Learning to rank: construct absolute ranking using pair-wise ranking approach

I am learning about the "pairwise approach" for learning to rank. As far as I understood, the training output is a partial ranking function $r$ that:

• given given some query $q$ and two document $d_i$ and $d_j$
• predicts whether $$r(d_i)>r(d_j)$$ or not

However, for a IR system to work, the ranking should be absolute.

The natural question next is how to construct the absolute rank using only the partial ranks output by $r$?

But partial ranks does not guarantee absolute rank. For example

$$r(x)>r(y), r(y)>r(z), r(z)>r(x)$$ gives a cycle.

I guess I am misunderstanding about how pairwise approach works for IR system. Can anyone correct me?