In your example in 3.3, I don’t think it’s true that FDT recommends one-boxing in scenario 2. Your choice of boxes is a product of (among other things) both your genes and of FDT’s recommendation (just the former if you don’t use FDT). But since “[t]he cases where the simulation is inaccurate are the same as the ones where there isn’t an overlap between your gene and which box you take”, it follows that your simulated action is unaffected by FDT’s recommendation. So FDT acts as if it has no control over your simulated action, and therefore two-boxes.
I think the weirdness of this example comes from the stipulation that “[t]he cases where the simulation is inaccurate are the same as the ones where there isn’t an overlap between your gene and which box you take”. This is actually a pretty strong hypothesis! It makes the scenario very different from how it would be if you just talked about a 99.9% accurate simulator.
A more minor issue: when you write “Imagine that there’s some gene that correlates 99.9% with two-boxing” it is not clear whether you refer to two-boxing in scenario 1 or two-boxing in scenario 2. They can be different, of course. But I think your argument is closest to correct if we assume you are talking about two-boxing in scenario 2.
In your example in 3.3, I don’t think it’s true that FDT recommends one-boxing in scenario 2. Your choice of boxes is a product of (among other things) both your genes and of FDT’s recommendation (just the former if you don’t use FDT). But since “[t]he cases where the simulation is inaccurate are the same as the ones where there isn’t an overlap between your gene and which box you take”, it follows that your simulated action is unaffected by FDT’s recommendation. So FDT acts as if it has no control over your simulated action, and therefore two-boxes.
I think the weirdness of this example comes from the stipulation that “[t]he cases where the simulation is inaccurate are the same as the ones where there isn’t an overlap between your gene and which box you take”. This is actually a pretty strong hypothesis! It makes the scenario very different from how it would be if you just talked about a 99.9% accurate simulator.
A more minor issue: when you write “Imagine that there’s some gene that correlates 99.9% with two-boxing” it is not clear whether you refer to two-boxing in scenario 1 or two-boxing in scenario 2. They can be different, of course. But I think your argument is closest to correct if we assume you are talking about two-boxing in scenario 2.