I have a set of ordered items A > B > C ... > F. For each element of the set I have a feature vector. Using these features I trained a neural network to predict the probability that A > B for any pair of items A and B. The neural network predictions are noisy. The output from the network may not be perfectly consistent with the true ranking.
My question is how do I go from having these pairwise ranking probabilities to a best-guess for the total ordering of the items in the set?