1. Introduction
@Michael, @noAxioms, @Pierre-Normand, @Sime, @TheEudemian, @Patterner, @Suny, @Pseudonym, @leo_starboy, @FlannelJesus
Unfortunately, I have to go off-site and return to the boring part of my life. This has been a very fun discussion so far, and I hope to return to it in the future.
Most people don’t change their mind on the Newcomb Paradox. Not after the first initial phase of discovering it, at least. In a way, we’re all engaged in a fool’s errand; the statistically-unlikely-to-succeed endeavour of changing each other’s minds.
Since we’re talking decision theory, I guess our decision to engage in this endeavour could be classified as rather low expected utility… 
And yet we do it, because we cannot bear letting declared falsities be unchallenged.
OBs look at those over-thinking, pseudo-intellectual, money-loathing, pretentious TBs, and they feel a rightful urge to correct what they perceive to be wrong.
TBs look at those under-thinking, pseudo-intellectual, money-crazed, confused OBs, and they too feel a righftul urge to correct what they perceive to be wrong.
The above adjectives are not my opinion of course. They are instead what is often felt by either side regarding the other. But both sides are united in two things:
- We want the truth.
- We want the money.
I am not accusing anyone of being overly emotional or angry in this thread. I simply commenting on the fact that this topic inspires so much anger and emotion in people. I myself have rarely gotten as frustrated and angry in philosophical discourse as I have in this conversation. I would understand it if my opponents have felt that way too at times in this thread.
Our passion here is good, but it also makes it harder to grasp the other side’s views.
As a TB, of course, I believe the OBs are mistaken about the nature of Version 1 of the Newcomb Game. In line with that view, I’d say they are the ones who would benefit the most from letting go of their emotions. And I don’t say this from a high horse.
I was an OB…
When I watched that linked-to Veritasium video for the first time, the answer was obvious. Who would I rather want to be?
A millionaire or a pretensious pseudo-intellectual who shoots themselves in the foot?
EDT’s expected utility calculations made perfect sense. “Of course we have to take the evidence our actions generate into account!” That was obvious, and of course it had to be right, because thinking that way made me a millionaire.
At this point, you could say I was playing Phase 1 of any V2 Newcomb Game potentially in my future very well.
I went to sleep as an OB that night.
I woke up as a TB. Really. It had been late at night, and I had gotten so angry at the TBers. But in the morning, I thought about it, and I saw the problem clearly. I saw I had suffered from outcome bias. That’s when I developed my understanding of the problem, and my definition of rationality had to evolve to account for the following fact:
Anyone can construct a hypothetical game that rewards irrationality before the decisions begin.
This fact is trivially true. You do not need to agree with me on WHAT is irrational, to see that that which is irrational remains irrational even in a game that rewards it… ASSUMING it rewards it BEFORE the DECISIONS begin…
This does not prove OBism is wrong. But it is a very important general fact. Irrationality remains irrationality, even if it is correlated with better outcomes in some games, assuming those games rewarded the irrationality before the decisions began.
Rational decision theory is all about the decisions you can make, after all. You cannot decide the past.
So, what do I want to do with this post? Well, I want to create a hub of links to all of my most important arguments, and then I want to add some extra arguments at the end.
2. Links to My Past Arguments
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The Time Travelling Rhetoritician (in same post as above)
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The Weak Anti-Newcomb Game (in same post as above)
In addition to this, I think the most important diagram I made is the one below here, as it really sums up the entire TB / CDT position, in my opinion.
The diagram is explained in What is P-determination?
I genuinely believe that if all the OBs in this thread read through all of those posts thoroughly, including the arguments in this post as well, then I think at least one OB would change their mind. Of course, I would never expect all that work from anyone for no reason.
But if any of you have lots of time on your hands, and you have the desire, I truly believe that a slow, back-to-back consumption of all of those arguments would change your mind.
With all of my main past arguments linked-to in one place, I will proceed to the last arguments I will offer in this thread, for now.
3. Irrelevant Knowledge
Let’s say we have a game G. In this game, there is an unknown U, and it has two possible values: a and b. U is not a variable, it is rather an unknown, but constant, thing/fact/number.
Now, is our knowledge regarding U relevant to our decision-making in the game G? Well, there’s a simple check.
- What is the rational decision if you know U = a?
- What what is the rational decision if you know U=b?
If the rational decisions in G remain the same in both scenarios, then all knowledge about U is irrelevant to rational decision-making in the game G.
Can we all agree on this?
3.1 Example
You are playing a game inside a room, and the single window has its curtains pulled together. The game is this:
The 3 Coins
You have 3 coins and a balance scale
Two coins are real. One is a fake that is slightly heavier. You are only allowed to touch two coins.
Your task is to figure out which coin is the fake one.
Now, let us see if we can find a U such that it is irrelevant to the game. Well, the curtains block your view of the weather outside. We have that U = Sunny Weather, or U = Not Sunny Weather.
The rational decision for how to play the 3-coin game is NOT changed whether U = Sunny Weather, or U = Not Sunny Weather.
So, all knowledge regarding the unknown U is rationally irrelevant to the 3-coin game.
4. Cheating the Newcomb Game
In the Newcomb Game, we have an unknown U. It is a very important unknown U. U is the amount of money in Box 2.
We can write this as U \in \{\$0, \ \$1\text{M} \}, but U is not a variable.
Instead, U is an unknown constant dollar amount, and we know its possible values as the elements of the set above.
Now, let’s ask ourselves, is knowledge about U rationally irrelevant knowledge?
Well, in the 3 coin game, we could find that out by pulling the curtains away, and seeing if it affected the rational decision in all possible scenarios: when it is sunny, and when it isn’t.
In both cases, the rational decision remained the same.
We can do the same thing for the Newcomb Game.
4.1 Alice the Cheater
Alice is in Phase 2 of Version 1 of the Newcomb Game. She is staring at the two boxes. She sees $1000 in one of them, and she looks at the mysterious Box 2.
She is unsure what to do. She laments, “Oh! If only I could know what was in Box 2!” The fear of losing the $1M by TBing is really stressing her out. Also, the fear of needlessly leaving $1000 on the table by OBing is also bugging her. She wants some security and clarity.
Little did the predictor know, she brought some magical glasses with her. Using them, she could look into Box 2. The predictor did not know of these glasses, and so it did not factor in to his prediction.
Alice puts them on and looks into Box 2. It contains… $0. So, she has learned that U = \$0.
What is the only rational decision now?
To say TBing is irrational here would be to say she could retro-causatively change the $0 into $1M. Or worse yet, it would be to say $0 > $1000.
So, Alice TBs, and she feels no regret. It wasn’t her fault that Box 2 contained $0, after all.
4.2 Bob the Cheater
Bob is in Phase 2 of Version 1 of the Newcomb Game. He is staring at the two boxes. He sees $1000 in one of them, and he looks at the mysterious Box 2.
He is unsure what to do. He laments, “Oh! If only I could know what was in Box 2!” The fear of losing the $1M by TBing is really stressing him out. Also, the fear of needlessly leaving $1000 on the table by OBing is also bugging him. He wants some security and clarity.
Little did the predictor know, he brought some magical glasses with him. Using them, he could look into Box 2. The predictor did not know of these glasses, and so it did not factor in to his prediction.
Bob puts them on and looks into Box 2. It contains… $1M. So, he has learned that U = \$1\text{M}.
What is the only rational decision now?
To say TBing is irrational here would be to say she could retro-causatively change the $1M into $0. Or even worse, it would be to say $1M > $1M + $1000.
So, Bob TBs, and he feels no regret. Why wouldn’t he take the extra $1000? It is free, after all.
4.3 But Cheating Gives an Edge!
So? The cheaters, using their advantage, rationally chose to TB. If the knowledge they gained was relevant, then what does it mean that all they used that extra knowledge for was to TB…
If all players who gain extra, illegal, relevant information all make the same decision, then that decision sounds like it is a very good one. If more information makes everyone take that decision in a one-move game, then the truth illuminates it as the best decision for everyone.
4.4 The Glasses Break the Premises!
It is true that it is a premise you cannot look into Box 2. But this does not prevent us from classifying U as irrelevant knowledge. We are just applying the definition from section 3.
Some may go further and say these magical glasses break the premise that the predictor is accurate 99% of the time. The predictor was not aware of the glasses, after all.
Well, if thousands of players had access to such glasses, then yes, the predictor would lose all its accuracy, because all OBs would TB.
But it does not logically follow from the mere conception of these glasses that many/all players have them.
We can say that only Alice and Bob had them, and taking into account the singular incorrect prediction it caused (Bob TBed instead of OBing), the predictor would still remain very accurate, and we could simply say the premise of 99% already takes into account that one, extra prediction failure.
These glasses are a logically innocent addition to the scenario. They do violate one premise, which is the ignorance premise, but it violates it on purpose, to show this premise was never rationally relevant.
The ignorance of U is rationally irrelevant because our thought experiment showed that all knowledge about U is rationally irrelevant.
4.5 Conclusion
Section 4 has shown that the money amount in Box 2 is, under the definition in section 3, rationally irrelevant knowledge.
Everything you know, or can know, about how much money there is in Box 2, be it absolutely certain knowledge, or 99% certain knowledge, is rationally irrelevant knowledge.
The reason: knowing what U is does not change the rational decision-making!
It is an irrelevant unknown. But it is also an important unknown, because it makes up the bulk of your potential payday. Important is not the same as rationally relevant to decision-making within the game, however.
Knowing about U is rationally irrelevant. And you cannot change U either, not in Phase 2 at least.
If you disagree with this, then it must be one of these things:
- You think the definition in section 3 is wrong.
- You think that knowing about the money in Box 2 actually changes what you should do.
The second point just flies right in the face of what Alice and Bob just taught us. And well, the first point will be hard to argue. Rationally irrelevant knowledge is literally defined as knowledge that has no impact on the rational decision-making for that game.
5. Expected Utility
Once you have digested section 3 and 4 above, you will be in a good position to understand section 5.
The expected utilities of one-boxing and two-boxing are the following:
We have that U is an unknown, a constant, and that all knowledge about U is rationally irrelevant knowledge. Clearly then, the expected utility of two-boxing is highest. It is a free, extra $1000, regardless of whether you won the $1M or not.
To make this clearer, let us look at the two possible values for U, given that U \in \{ \$0, \ \$1\text{M} \}
5.1 Possibility One
Let’s look at the expected utilities when U = \$ 0
In this case, two-boxing is clearly best.
5.2 Possibility Two
Let’s look at the expected utilities when U = \$ 1\text{M}
In this case also, two-boxing is clearly best.
Taking section 5.1 and 5.2 together, we say that two-boxing dominates.
5.3 The Non-Possibility
OB logic is that of comparing apples and oranges. OB logic looks at the two sections above, and protests that the real situation looks more like this:
In this case, of course, one-boxing is clearly best.
But this case is impossible. If you map the above equations to a physical, classical, spatiotemporal situation, then you are saying that the money can both be $0 and $1M at the same time… or you are saying your decision can cause the past to change, thus causing the money inside Box 2 to change.
The fact that one-boxers’ payout usually looks like the first one, and two-boxers’ payout usually looks like the second one, is because the game was constructed to create a non-causative correlation between the two.
I refer you back to my diagram for the Newcomb Game in section 2, if you want to understand the structure of this non-causative correlation. Remember, correlation due to a common cause is not itself causation!
It is a kind of non-causative correlation.
6. The Bank Transfer Newcomb Game
In the above sections, and in most of my former arguments, I’ve been approaching this using logic. In sections 6 and 7, I will approach this using intuition.
6.1 The Bank Transfer
Consider the normal Newcomb Game, but instead of two boxes, there is instead just $1000 on the table.
On the day before the Newcomb Game, the predictor predicted whether the player would “OB” or “TB”. If they predicted that the player would OB, then they sent $1M to the player’s bank account. If they predicted the player would TB, then they didn’t.
The player has been prevented from seeing any notifications from their bank. They have no idea if they got it or not.
When the player enters the room, they are told that this game’s equivalent to TBing is just grabbing the $1000 on the table. Conversely, OBing means just exiting the room.
So OBs, what do you do here? Do you grab the free $1000 on the table, or do you leave with nothing? The $1M is already in your bank account right now, or it already isn’t.
7. The Final Argument
Bob is playing Version 1 of the Newcomb Game. He is in Phase 2 right now. He’s staring at Box 2, and he’s stressing.
He feels like he’s risking the $1M. But it doesn’t quite make sense to him to just take Box 2. But everytime he thinks like that, his heart races. “Am I a TB? Oh God, then Box 2 is probably empty…”
“Maybe I should just play it safe. I don’t want to risk the $1M”.
He realizes something. Regardless of if he TBs or OBs, he is taking Box 2 anyways. The stress he’s feeling right now could perhaps be stilled if he could just… secure Box 2.
Not commit to OBing or TBing just yet, but he wants Box 2.
He asks the game organizers if it’s fine, and they say there is nothing in the rules preventing his ask.
So, he lifts Box 2. It is made to be impossible to feel if there’s anything in it. He gains no information.
He carries it out of the room and into the neighboring room. His wife sits there and smiles at him. He sits Box 2 down on her lap. He tells her this box belongs to them. The money or air that is in it, is theirs. They own it. Right now, they own it.
He tells her the game is still ongoing, but that she can open it already if she wants… but she has to wait till he’s turned around so he gains no information. And she cannot make any noise.
He turns around, and in his peripheral, he sees her opening Box 2. He doesn’t see her facial expression. And she doesn’t make a noise. He exits the room. He has gained no information.
But his wife has. She knows if they’ve already won the $1M, or won air.
Bob enters the game room again. Box 1 stands there, filled with the stack of $1000. Bob wonders:
“Should I take them?”