Each oracle is running a simulation of the world. Within that simulation, they search for any computational process with the same logical structure as themselves. This will find both their virtual model of their own hardware, as well as any other agenty processes trying to predict them. The oracle then deletes the output of all these processes within its simulation.
Imagine running a super realistic simulation of everything, except that any time anything in the simulation tries to compute the millionth digit of pi, you notice, pause the simulation and edit it to make the result come out as 7. While it might be hard to formally specify what counts as a computation, I think that this intuitively seems like meaningful behavior. I would expect the simulation to contain maths books that said that the millionth digit of pi was 7, and that were correspondingly off by one about how many 7s were in the first n digits for any n>1000000.
Each oracle is running a simulation of the world. Within that simulation, they search for any computational process with the same logical structure as themselves. This will find both their virtual model of their own hardware, as well as any other agenty processes trying to predict them. The oracle then deletes the output of all these processes within its simulation.
Imagine running a super realistic simulation of everything, except that any time anything in the simulation tries to compute the millionth digit of pi, you notice, pause the simulation and edit it to make the result come out as 7. While it might be hard to formally specify what counts as a computation, I think that this intuitively seems like meaningful behavior. I would expect the simulation to contain maths books that said that the millionth digit of pi was 7, and that were correspondingly off by one about how many 7s were in the first n digits for any n>1000000.
The principle here is the same.