The stubborn Rationalist repeats but one-boxing will leave me richer, and so I will choose to one-box.
That’s not the crux, the usual claim is closer to saying that the agent in Newcomb’s problem has some kind of free will (not incompatible with determinism) to choose whatever, and that choice in particular controls what the predictor is going to conclude, even in the past, before the decision is made by the agent. One-boxing just happens to be the better choice, so that’s what you choose. See also Transparent Newcomb’s Problem, Functional Decision Theory, MIRI/OP exchange about decision theory.
That’s not the crux, the usual claim is closer to saying that the agent in Newcomb’s problem has some kind of free will (not incompatible with determinism) to choose whatever, and that choice in particular controls what the predictor is going to conclude, even in the past, before the decision is made by the agent. One-boxing just happens to be the better choice, so that’s what you choose. See also Transparent Newcomb’s Problem, Functional Decision Theory, MIRI/OP exchange about decision theory.