Of course, no actual individual or program is a pure Bayesian. Pure Bayesian updating presumes logical omniscience after all. Rather, when we talk about Bayesian reasoning we idealize individuals as abstract agents whose choices (potentially none) have a certain probabilistic effect on the world, i.e., basically we idealize the situation as a 1 person game.
You basically raise the question of what happens in Newcomb like cases where we allow the agent’s internal deliberative state to affect outcomes independent of explicit choices made. But whole model breaks down the moment you do this. It no longer even makes sense to idealize a human as this kind of agent and ask what should be done because the moment you bring the agent’s internal deliberative state into play it no longer makes sense to idealize the situation as one in which there is a choice to be made. At that point you might as well just shrug and say ‘you’ll choose whatever the laws of physics says you’ll choose.’
Now, one can work around this problem by instead posing a question for a different agent who might idealize a past self, e.g., if I imagine I have a free choice about which belief to commit to having in these sorts of situations which belief/belief function should I presume.
As an aside I would argue that, while a perfectly valid mathematical calculation, there is something wrong in advocating for timeless decision theory or any other particular decision theory as the correct way to make choices in these Newcomb type scenarios. The model of choice making doesn’t even really make sense in such situations so any argument over which is the true/correct decision theory must ultimately be a pragmatic one (when we suggest actual people use X versus Y they do better with X) but that’s never the sense of correctness that is being claimed.
Of course, no actual individual or program is a pure Bayesian. Pure Bayesian updating presumes logical omniscience after all. Rather, when we talk about Bayesian reasoning we idealize individuals as abstract agents whose choices (potentially none) have a certain probabilistic effect on the world, i.e., basically we idealize the situation as a 1 person game.
You basically raise the question of what happens in Newcomb like cases where we allow the agent’s internal deliberative state to affect outcomes independent of explicit choices made. But whole model breaks down the moment you do this. It no longer even makes sense to idealize a human as this kind of agent and ask what should be done because the moment you bring the agent’s internal deliberative state into play it no longer makes sense to idealize the situation as one in which there is a choice to be made. At that point you might as well just shrug and say ‘you’ll choose whatever the laws of physics says you’ll choose.’
Now, one can work around this problem by instead posing a question for a different agent who might idealize a past self, e.g., if I imagine I have a free choice about which belief to commit to having in these sorts of situations which belief/belief function should I presume.
As an aside I would argue that, while a perfectly valid mathematical calculation, there is something wrong in advocating for timeless decision theory or any other particular decision theory as the correct way to make choices in these Newcomb type scenarios. The model of choice making doesn’t even really make sense in such situations so any argument over which is the true/correct decision theory must ultimately be a pragmatic one (when we suggest actual people use X versus Y they do better with X) but that’s never the sense of correctness that is being claimed.