  Many web services like eBay, Tripadvisor, Epinions, etc, provide historical
product ratings so that users can evaluate the quality of products. Product
ratings are important since they affect how well a product will be adopted by
the market. The challenge is that we only have {\em "partial information"} on
these ratings: Each user provides ratings to only a "{\em small subset of
products}". Under this partial information setting, we explore a number of
fundamental questions: What is the "{\em minimum number of ratings}" a product
needs so one can make a reliable evaluation of its quality? How users' {\em
misbehavior} (such as {\em cheating}) in product rating may affect the
evaluation result? To answer these questions, we present a formal mathematical
model of product evaluation based on partial information. We derive theoretical
bounds on the minimum number of ratings needed to produce a reliable indicator
of a product's quality. We also extend our model to accommodate users'
misbehavior in product rating. We carry out experiments using both synthetic
and real-world data (from TripAdvisor, Amazon and eBay) to validate our model,
and also show that using the "majority rating rule" to aggregate product
ratings, it produces more reliable and robust product evaluation results than
the "average rating rule".
