Optimal Simple Ratings
研究了将卖家分成有限等级的最优简单评级系统，发现最优评级必须是阈值划分，且在线性供给和古诺竞争下阈值由k均值聚类决定，并应用于eBay和Medicare Advantage数据。
ABSTRACT 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% of maximum welfare gains from full disclosure, with five tiers typically achieving over 90%. Applications to eBay and Medicare Advantage data illustrate our method.