> it's fair to ask (as another poster suggested) whether or not the machine in the paradox can ever exist.
Here's something interesting to think about: assuming the machine could exist in some possible world, how does causality work in that world?
To be certain about your future behavior, the machine would need a "time oracle" that allowed it to view the future. The machine consults its time oracle, it sees you making a box choice, and it puts money in the boxes based on the choice you made.
But this is literally you having causal agency over the machine's decision, isn't it? After all, it acted because of what it saw you do.
Now, imagine that the machine has the same time oracle but it's randomly unreliable and gives the machine the wrong idea 10% of the time. Then that expected utility calculation starts looking pretty good, doesn't it? Because 90% of the time your actions causally determine the machine's.
Here's something interesting to think about: assuming the machine could exist in some possible world, how does causality work in that world?
To be certain about your future behavior, the machine would need a "time oracle" that allowed it to view the future. The machine consults its time oracle, it sees you making a box choice, and it puts money in the boxes based on the choice you made.
But this is literally you having causal agency over the machine's decision, isn't it? After all, it acted because of what it saw you do.