A full explanation to Newcomb's paradox.

by solomon alon3 min read12th Oct 202012 comments

-6

Newcomb's ProblemDecision TheoryRationality
Frontpage

Since I’ve read of Newcomb’s paradox on the sequences on less wrong, I’ve always thought there is something fundamentally wrong about timeless decision theory. I would end up coming up with an alternate explanation that seemed correct to me. I then searched it on Wikipedia and found that what I said was already said of course. But I’m still curios what the community thinks on the topic. 

Newcomb’s paradox according to Wikipedia is as follows.

There is an infallible predictor, a player, and two boxes designated A and B. The player is given a choice between taking only box B, or taking both boxes A and B. The player knows the following:[4]

  • Box A is clear, and always contains a visible $1,000.
  • Box B is opaque, and its content has already been set by the predictor:
    • If the predictor has predicted the player will take both boxes A and B, then box B contains nothing.
    • If the predictor has predicted that the player will take only box B, then box B contains $1,000,000.

The player does not know what the predictor predicted or what box B contains while making the choice.

To be clear when we say the predictor is infallible we can either mean that the predictor has not made a single mistake, over hundreds of witnessed occurrences or that we are dealing with a actual infallible predictor either way what I am going to say is valid.

There are four possible ways in which the predictor is making his predictions.

1. He’s not actually making any predictions and is cheating. This form of cheating can be either changing what’s in the box after you choose. Using mind control on you or any way of cheating the problem. either way if this is the case you should obviously choose just box B since your decision changes what’s in the box.

2. The predictor can in some way see the future. In this case you should obviously choose just box B because your choice affects the past since the predictor knowing the future reverses the casualty of time and what you do now actually changes what was their in the past without any paradox. 

3. The predictor is really good at figuring out personalities. This seems highly unlikely because all we would need would be for one person to come in with a dice or a coin, who has a personality of wanting to flip a coin to decide. However, they could be using tricks like only selecting people who they are extremely sure of. Either way, since the money is already in the box you should obviously choose both boxes since your choice in no way affects the past.

4. The predictor is running a full or partial simulation of the situation. In this case it depends on whether you are able to differentiate between real life and the simulation. Because if you know that you are the real-life person than you should obviously choose both since your choice affects nothing. It doesn’t affect what your simulation chooses and it doesn’t affect what is in the boxes. And if you’re the you in the simulation than you should just choose box B since your choice affects what is going to be in the box. The impossible part is that you have absolutely no idea if you are the you in the simulation or the real you. Since in order for it to be a exact simulation of you the simulation must also think it exists in the real world in order for it to be accurate, or else it would make a different choice then you since the choice you made is dependant on the knowledge that you’re the real you and the simulation would not have that. Therefore, you should choose box just box B since you might be the you in the simulation.

In the end I think the correct choice is to choose box B since I think 1 is the most likely followed by 4. With both 2 and 3 being extremely unlikely.

A huge difference between this and roko's basilisk is that the AI has no reason to think its in a perfectly accurate simulation and therefore has no incentive to torture people. Since what it does in the future cannot affect the past. While it seems like in newcomb's problem your decision now is affecting the simulations decision. It's can be looked at as the reverse, your simulations decision is deciding your decision. 

A Interesting corollary to newcomb's problem is the Psychological Twin Prisoner’s Dilemma. An agent and her twin must both choose to either “cooperate” or “defect.” If both cooperate, they each receive $1,000,000.1 If both defect, they each receive $1,000. If one cooperates and the other defects, the defector gets $1,001,000 and the cooperator gets nothing. The agent and the twin know that they reason the same way, using the same considerations to come to their conclusions. However, their decisions are causally independent, made in separate rooms without communication. Should the agent cooperate with her twin?

This problem at first glance seems to evade the solution I have previously proposed. Since each agent is trying to maximise their own utility as opposed to in the previous case where the person in the simulation is trying to maximise the real persons utility. This to me gets at the heart of the problem of choice. Since it would seem that the choice you make affects your twin since whatever you choose it changes what your twin does, yet you and your twin are causally independent. This also hints at even more annoying problem. What does it mean to choose if all choices are predestined.     

-6