A game can be rigged against any kind of belief, which does not make that belief necessarily fallible.
If Game 1 makes applying Belief 1 bad, then Game 1 has demonstrated the fallibility of Belief 1.
If Game 2 makes the past believing in Belief 2 bad, but not the present application of it, then Game 2 has not demonstrated the fallibility of Belief 2.
When I am in Phase 2 of Version 1 of the Newcomb Game, I have a belief.
I believe that I cannot affect how much money is in Box 2, right now in Phase 2. It follows logically from this belief that I should take both boxes. My action to do so does not impact the contents of Box 2.
So, applying my belief does not harm me here.
But, in the past, having believed in this belief did harm me, because that’s how the game is set up. I cannot change this, and I am not at fault for this. My belief is not at fault for this. My belief did not cause the game to be constructed as such.
So, let’s set up a different game.
The Anti-Newcomb Game
- Participants do not know about this game, even in theory, before entering the room.
- Before the participants have entered the room, the predictor has predicted whether they will OB or TB. The predictor has filled Box 2 accordingly.
- Box 2 contains $1M if the near-perfect predictor predicted the participant would TB. It contains $0 if it predicted the participant would OB.
- The predictor lies, and presents the participants with the normal Newcomb Dilemma, with the visible $1000 in Box 1, and the opaque Box 2.
The OBs have already lost compared to the TBs when they enter. They have been punished for their belief.
How do TBs deal with this game?
So, a TB finds themselves in Phase 2. They’ve just been lied to and told that they’re in the Newcomb Game.
They look at Box 2, and realize the $1M is already there, or already not there. Their heart sinks, because they realize that this realization probably means they’re a TB. And if they are, then the predictor probably did not put the $1M there.
But, there is nothing for them to do about the past. So, they accept that they lost before they even consciously played: that this game merely punished them for their belief in TBism/CDT, but it cannot punish their application of CDT… because applying CDT now, in Phase 2, is simply taking the $1000 that is there, despite the bad news it entails (because it does not cause a bad past… the bad past has already happened, or it hasn’t).
The news of what likely happened in the past… does not cause that to have happened the past.
When the TBs are done playing, most of them get a pleasant surprise. There was $1M in Box 2 after all. And now they have won $1M + $1000.
You see, TBs weren’t punished for their past (and thus unchangeable) belief in this game. In addition that, they weren’t punished for applying their belief in this game. No game punishes the application of their belief, because their belief is simply true.
In this game, TBs were lied to. But it didn’t matter. They didn’t need accurate knowledge regarding the correlations between their current actions and the past, because that correlation was never relevant to making a rational choice in the present anyways. Correlation is not causation. The present/future does not impact the past.
How do OBs deal with this game?
OBs find themselves in Phase 2. Their actions now cannot impact the contents of Box 2. If they were rational, they would recognize this. They would know it is not possible to risk the $1M. They either already have it, or they don’t
But they don’t recognize this. Instead, they use their OB magical thinking. They think, “I want to take one box.” Then they start feeling excited, because this is growing evidence that there is in fact $1M in that box.
This is false evidence, because it is based on false premises. That is not nice.
But it isn’t unfair, because TBs were faced with the same lie.
Now, the OB, by their nature, would probably grab only Box 2. They would be met with a nasty surprise. They get $0. But, they could have gotten $1000!
So here, unlike TBs in the original Newcomb Game, the OBs are being punished for the application of their belief.
Yes, they started out being punished for their belief… But they didn’t need to leave that $1000 on the table for no reason!
And TBs were punished for their belief in the Newcomb Game too! But TBs didn’t leave the $1000 on the table in that game. And they didn’t do it in this game either.
Now, by your logic, the Anti-Newcomb Game demonstrates the fallibility of OBism, because in this game, OBism loses.
Conclusion
Does this feel wrong? Unfair? Like the game was rigged against OB people? Well, there is no such thing, you say!
The Anti-Newcomb Game is rigged against OB thinking. TBs will usually be guaranteed $1M before they’ve even made a decision, and OBs will not have this privelege.
But the Anti-Newcomb Game actually goes one step further, and punishes OBs for applying their OB belief.
The Newcomb Game does not punish TBs for applying their belief. This is because TBs, by applying their belief, walk away with $1000 instead of $0. The Newcomb Game merely punishes them for having had that belief in the past, by making the $1M not even be attainable in Phase 2.
And the Anti-Newcomb Game punishes OBs by making the $1M not even attainable in Phase 2 for OBs instead, due to their past, now unchangeable belief. But most OBs, by their nature, will forego the $1000. They did not have any rational reason to do so, but they of course thought they did. The Anti-Newcomb Game starts off by punishing OBs for having their belief, but it also punishes them for applying it.
AND SO DOES THE NEWCOMB GAME! You see, even the Newcomb Game punishes OBs by applying their belief. By the time OBs have reached Phase 2 of the Newcomb Game (V1 specifically), they could have grabbed that extra $1000, and had they been rational, they would have done so. There would have been no risk to their $1M, because it was already won in Phase 1, through no merit of their own (it was due to a disposition they had, that they weren’t even aware of, because they were not aware of the game, by premise 8 in the OP).
So we have the following:
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The Newcomb Game punishes TBs for having their TB-belief in Phase 1.
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The Newcomb Game rewards TBs for applying their TB-belief in Phase 2.
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The Newcomb Game rewards OBs for having their OB-belief in Phase 1.
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The Newcomb Game punishes OBs for applying their OB-belief in Phase 2.
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The Anti-Newcomb Game rewards TBs for having their TB-belief in Phase 1.
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The Anti-Newcomb Game rewards TBs for applying their TB-belief in Phase 2.
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The Anti-Newcomb Game punishes OBs for having their OB-belief in Phase 1.
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The Anti-Newcomb Game punishes OBs for applying their OB-belief in Phase 2.
I ask you, what are the invariants here?
The application of the OB-belief in Phase 2 is ALWAYS punished.
The application of the TB-belief in Phase 2 is ALWAYS rewarded.
This demonstrates why TBism is rational, and OBism is irrational. But in some games, OBs will outperform TBs. Why? Because some games can reward the past holding of the OB-belief, and thus equivalently, these games punish the past holding of the TB-belief.
If this rewarding/punishing of past holding of belief outweighs the rewarding/punishing of later application of belief, then the OBs will outperform the TBs. Whoop-te-doo!
It does not matter if you can construct a game that punishes me for having had the TB belief. I can construct a game that does the opposite.
We have to ask, which belief wins according to application?
It is impossible to punish the application of TBism, or CDT, because it is based on nothing but truth. It is based on the unidirectionality of causation, and the non-conflation of correlation and causation.
Equivalently:
It is impossible to reward the application of OBism, or FDT/LDT/EDT, because it is based on some falsity. It is based on the conflation of correlation and causation, and possibly the bidirectionality of causation.
I know it is counter-intuitive for me to say that TBism is rational despite it being a belief correlated with loss in the Newcomb Game.
But if that is impossibly counter-intuitive to you, then it should also be impossible for OBism to be rational, because it is a belief correlated with loss in the Anti-Newcomb Game.
The predictor lying doesn’t change a thing, because the predictor lies to both the TBs and the OBs in the Anti-Newcomb Game. They both face the same challenge of deception, and the same psychological pressure. One of them was fucked from the start, but they could have made the best of it. They did not, because they left the $1000 on the table. Most of them, at least.
Contrast this with the Newcomb Game. TBs and OBs both face the same challenge. One of the was fucked from the start, but they could have made the best of it. And they did! They took the damn $1000, instead of leaving with $0. Most of them, at least.
TBs make the best of it. OBs don’t. Some hypothetical games can be constructed to punish the past holding of the TB-belief. And some hypothetical games can be constructed to punish the past holding of the OB-belief.
But in all games where not conflating correlation with causation is important to the game, TB-ism / CDT will be rewarded, and equivalently, OB-ism / FDT/LDT/EDT will be punished.
Therefore, TB-ism is rational. TB-ism starts from a place of truth, and always achieves higher winnings when applied… TB-ism not always correlated with higher winnings in some games. But, that only happens when the game is rigged against TB-ism from before the decisions even begin!
CDT is a decision-theory, and it is the right one. It will always win when applied. In the Newcomb Game, it is not the application of CDT that loses; it is the past (and thus unchangeable) fact that the appliers of CDT happened to be likely adherents thereof before the decisions even started (which is Phase 1). Can you fault a decision-theory for “failing” when it is faced with the lack of decision-making impact on the most critical aspect? CDT cannot magic the $1M into Box 2, and FDT/LDT/EDT cannot either. But the game was made to create a correlation between FDT/LDT/EDT and winning at least $1M.
We can construct infinitely many such games, and infinitely many games that do the opposite. This does not change our definition of rationality.
And most expert decision theorists agree with me:
You can find this statistic on this interactive PhilPapers site. I am not appealing to expert opinion here because I think it somehow settles this.
Instead, I am saying that all this is about upholding a usable definition of rationality, one that accounts for the truth, and thus intuitively accounts for most realistic games (but nonetheless fully accounts for all games, just sometimes counter-intuitively so, to some).
And well, who has thought the most about all the consequences and all the unavoidable counter-intuitive consequences of both TB-ism and OB-ism? Expert decision theorists, of course.
Surveying philosophers in general, there is only slightly more people in favor of TBism than OBism, and TBism isn’t even a majority view among all the views for philosophers in general. But that’s just philosophers in general.