Efficient stopping of a random series of partially ordered points

The now classical secretary problem ([1],p.51,[2],p.35–39) can be described as follows: Consider n objects numbered l,2,…,n so that the object with the number 1 is classified as the best, the object numbered 2 is the second-best and so on. The objects successively arrive in a random order; this means that all n! permutations are equally probable. Given two objects we can decide which one is better, but their numbers still remain unknown.