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").
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").