vitus points out the very cool instance of Monoid for Ordering. If you combine it with the instance instance Monoid b => Monoid (a -> b) it turns out your composition function is just (get ready):
mappend
Check it out:
Prelude Data.Monoid> let f a b = EQ
Prelude Data.Monoid> let g a b = LT
Prelude Data.Monoid> :t f `mappend` g
f `mappend` g :: t -> t1 -> Ordering
Prelude Data.Monoid> (f `mappend` g) undefined undefined
LT
Prelude Data.Monoid> let f a b = GT
Prelude Data.Monoid> (f `mappend` g) undefined undefined
GT
+1 for powerful and simple abstractions