Balancing Producer Fairness and Efficiency via Bayesian Rating System Design

Online marketplaces use rating systems to promote discovery of high quality products. However, these systems also lead to high variance in producers' economic outcomes: a new producer who sells high-quality items, may, by luck, receive one low rating early on, negatively impacting their popularity with future customers. We investigate the design of rating systems that balance the goals of identifying high quality products ("efficiency") and minimizing the variance in economic outcomes of producers of similar quality (individual "producer fairness"). We observe that there is a trade-off between these two goals: rating systems that promote efficiency are necessarily less individually fair to producers. We introduce Bayesian rating systems as an approach to managing this trade-off. Informally, the systems we propose set a system-wide prior for the quality of an incoming product, and subsequently the system updates that prior to a Bayesian posterior on quality based on user-generated ratings over time. Through calibrated simulations, we show that the strength of the prior directly determines the operating point on the identified trade-off: the stronger the prior, the more the marketplace discounts early ratings data (so individual producer fairness increases), but the slower the platform is in learning about true item quality (so efficiency suffers). Importantly, the prevailing method of ratings aggregation -- displaying the sample mean of ratings -- is an extreme point in this design space, that maximally prioritizes efficiency at the expense of producer fairness. Instead, by choosing a Bayesian rating system design with an appropriately set prior, a platform can be intentional about the consequential choice of a balance between efficiency and producer fairness.