Market share and quality, or customer satisfaction, go together. Yet inferring one from the other appears difficult. Indeed, such an inference would need detailed information about customer behavior, and might be clouded by modes of behavior such as herding (following popularity) or elitism, where customers avoid popular products. We investigate a fixed-price model where customers are informed about their history with products and about market share data. We find that it is in fact correct to make a Bayesian inference that the product with the higher market share has the better quality under few and unrestrictive assumptions on customer behavior.