Are imperfect reviews helpful in social learning?

Social learning encompasses situations in which agents attempt to learn from observing the actions of other agents. It is well known that in some cases this can lead to information cascades in which agents blindly follow the actions of others, even though this may not be optimal. Having agents provide reviews in addition to their actions provides one possible way to avoid 'bad cascades.' In this paper, we study one such model where agents sequentially decide whether or not to purchase a product, whose true value is either good or bad. If they purchase the item, agents also leave a review, which may be imperfect. Conditioning on the underlying state of the item, we study the impact of such reviews on the asymptotic properties of cascades. For a good underlying state, using Markov analysis we show that depending on the review quality, reviews may in fact increase the probability of a wrong cascade. On the other hand, for a bad underlying state, we use martingale analysis to bound the tail-probability of the time until a correct cascade happens.