We consider (ε,δ)-PAC maximum-selection and ranking using pairwise comparisons for general probabilistic models whose comparison probabilities satisfy strong stochastic transitivity an stochastic triangle inequality. Modifying the popular knockout tournament, we propose a simple maximum-selection algorithm that uses comparisons, optimal up to a constant factor. We then derive a general framework that uses noisy binary search to speed up many ranking algorithms, and combine it with merge sort to obtain a ranking algorithm that uses comparisons for optimal up to factor.