  Motivated by crowd-sourcing applications, we consider a model where we have
partial observations from a bivariate isotonic n x d matrix with an unknown
permutation $\pi$ * acting on its rows. Focusing on the twin problems of
recovering the permutation $\pi$ * and estimating the unknown matrix, we
introduce a polynomial-time procedure achieving the minimax risk for these two
problems, this for all possible values of n, d, and all possible sampling
efforts. Along the way, we establish that, in some regimes, recovering the
unknown permutation $\pi$ * is considerably simpler than estimating the matrix.
