“the dominant consensus in modern decision theory is that one should two-box...there’s a common attitude that verbal arguments for one-boxing are easy to come by, what’s hard is developing a good decision theory that one-boxes”
This may be more a statement about the relevance and utility of decision theory itself as a field (or lack thereof) than the difficulty of the problem, but it is at least philosophically intriguing.
From a physical and computational perspective, there is no paradox, and one need not invoke backwards causality, ‘pre-commitment”, or create a new ‘decision theory’.
The chain of physical causality just has a branch:
M0-> O(D)-> B
M0-> M1-> M2-> .. MN ->D
and O(D) = D
Where M0, M1, M2 .. . MN are the agent’s mind states, D is the agent’s decision, O is Omega’s prediction of the decision, and B is the content of box B.
Your decision does not physically cause the contents of box B to change. Your decision itself however is caused by your past state of mind, and this prior state is also the cause of the box’s current contents (via the power of Omega’s predictor). So your decision and the box’s contents are casually linked, entangled if you will.
From your perspective, the box’s contents are unknown. Your final decision is also unknown to you, undecided, until the moment you make that decision by opening the box. Making the decision itself reveals this information about your mind history to you, along with the contents of the box.
One way of thinking about it is that this problem is an illustration of the dictum that any mind or computational system can never fully predict itself from within.
Note that in the context of actual AI in computer science, this type of reflective search (considering a potential decision, then agent B’s consequent decision, your next decision, and so on, exploring a decision tree) is pretty basic stuff. In this case the Omega agent essentially has an infinite branching depth, but the decision at each point is pretty simple—because Omega always gets the ‘last move’.
You may start as a ‘one boxer’, thinking that after the scan, you can now outwit Omega by ‘self-modifying’ into a ‘two-boxer’ (which really can be just as simple as changing your internal register), but Omega already predicted this move .. and your next reactive move of flipping back to a ‘one-boxer’ . . and the next, on and on to infinity . . .until you finally run out of time and the register is sampled. You can continue chaining M’s to infinity, but you can’t change the fact that MN->D and O(D) = D.
Part of the confusion experienced by the causal decision camp may stem from the subjectivity of the solution.
The optimal decision for some abstract algorithm, divorced from Omega’s predictive brainscan, will of course choose to two-box, simply because it’s decision is not causally linked to the box’s contents.
But your N-box register is linked to the box’s contents, so you should set it to 1.
“the dominant consensus in modern decision theory is that one should two-box...there’s a common attitude that verbal arguments for one-boxing are easy to come by, what’s hard is developing a good decision theory that one-boxes”
This may be more a statement about the relevance and utility of decision theory itself as a field (or lack thereof) than the difficulty of the problem, but it is at least philosophically intriguing.
From a physical and computational perspective, there is no paradox, and one need not invoke backwards causality, ‘pre-commitment”, or create a new ‘decision theory’.
The chain of physical causality just has a branch:
M0-> O(D)-> B
M0-> M1-> M2-> .. MN ->D
and O(D) = D
Where M0, M1, M2 .. . MN are the agent’s mind states, D is the agent’s decision, O is Omega’s prediction of the decision, and B is the content of box B.
Your decision does not physically cause the contents of box B to change. Your decision itself however is caused by your past state of mind, and this prior state is also the cause of the box’s current contents (via the power of Omega’s predictor). So your decision and the box’s contents are casually linked, entangled if you will.
From your perspective, the box’s contents are unknown. Your final decision is also unknown to you, undecided, until the moment you make that decision by opening the box. Making the decision itself reveals this information about your mind history to you, along with the contents of the box.
One way of thinking about it is that this problem is an illustration of the dictum that any mind or computational system can never fully predict itself from within.
Note that in the context of actual AI in computer science, this type of reflective search (considering a potential decision, then agent B’s consequent decision, your next decision, and so on, exploring a decision tree) is pretty basic stuff. In this case the Omega agent essentially has an infinite branching depth, but the decision at each point is pretty simple—because Omega always gets the ‘last move’.
You may start as a ‘one boxer’, thinking that after the scan, you can now outwit Omega by ‘self-modifying’ into a ‘two-boxer’ (which really can be just as simple as changing your internal register), but Omega already predicted this move .. and your next reactive move of flipping back to a ‘one-boxer’ . . and the next, on and on to infinity . . .until you finally run out of time and the register is sampled. You can continue chaining M’s to infinity, but you can’t change the fact that MN->D and O(D) = D.
Part of the confusion experienced by the causal decision camp may stem from the subjectivity of the solution.
The optimal decision for some abstract algorithm, divorced from Omega’s predictive brainscan, will of course choose to two-box, simply because it’s decision is not causally linked to the box’s contents.
But your N-box register is linked to the box’s contents, so you should set it to 1.