Abstract: We consider the problem of estimating the probability matrix governing a tournament or linkage in graphs. We assume that the probability matrix satisfies natural monotonicity constraints after being permuted in both rows and columns by the same latent permutation. The minimax rates of estimation for this problem under a mean squared error loss turns out to be O(1/n) upto logarithmic factors. This minimax rate is achieved by the overall least squares estimate which is perhaps impractical to compute because of the need to optimize over the set of all permutations. Therefore, we investigate in detail a simple two stage estimator which is computationally tractable. We prove that the maximum squared error risk of our estimator scales like O(1/√n) up to log factors. In addition, we prove an automatic adaptation property of our estimator, meaning that the risk of our estimator scales like O(1/n) upto log factors for several sub classes of our parameter space which are of natural interest. These sub classes include probability matrices satisfying appropriate notions of smoothness, and subsume the popular Bradley Terry Model in the tournament case and the β model and Stochastic Block Models with monotonicity, in the graph case.