Roman Malov comments on Weak-To-Strong Generalization

[Roman Malov]

such an assumption is not strong enough to guarantee that $P_s$ has a 50-50 coinflip hypothesis.

What do you mean by 50-50 hypothesis? Is it $E_{1/2}$ such that $\forall n:P\left(T_{h_n}|E_{1/2}\right)=P\left(T_{t_n}|E_{1/2}\right)=1/2$? If that’s the case, it doesn’t seem fair to ask from a student to have such hypothesis: the task is to learn to imitate teacher, and teacher doesn’t actually perform behavior like HTHHT, it can be either perform either HHHHH or TTTTTT.