I have a physical definition of causation too. This is why I think CDT 1-boxes. Our universe is causal.
Our universe is also logical, as I’ll explain in a bit. But, importantly, if you think CDT one-boxes then your ‘physical definition of causation’ is different from the definition of causation held by people who think CDT two-boxes.
Consider the twin prisoner dilemma. You and your psychological twin are put into rooms, have to choose whether to cooperate or defect, etc.; you might have the belief in a logical connection between your reasoning and your twin’s reasoning (such that if your reasoning leads you to defect, theirs will as well, and if your reasoning leads you to cooperate, then theirs will as well), but you can’t believe in a physical connection between your reasoning and your twin’s reasoning (this particular voltage in your brain is in the causal history of that particular voltage in their brain). And so if you only reason based on the physical effects that you have on the universe, you end up defecting, because as much as you would like to signal your willingness to cooperate to your twin (and get a guarantee from them) you don’t have the mechanism to do so.
If one has a logical definition of causation (as well as a physical one), then you reason as follows: two calculators, even if physically separated, will get the same answer if they run the same computation. What my decision is doing is working out how a particular computation terminates, so I can think as if I’m choosing both my action and my psychological twin’s action, much like one calculator can expect other calculators will reach the same mathematical result. So reasoning “If I cooperate, then my twin will also cooperate” is valid for the same reasons that “if my calculator says 3*17 is 51, then other calculators will say the same.” [Note that this is actually a different sort of validity than “if I place a ball in a bowl, it will stay there”—if I placed the ball on a hill instead, the ball would roll, but if my calculator miscalculated 3*17 as 37, that wouldn’t change math—and that different sort of validity is why CDT doesn’t respect it.]
If Omega is a perfect predictor, and you are presented the two boxes, well, the only possible answer is yes.
This is not how CDT reasons about its possible actions; it assumes that it can sever all connections to parent nodes whenever it makes a choice. So even in the 100% world, CDT using the causal graphs you provided and would two-box. This is actually a feature. [Thus, the way Omega maintains perfect predictive ability is you never seeing the full box.]
The correct action in transparent Newcomb’s is to one-box when you see the money, even if Omega is only 99% accurate. [Depending on the formulation, it can also be right to one-box when you don’t see the money, but it’s cleaner to assume Omega’s prediction only depends on what you do when you see the money.] Notice that your decision theory does better when it closes its eyes, which seems like a weird feature for a decision theory to have.
Logic is prior to physics. It could be the case that physics is different; it could not be the case that logic is different. (Put another way, logic occupies a higher level of the Tegmark multiverse, kind of; one can hypothesize a Tegmark V where logic is different. We don’t have a formal model of what “counterlogical reasoning” looks like yet, that is, reasoning about what it would be like if logic were different, whereas we have solid formal models of reasoning about what it would look like if physics were different (either in terms of dynamics or boundary conditions).)
You are saying that CDT don’t understand common causes.
Of an agent’s decisions, because the CDT procedure views actions as interventions, which uproot the relevant node (using the terminology of this paper), that is, delete all of its parents besides the intervention. Observations are distinct from interventions; on observing the weather online, CDT is able to infer about whether or not the grass is wet or dry. On editing the webpage to say that it is raining, CDT does not infer that the grass is wet—which is correct!
I literally just gave arguments about why it’s not the correct action. You repeating this and not countering any of the arguments I brought up doesn’t really help.
Suppose you are building a robot that will face this challenge, and programming what it does in the case where it sees that the box is full. You consider the performance of a one-boxer. It will see the $1M 99% of the time, and take only it, and see only the $1k 1% of the time, and take that. Total expected reward: $990,010.
A two-boxer will see the $1M 1% of the time, and take both, and see only the $1k 99% of the time, and take that. Total expected reward: $11,000.
Since you like money, you program the robot to one-box.
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To check, do you think it’s correct to pay the driver in Parfit’s Hitchhiker once you reach town?
Our universe is also logical, as I’ll explain in a bit. But, importantly, if you think CDT one-boxes then your ‘physical definition of causation’ is different from the definition of causation held by people who think CDT two-boxes.
Consider the twin prisoner dilemma. You and your psychological twin are put into rooms, have to choose whether to cooperate or defect, etc.; you might have the belief in a logical connection between your reasoning and your twin’s reasoning (such that if your reasoning leads you to defect, theirs will as well, and if your reasoning leads you to cooperate, then theirs will as well), but you can’t believe in a physical connection between your reasoning and your twin’s reasoning (this particular voltage in your brain is in the causal history of that particular voltage in their brain). And so if you only reason based on the physical effects that you have on the universe, you end up defecting, because as much as you would like to signal your willingness to cooperate to your twin (and get a guarantee from them) you don’t have the mechanism to do so.
If one has a logical definition of causation (as well as a physical one), then you reason as follows: two calculators, even if physically separated, will get the same answer if they run the same computation. What my decision is doing is working out how a particular computation terminates, so I can think as if I’m choosing both my action and my psychological twin’s action, much like one calculator can expect other calculators will reach the same mathematical result. So reasoning “If I cooperate, then my twin will also cooperate” is valid for the same reasons that “if my calculator says 3*17 is 51, then other calculators will say the same.” [Note that this is actually a different sort of validity than “if I place a ball in a bowl, it will stay there”—if I placed the ball on a hill instead, the ball would roll, but if my calculator miscalculated 3*17 as 37, that wouldn’t change math—and that different sort of validity is why CDT doesn’t respect it.]
This is not how CDT reasons about its possible actions; it assumes that it can sever all connections to parent nodes whenever it makes a choice. So even in the 100% world, CDT using the causal graphs you provided and would two-box. This is actually a feature. [Thus, the way Omega maintains perfect predictive ability is you never seeing the full box.]
The correct action in transparent Newcomb’s is to one-box when you see the money, even if Omega is only 99% accurate. [Depending on the formulation, it can also be right to one-box when you don’t see the money, but it’s cleaner to assume Omega’s prediction only depends on what you do when you see the money.] Notice that your decision theory does better when it closes its eyes, which seems like a weird feature for a decision theory to have.
Logic is prior to physics. It could be the case that physics is different; it could not be the case that logic is different. (Put another way, logic occupies a higher level of the Tegmark multiverse, kind of; one can hypothesize a Tegmark V where logic is different. We don’t have a formal model of what “counterlogical reasoning” looks like yet, that is, reasoning about what it would be like if logic were different, whereas we have solid formal models of reasoning about what it would look like if physics were different (either in terms of dynamics or boundary conditions).)
Of an agent’s decisions, because the CDT procedure views actions as interventions, which uproot the relevant node (using the terminology of this paper), that is, delete all of its parents besides the intervention. Observations are distinct from interventions; on observing the weather online, CDT is able to infer about whether or not the grass is wet or dry. On editing the webpage to say that it is raining, CDT does not infer that the grass is wet—which is correct!
Suppose you are building a robot that will face this challenge, and programming what it does in the case where it sees that the box is full. You consider the performance of a one-boxer. It will see the $1M 99% of the time, and take only it, and see only the $1k 1% of the time, and take that. Total expected reward: $990,010.
A two-boxer will see the $1M 1% of the time, and take both, and see only the $1k 99% of the time, and take that. Total expected reward: $11,000.
Since you like money, you program the robot to one-box.
---
To check, do you think it’s correct to pay the driver in Parfit’s Hitchhiker once you reach town?