Learning to rank: construct absolute ranking using pair-wise ranking approach
Creating a total ranking from pairwise comparisons that don’t necessarily follow the axioms or rational preferences would certainly require some optimization, and you would need to compute a quadratic number of such comparisons in order to produce a ranking.

There is however one trick to do this easily: if the function that classifies whether one element is ranked above the other is linear in all the features, you can, intuitively, compare each element to a null element (i.e. just apply the decision function to the element alone), get a score assigned to them, and sort them by this score.

So, intuitively, your linear classifier would be something like this: element 1 is above element 2 if:
F(el1 – el2)>0 [function has to be symmetrical, thus there can't be a non-zero threshold] --> F(el1) – F(el2) >0 (only when F is linear!!!)
Which implies that el1 > el2 iff F(el1)>F(el2)