Recommenders and Sales Diversity
At the EC '07
conference, Kartik Hosanagar presented a paper modeling the impact of recommender systems on sales diversity. Do they contribute to a long tail, where lots of products get a few sales, or do they reinforce blockbusters. The paper suggests the latter.
There are actually two effects that we should expect from recommenders. One is discovery-- once one person discovers an item, some other people with similar tastes who would not have found that item do find it. The other is reinforcement-- an item that many people have sampled will be more likely to get recommended.
The paper provides a simple two-item, two-player, two-urn model in section 4. Unfortunately, it begins with an assumption that both players have the same probabilities of choosing the two items, in the absence of a recommender. Without diversity in what people who choose without the recommender, it doesn't seem to capture the discovery effect for recommenders.
Section 5 seems to provide a more promising simulation framework. Consumers have different "ideal points" in the space, and thus are likely to select some distribution of items in absence of a recommender. The recommender that increases the salience of some items to people that are little farther from their ideal point. Even here, however, it doesn't quite seem to capture the phenomenon that the recommender makes salient an item that is in fact closer to the consumer's ideal than what the consumer would have found. It seems to me that you'd need a variant of the Hotelling model where there's a separate model of item salience that is not completely determined by the distance from the customer's ideal. Things that are already blockbusters would be more likely to be noticed and chosen, even if farther from the customer's ideal. That's kind of how the recommender is modeled, but I think it needs to be applied to the base choice model, not just the effect of the recommender system.
D. Fleder, K. Hosanagar "Recommender Systems and Their Impact on Sales Diversity", Proceedings of ACM EC '07, pp.192-199.