Free idea: social recommender systems should use statistical interactions

Social recommender systems typically allow you to find things that are correlated with one other thing. Correlated means that people who say they like one song/movie/book/whatever are more likely to say they like the other one. Recent attempts have been made to move beyond this by allowing users to specify more than one item that they like. This has enormous potential that has not yet been realized. Specifying multiple items can allow a user to narrow a search to some attribute that those items have in common. For example, if I pick one song by Joao Gilberto and one by Iron & Wine, by putting those together I am communicating to the recommender system that I want mellow music - not merely that I want some Brazilian music and I also want some folk music.

In statistical terms, what I want is recommendations based on the interaction of the two songs. The results of an interaction recommendation can't be computed by combining the results of recommendations based on the two items alone. In other words it can't be done either by adding the Joao Gilberto recommendations to the Iron & Wine recommendations or by looking for recommendations that appear on both lists. The former would broaden instead of narrow the search, bringing in anything related to either song. The latter would miss songs that are not related to either song but are related to their combination, which is exactly the kind of song I would be happiest to find (i.e. a song with the same kind of feeling from a completely unexpected artist or genre).