1 Inferring popularity from ranked items Let's recall the ranking model we discussed in the lectures: The user encounters a list of ranked items in order I1, I2, . . . , In. When they encounter item Ij in the list: - They find Ij interesting with probability pj , independently of their decisions about previous items. - If they find Ij interesting, they consume it and leave the platform. - If they don't find Ij interesting, they leave the platform anyway with probability q (due to their impatience). - Otherwise they move on to consider item Ij+1. For ease of reference, in Figure 1 we reproduce a diagram from the class lecture slides, showing how a user moves through a set of two items in this ranking model. Let's consider a platform that is setting up a Web page showing two news articles I1 and I2, with item I1 placed above item I2. They are using the ranking model to estimate how many users will consume each article in expectation