“events flowing from (α,β,1)” : oops, sorry, that was a remnant of the old version; now corrected.
“I assume u is a causal descendent of A.” : Iu (the fact that u is chosen by the human as the correct utility function) is a causal descendant of A. But u itself is simply a utility function, and we can estimate its value whether or not Iu happens.
“Also, how can you condition on the action a if you just set the action to ∅.” : setting the action to ∅ (and Iu to some value), you have modified the distribution (or not, if things are independent) for all nodes that are not descendants of A. Then you set A=a, and deduce what happens at other nodes, given P∅,u and A=a.
“events flowing from (α,β,1)” : oops, sorry, that was a remnant of the old version; now corrected.
“I assume u is a causal descendent of A.” : Iu (the fact that u is chosen by the human as the correct utility function) is a causal descendant of A. But u itself is simply a utility function, and we can estimate its value whether or not Iu happens.
“Also, how can you condition on the action a if you just set the action to ∅.” : setting the action to ∅ (and Iu to some value), you have modified the distribution (or not, if things are independent) for all nodes that are not descendants of A. Then you set A=a, and deduce what happens at other nodes, given P∅,u and A=a.