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We revisit the fundamental problem of sorting objects using crowdsourced pairwise comparisons. Prior work either treats these comparisons as independent tasks -- in which case the resulting judgments may end up being inconsistent, or fails to capture the accuracies of workers or difficulties of the pairwise comparisons -- in which case the resulting judgments may end up being consistent with each other, but ultimately more inaccurate. We adopt a holistic approach that constructs a graph across the set of objects respecting consistency constraints. Our key contribution is a novel method of encoding difficulty of comparisons in the form of constraints on edges. We couple that with an iterative E-M-style procedure to uncover information about latent variables and constraints, along with the graph structure. We show that our approach predicts edge directions as well as difficulty values more accurately than baselines on both real and simulated data, across graphs of various sizes.

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