  We propose a novel combinatorial inference framework to conduct general
uncertainty quantification in ranking problems. We consider the widely adopted
Bradley-Terry-Luce (BTL) model, where each item is assigned a positive
preference score that determines the Bernoulli distributions of pairwise
comparisons' outcomes. Our proposed method aims to infer general ranking
properties of the BTL model. The general ranking properties include the "local"
properties such as if an item is preferred over another and the "global"
properties such as if an item is among the top $K$-ranked items. We further
generalize our inferential framework to multiple testing problems where we
control the false discovery rate (FDR), and apply the method to infer the
top-$K$ ranked items. We also derive the information-theoretic lower bound to
justify the minimax optimality of the proposed method. We conduct extensive
numerical studies using both synthetic and real datasets to back up our theory.
