I Will Have Order! Optimizing Orders for Fair Reviewer Assignment.

Scientific advancement requires effective peer review. Papers should be reviewed by experts in the subject area, but it is equally important that reviewer quality is fairly distributed amongst papers. We model reviewer assignment as an instance of a fair allocation problem, presenting an extension of the classic round-robin mechanism, called Reviewer Round Robin (RRR). Round-robin mechanisms are a standard tool to ensure envy-free up to one item (EF1) allocations. However, fairness often comes at the cost of decreased efficiency. To overcome this challenge, we carefully select an approximately optimal round-robin order. Applying a relaxation of submodularity, $\gamma$-weak submodularity, we show that greedily inserting papers into an order yields a ${(1+\gamma^2)}$-approximation to the maximum welfare attainable by our round-robin mechanism under any order. Our approach outputs highly efficient EF1 allocations for three real conference datasets, outperforming several state-of-the-art paper assignment methods in fairness, efficiency and runtime.