuine or not, respond with yes/no:

Can I make the same arguments in the IQ test problem?

537

That part comes later. I’ve cleaned up the second half of that post to make it clearer.

What’s the argument? I assume it takes this form:

  1. I will take the IQ test
  2. ?
  3. Therefore, I will almost certainly have mental health problems

You tell me what your second premise is and I’ll tell you if it’s true, if the argument is valid, and if it’s at all comparable to my arguments.

538

(2) is “I will almost certainly have psychological troubles”

539

So your argument is this?

  1. I will take the IQ test
  2. I will almost certainly have psychological troubles
  3. Therefore, I will almost certainly have psychological troubles

Firstly, is (2) true?

Secondly, unlike my arguments, this argument begs the question because premise (2) is the same as the conclusion (3).

Thirdly, (1) is doing nothing here, whereas it plays an essential part in my arguments.

540

It’s the exact same logic as your argument.

541

No it’s not.

This is my argument:

  1. I will one-box
  2. I will almost certainly be predicted to one-box
  3. Therefore, I will almost certainly win exactly $1,000,000

This is your argument:

  1. I will take the IQ test
  2. I will almost certainly have psychological troubles
  3. Therefore, I will almost certainly have psychological troubles

Notice that my (2) and (3) do not say the same thing, whereas your (2) and (3) do say the same thing. For my argument to be the same as your argument my argument would have to be:

  1. I will one-box
  2. I will almost certainly win exactly $1,000,000
  3. Therefore, I will almost certainly win exactly $1,000,000

But this isn’t my argument.