An Isotonic Mechanism for Overlapping Ownership

This paper extends the Isotonic Mechanism from the single-owner to multi-owner settings, in an effort to make it applicable to peer review where a paper often has multiple authors. Our approach starts by partitioning all submissions of a machine learning conference into disjoint blocks, each of which shares a common set of co-authors. We then employ the Isotonic Mechanism to elicit a ranking of the submissions from each author and to produce adjusted review scores that align with both the reported ranking and the original review scores. The generalized mechanism uses a weighted average of the adjusted scores on each block. We show that, under certain conditions, truth-telling by all authors is a Nash equilibrium for any valid partition of the overlapping ownership sets. However, we demonstrate that while the mechanism's performance in terms of estimation accuracy depends on the partition structure, optimizing this structure is computationally intractable in general. We develop a nearly linear-time greedy algorithm that provably finds a performant partition with appealing robust approximation guarantees. Extensive experiments on both synthetic data and real-world conference review data demonstrate the effectiveness of this generalized Isotonic Mechanism.