Modeling User Consumption Sequences

We study sequences of consumption in which the same item may be consumed multiple times. We identify two macroscopic behavior patterns of repeated consumptions. First, in a given user's lifetime, very few items live for a long time. Second, the last consumptions of an item exhibit growing inter-arrival gaps consistent with the notion of increasing boredom leading up to eventual abandonment. We then present what is to our knowledge the first holistic model of sequential repeated consumption, covering all observed aspects of this behavior. Our simple and purely combinatorial model includes no planted notion of lifetime distributions or user boredom; nonetheless, the model correctly predicts both of these phenomena. Further, we provide theoretical analysis of the behavior of the model confirming these phenomena. Additionally, the model quantitatively matches a number of microscopic phenomena across a broad range of datasets. Intriguingly, these findings suggest that the observation in a variety of domains of increasing user boredom leading to abandonment may be explained simply by probabilistic conditioning on an extinction event in a simple model, without resort to explanations based on complex human dynamics.