  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.
