  This technical report studies the problem of ranking from pairwise
comparisons in the classical Bradley-Terry-Luce (BTL) model, with a focus on
score estimation. For general graphs, we show that, with sufficiently many
samples, maximum likelihood estimation (MLE) achieves an entrywise estimation
error matching the Cram\'er-Rao lower bound, which can be stated in terms of
effective resistances; the key to our analysis is a connection between
statistical estimation and iterative optimization by preconditioned gradient
descent. We are also particularly interested in graphs with locality, where
only nearby items can be connected by edges; our analysis identifies conditions
under which locality does not hurt, i.e. comparing the scores between a pair of
items that are far apart in the graph is nearly as easy as comparing a pair of
nearby items. We further explore divide-and-conquer algorithms that can
provably achieve similar guarantees even in the regime with the sparsest
samples, while enjoying certain computational advantages. Numerical results
validate our theory and confirm the efficacy of the proposed algorithms.
