Relation between Shanon entropy via relation of probabilities

Question

We have two vectore of probabilities, $P=\left(p_1,p_2,p_3,p_4\right)$ and $Q=\left(q_1,q_2,q_3,q_4\right)$. Assume that we know only the ralation between $p_i$ and $q_i$. To be more specific we know that $p_1 >q_1, p_4>q_4, p_2<q_2,p_3<q_3$', additionally we can calculate the relations between each pair. I'm interested to know, the relation between entropies of this vectors.