Based on your discussion of agent types, you seem to be aware that two-boxers (apparently) make these assumptions: 1) that your decision at game time has no causal impact on the agent type at the time of prediction 2) that your agent type at the time of prediction causes the prediction
To see why the two boxers assume the first point, consider if it were false that two boxers assume this. Then it would mean that two boxers entertain the possibility that your decision at game time has a causal impact on the agent type you display at the time of prediction. But if your decision at game time causally impacts your agent type at the time of prediction, then by assumption #2, it would mean that your decision at game time causally impacts the very thing that causes the prediction, in which case two boxers would, by their own logic, commit to one boxing, since your decision to one box would causally impact your ability to get a million dollars. But they are in fact two boxers, so they must assume the first point after all.
As for why two boxers assume the second point, I don't think I'll get much pushback on the core idea, though maybe I could word it better. Basically, as you argued in your article, two boxers believe the predictor sizes your agent type up, and makes a prediction off of that.
OK, so now the big question is whether these assumptions are sound.
It seems quite intuitive that your decision at game time has no causal impact on your agent type at the time of prediction, because to believe otherwise would mean that a decision in the future has a causal impact on your agent type in the past. But the past is unchangeable. If the past is unchangeable, then future events cannot influence past events, for if they did, then the future could cause the past to change, which would contradict the notion that the past is unchangeable.
But notice, then, that the question of whether to one box or two box boils down to the more fundamental question of whether retro-causality is possible.
Quantum mechanics suggests that it might be. However, many interpretations of the evidence have been created precisely to sidestep the implication that retro-causality is a feature of the universe. So now a two boxer has to believe those interpretations of quantum mechanics that are consistent with ruling out retro-causality. And this is totally a feasible thing to do. I just wanted to bring this up as an empirical basis outside of philosophizing to suggest that retro-causality is possible (and hence that the first assumption of two boxers is mistaken).
To really see that assumption #1 might be mistaken, imagine someone is a two-boxer agent type at the time of prediction. (By assumption #2, this means that the prediction is made accordingly to only place a total of $1000.)
Further imagine that this person who was a two boxer agent type at prediction time somehow decides to one box at game time anyway. Is it really possible to one box at game time even though you were a two boxer agent type at prediction time? I wager that, yes, this is completely possible because your agent type at game time could have evolved to be a different agent type at game time than the agent type you were at prediction time.
I mean, perhaps in the time they were mulling over which decision to make, they took the time to read some ardent one boxers' posts in these LessWrong forums, and became convinced to one box, maybe even because of this very post.
So it is possible for someone to one box despite having been, at prediction time, of the two boxing agent type.
But then, ask yourself this: if someone was the type of person who would look up information about Newcomb's problem, and furthermore have been the type of person who, upon examining the information that they looked up, would end up one boxing, then wouldn't that mean that they were of the one boxing agent type all along? Then that means that the act of choosing to one box caused them to be the type of person who was a one boxer all along!
"Not so fast," the two boxer says. The character traits that caused this person to not only seek out LessWrong forums, but also be receptive to being convinced by them, were present at prediction time, even if they hadn't been manifested yet. So that would mean that, contrary to our initial assumption, they were never truly a two boxer agent type to begin with. They always had the traits of a one-boxer-in-the-making.
And that is precisely my point. If the initially two-boxing agent-type player somehow one boxes anyway, then that decision rests on reasons that can eventually be traced back to something fundamental in their character as of prediction time. But then the very decision they make at game time reveals what agent type they were all along.
The two boxer might object by saying instead that you can't decide to do otherwise than what your agent type "initially" was. But if you believe this, then that's all the more reason to agree with me that your decision at game time reveals what agent type you were all along. But if your decision at game time reveals what agent type you were all along, then whatever decision you make ends up being who you were all along.
Based on your discussion of agent types, you seem to be aware that two-boxers (apparently) make these assumptions:
1) that your decision at game time has no causal impact on the agent type at the time of prediction
2) that your agent type at the time of prediction causes the prediction
To see why the two boxers assume the first point, consider if it were false that two boxers assume this. Then it would mean that two boxers entertain the possibility that your decision at game time has a causal impact on the agent type you display at the time of prediction. But if your decision at game time causally impacts your agent type at the time of prediction, then by assumption #2, it would mean that your decision at game time causally impacts the very thing that causes the prediction, in which case two boxers would, by their own logic, commit to one boxing, since your decision to one box would causally impact your ability to get a million dollars. But they are in fact two boxers, so they must assume the first point after all.
As for why two boxers assume the second point, I don't think I'll get much pushback on the core idea, though maybe I could word it better. Basically, as you argued in your article, two boxers believe the predictor sizes your agent type up, and makes a prediction off of that.
OK, so now the big question is whether these assumptions are sound.
It seems quite intuitive that your decision at game time has no causal impact on your agent type at the time of prediction, because to believe otherwise would mean that a decision in the future has a causal impact on your agent type in the past. But the past is unchangeable. If the past is unchangeable, then future events cannot influence past events, for if they did, then the future could cause the past to change, which would contradict the notion that the past is unchangeable.
But notice, then, that the question of whether to one box or two box boils down to the more fundamental question of whether retro-causality is possible.
Quantum mechanics suggests that it might be. However, many interpretations of the evidence have been created precisely to sidestep the implication that retro-causality is a feature of the universe. So now a two boxer has to believe those interpretations of quantum mechanics that are consistent with ruling out retro-causality. And this is totally a feasible thing to do. I just wanted to bring this up as an empirical basis outside of philosophizing to suggest that retro-causality is possible (and hence that the first assumption of two boxers is mistaken).
To really see that assumption #1 might be mistaken, imagine someone is a two-boxer agent type at the time of prediction. (By assumption #2, this means that the prediction is made accordingly to only place a total of $1000.)
Further imagine that this person who was a two boxer agent type at prediction time somehow decides to one box at game time anyway. Is it really possible to one box at game time even though you were a two boxer agent type at prediction time? I wager that, yes, this is completely possible because your agent type at game time could have evolved to be a different agent type at game time than the agent type you were at prediction time.
I mean, perhaps in the time they were mulling over which decision to make, they took the time to read some ardent one boxers' posts in these LessWrong forums, and became convinced to one box, maybe even because of this very post.
So it is possible for someone to one box despite having been, at prediction time, of the two boxing agent type.
But then, ask yourself this: if someone was the type of person who would look up information about Newcomb's problem, and furthermore have been the type of person who, upon examining the information that they looked up, would end up one boxing, then wouldn't that mean that they were of the one boxing agent type all along? Then that means that the act of choosing to one box caused them to be the type of person who was a one boxer all along!
"Not so fast," the two boxer says. The character traits that caused this person to not only seek out LessWrong forums, but also be receptive to being convinced by them, were present at prediction time, even if they hadn't been manifested yet. So that would mean that, contrary to our initial assumption, they were never truly a two boxer agent type to begin with. They always had the traits of a one-boxer-in-the-making.
And that is precisely my point. If the initially two-boxing agent-type player somehow one boxes anyway, then that decision rests on reasons that can eventually be traced back to something fundamental in their character as of prediction time. But then the very decision they make at game time reveals what agent type they were all along.
The two boxer might object by saying instead that you can't decide to do otherwise than what your agent type "initially" was. But if you believe this, then that's all the more reason to agree with me that your decision at game time reveals what agent type you were all along. But if your decision at game time reveals what agent type you were all along, then whatever decision you make ends up being who you were all along.