I like these observations! As for your last point about ranges and bounds, I’m actually moving towards relaxing those in future posts: basically I want to look at the tree case where you have more than one variable feeding into each node and I want to argue that even if the conditional probabilities are all 0′s and 1′s (so we don’t get any hard bounds with arguments like the one I present here) there can still be strong concentration towards one answer.
I like these observations! As for your last point about ranges and bounds, I’m actually moving towards relaxing those in future posts: basically I want to look at the tree case where you have more than one variable feeding into each node and I want to argue that even if the conditional probabilities are all 0′s and 1′s (so we don’t get any hard bounds with arguments like the one I present here) there can still be strong concentration towards one answer.