Fast and slow learning from reviews

This paper develops a model of Bayesian learning from online reviews, and investigates the conditions for asymptotic learning of the quality of a product and the speed of learning under different rating systems. A rating system provides information about reviews left by previous customers. A sequence of potential customers decide whether to join the platform. After joining and observing the ratings of the product, and conditional on her ex ante valuation, a customer decides whether to purchase or not. If she purchases, the true quality of the product, her ex ante valuation, an ex post idiosyncratic preference term and the price of the product determine her overall satisfaction. Given the rating system of the platform, she decides to leave a review as a function of her overall satisfaction. We study learning dynamics under two classes of rating systems: full history, where customers see the full history of reviews, and summary statistics, where the platform reports some summary statistics of past reviews. In both cases, learning dynamics are complicated by a selection effect — the types of users who purchase the good and thus their overall satisfaction and reviews depend on the information that they have available at the time of their purchase. We provide conditions for asymptotic learning under both full history and summary statistics, and show how the selection effect becomes more difficult to correct for with summary statistics. Conditional on asymptotic learning, the speed (rate) of learning is always exponential and is governed by similar forces under both types of rating systems, though the exact rates differ. Using this characterization, we provide the rate of learning under several different types of rating systems. We show that providing more information does not always lead to faster learning, but strictly finer rating systems always do. We also illustrate how different rating systems, with the same distribution of preferences, can lead to very fast or very slow speeds of learning.