Consider the following scenario:
Alice subscribes to a video rental service that allows her to watch movies. Every time A watches a movie, she rates it either thumbs up (1) or thumbs down (0), and she then chooses the next movie she wants to watch. Every movie belongs to exactly one director, and a director can have directed many movies. The question is, what is the best way to determine who A's "favorite" director is?
My initial thought was do something like:
- For each director of at least one movie that A watched, calculate the lower bound of some binomial confidence interval (e.g. Wilson score interval) as A's "favorability" score for that director
However, this binomial approach seems flawed because it ignores a seemingly crucial piece of information: Alice has an entire universe of movies to choose from, and if she consistently chooses to watch movies from a certain director, then doesn't that tell us something about her preference for that director, even if she then rates that director's movies below her average? I feel like there must be some element of "voting with one's feet" that is ignored if we only consider ratings on the movies that were watched.
What is the best way to combine both the selection of movie/director with the ratings on individual movies to determine who is A's favorite director? It seems like A's preference for director D has to be a function of A's ratings on D's movies that she watched, and also the % of all of D's movies that A chose to watch.
UPDATE: I should make clear, the problem I'm dealing with isn't quite as simple as the thumbs up/thumbs down case, it's really more like "A watches a movie and then checks a box if she liked it." So each viewing does result in a 0 or a 1, but the absence of checking a box isn't quite the same thing as a "thumbs down" because the viewer might only feel compelled to check the "approve" box if she really likes something. All the more reason that the choice of what to watch has to factor into preferences