Optimal ranking of tournaments

Let us be given a tournament Tn (i-e., a complete directed graph) on n players. It is natural to look for a ranking (linear order) L on the n players that best reflects the tournament result. Thinking of L as a complete directed transitive graph we may use IE(T) fl E(L) I, where E(T) = edge set of T, as a measure of how good a fit L is. We ask, what is the worst case. Set f (n) = min max IE(T ) nE(L) 1 . n Tn