How Should We Measure Filter Bubbles? A Regression Model and Evidence for Online News

News media play an important role in democratic societies. Central to fulfilling this role is the premise that users should be exposed to diverse news. However, news recommender systems are gaining popularity on news websites, which has sparked concerns over filter bubbles. More specifically, editors, policy-makers and scholars are worried that these news recommender systems may expose users to less diverse content over time. To the best of our knowledge, this hypothesis has not been tested in a longitudinal observational study of real users that interact with a real news website. Such observational studies require the use of research methods that are robust and can account for the many covariates that may influence the diversity of recommendations at any given time. In this work, we propose an analysis model to study whether the variety of articles recommended to a user decreases over time in such an observational study design. Further, we present results from two case studies using aggregated and anonymized data that were collected by two western European news websites employing a collaborative filtering-based news recommender system to serve (personalized) recommendations to their users. Through these case studies we validate empirically that our modeling assumptions are sound and supported by the data, and that our model obtains more reliable and interpretable results than analysis methods used in prior empirical work on filter bubbles. Our case studies provide evidence of a small decrease in the topic variety of a user's recommendations in the first weeks after they sign up, but no evidence of a decrease in political variety.