Ranking with Popularity Bias: User Welfare under Self-Amplification Dynamics

While popularity bias is recognized to play a role in recommmender (and other ranking-based) systems, detailed analyses of its impact on user welfare have largely been lacking. We propose a general mechanism by which item popularity, item quality, and position bias can impact user choice, and how it can negatively impact the collective user utility of various recommender policies. Formulating the problem as a non-stationary contextual bandit, we highlight the importance of exploration, not to eliminate popularity bias, but to mitigate its negative effects. First, naive popularity-biased recommenders are shown to induce linear regret by conflating item quality and popularity. More generally, we show that, even in linear settings, identifiability of item quality may not be possible due to the confounding effects of popularity bias. However, under sufficient variability assumptions, we develop an efficient UCB-style algorithm and prove efficient regret guarantees. We complement our analysis with several simulation studies.