Would performance of atomic models matter in ensemble methods?

Suppose I have two fitted ensemble models $$F_1 := (f_1, f_2, f_3, \cdots f_n)$$ and $$G_1 := (g_1, g_2, g_3, \cdots g_n)$$.

And they were using the same ensemble methods (boosting or bagging).

And I am using some measurement for model performance $$M: f_i \to \mathbb{R}^+$$, higher the better.

And I know beforehand $$M(f_i) \gt M(g_i), \forall i \in [1,n]$$, can I conclude $$M(F) \gt M(G)$$ ?

• Do you know $M(f_i) \gt M(g_i), \forall i \in [1,n]$ or is $M(f_i) \gt M(g_i)$ only for a specific $i$? – Neil Slater Nov 2 '20 at 5:15
• All $i$ in this case – yupbank Nov 15 '20 at 0:12