  We consider $(\epsilon,\delta)$-PAC maximum-selection and ranking for general
probabilistic models whose comparisons probabilities satisfy strong stochastic
transitivity and stochastic triangle inequality. Modifying the popular knockout
tournament, we propose a maximum-selection algorithm that uses
$\mathcal{O}\left(\frac{n}{\epsilon^2}\log \frac{1}{\delta}\right)$
comparisons, a number tight up to a constant factor. We then derive a general
framework that improves the performance of many ranking algorithms, and combine
it with merge sort and binary search to obtain a ranking algorithm that uses
$\mathcal{O}\left(\frac{n\log n (\log \log n)^3}{\epsilon^2}\right)$
comparisons for any $\delta\ge\frac1n$, a number optimal up to a $(\log \log
n)^3$ factor.
