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You say no, but you also state that a node with 2 yes and 2 no is higher... higher what? Higher information gain? If so, why do you say no? Can you be more concise / precise please?
But does this mean that you first need to check what comes AFTER you would hypothetically choose some root? I mean, do you choose the root here because it's 2 YES and 2 NO or because of the possibilities after you would choose this?