The equilibrium probability might not be well defined. (E.g., if for whatever reason you form a sufficiently firm intention to falsify whatever the oracle tells you.)
The point (or at least a point) is that there might not be a fixed point. I suppose what that might mean is that in a universe containing such a predictor you’re unable to form such intentions as would lead to the failure. This seems sufficiently far removed from the real world that it would probably be better to consider scenarios that don’t flirt so brazenly with paradox.
The closed-timelike-curve paper weakens the guarantee of the predictor, so instead of saying “A with 25% probability, B with 75% probability”, it will stochastically say either “A” or “B”. So the kind of fixpoint it considers is less impressive.
I guess it would still be well-defined as a fixpoint though, like in “Closed Timelike Curves Make Quantum and Classical Computing Equivalent”. Although by the same paper, it would be computationally infeasible for a predictor to actually find the fixpoint...
The point (or at least a point) is that there might not be a fixed point. I suppose what that might mean is that in a universe containing such a predictor you’re unable to form such intentions as would lead to the failure. This seems sufficiently far removed from the real world that it would probably be better to consider scenarios that don’t flirt so brazenly with paradox.
Yeah, you’re are right.
The closed-timelike-curve paper weakens the guarantee of the predictor, so instead of saying “A with 25% probability, B with 75% probability”, it will stochastically say either “A” or “B”. So the kind of fixpoint it considers is less impressive.