Optimal Simple Ratings

We study optimal simple rating systems that partition sellers into a finite number of tiers. We show that optimal ratings must be threshold partitions, and that for linear supply and Cournot competition with constant marginal cost, optimal thresholds solve a k-means clustering problem requiring only the quality distribution. For convex (concave) supply functions, optimal thresholds are higher (lower) than the k-means solution. For log-concave distributions, two-tier certification captures at least 50 percent of maximum welfare gains from full disclosure, with five tiers typically achieving over 90 percent. Applications to eBay and Medicare Advantage data illustrate our method.