An Isotonic Mechanism for Overlapping Ownership

Motivated by the problem of improving peer review at large scientific conferences, this paper studies how to elicit self-evaluations to improve review scores in a natural many-to-many owner-item (e.g., author-paper) situation with overlapping ownership. We design a simple, efficient and truthful mechanism to elicit self-evaluations from item owners that can be used to calibrate their noisy review scores in the existing evaluation process (e.g., papers' review scores from peers). Our approach starts by partitioning the owner-item relation structure into disjoint blocks, each sharing a common set of co-owners. We then elicit the ranking of items from each owner and employ isotonic regression to produce adjusted item scores, aligning with both the reported rankings and raw item review scores. We prove that truth-telling by all owners is a payoff dominant Nash equilibrium for any valid partition of the overlapping ownership sets under natural conditions. Moreover, the truthfulness depends on eliciting rankings independently within each block, making block partition optimization crucial for improving statistical efficiency. Despite being computationally intractable in general, we develop a nearly linear-time greedy algorithm that provably finds a performant block partition with appealing robust approximation guarantees. Extensive experiments on both synthetic data and real-world conference review data demonstrate the effectiveness of our mechanism in a pressing real-world problem.