Thanks for writing this up! I was wondering how this formalization works for Newcomb’s problem. (I’ll take box A to be the transparent box containing a thousand dollars, and box B to be the opaque box containing a million dollars or nothing.)
I would like to say that the actions are A={‘‘Take only box B",‘‘Take both boxes"}, the states are S={‘‘Box B is full",‘‘Box B is empty"}, and the outcomes O are the four different ways of combining the actions and states.
But it seems like I’ve violated the definition of a state given in the post:
By ‘no direct control’, we mean that the probability of the state is independent of the action performed.
After all, the probability of the state ‘‘Box B is full" certainly depends on the action of the agent, in the sense that P(‘‘Box B is full"|‘‘Take only box B")≠P(‘‘Box B is full"|‘‘Take both boxes").
In my understanding, you are on the right track, but note the difference between taking the action and observing the action.
EDT doesn’t assume the agent’s action causally determines the state, but rather that you are not restricted (as in CDT) from considering how observing the action may work as evidence about the state. Consider the problem from a detached perspective. If you saw an agent one-box but did not see the outcome of that choice, then you would still be justified in believing P(‘‘Box B is full")>0.5 because the Newcomb predictor is usually accurate, right?
So, more precisely, your formulation could be stated as:
P(‘‘B is full"|‘‘Observing the agent one-boxing")≠P(‘‘B is full"|‘‘Observing the agent two-boxing")
In other words the action is independent of the state, but the observation of the action isn’t necessarily. Also see e.g. Joe Carlsmith’s discussion of this, most interestingly:
In particular, I suspect that attractive versions of EDT (and perhaps, attractive attempts to recapture the spirit of CDT) require something in the vicinity of “following the policy that you would’ve wanted yourself to commit to, from some epistemic position that ‘forgets’ information you now know.”
The epistemic position you have to use to evaluate EDT is strange. But thinking about yourself as a detached observer of actions (past, present, and anticipated/hypothetical future) is a useful framing for me.
Thanks for writing this up! I was wondering how this formalization works for Newcomb’s problem. (I’ll take box A to be the transparent box containing a thousand dollars, and box B to be the opaque box containing a million dollars or nothing.)
I would like to say that the actions are A={‘‘Take only box B",‘‘Take both boxes"}, the states are S={‘‘Box B is full",‘‘Box B is empty"}, and the outcomes O are the four different ways of combining the actions and states.
But it seems like I’ve violated the definition of a state given in the post:
After all, the probability of the state ‘‘Box B is full" certainly depends on the action of the agent, in the sense that P(‘‘Box B is full"|‘‘Take only box B")≠P(‘‘Box B is full"|‘‘Take both boxes").
In my understanding, you are on the right track, but note the difference between taking the action and observing the action.
EDT doesn’t assume the agent’s action causally determines the state, but rather that you are not restricted (as in CDT) from considering how observing the action may work as evidence about the state. Consider the problem from a detached perspective. If you saw an agent one-box but did not see the outcome of that choice, then you would still be justified in believing P(‘‘Box B is full")>0.5 because the Newcomb predictor is usually accurate, right?
So, more precisely, your formulation could be stated as:
P(‘‘B is full"|‘‘Observing the agent one-boxing")≠P(‘‘B is full"|‘‘Observing the agent two-boxing")
In other words the action is independent of the state, but the observation of the action isn’t necessarily. Also see e.g. Joe Carlsmith’s discussion of this, most interestingly:
The epistemic position you have to use to evaluate EDT is strange. But thinking about yourself as a detached observer of actions (past, present, and anticipated/hypothetical future) is a useful framing for me.