A central role in shaping the experience of users online is played by recommendation algorithms. On the one hand they help retrieving content that best suits users taste, but on the other hand they may give rise to the so-called “filter bubble” effect, favoring the rise of polarization.

In the present paper we study how a user-user collaborative-filtering algorithm affects the behavior of a group of agents repeatedly exposed to it.

By means of analytical and numerical techniques we show how the system stationary state depends on the strength of the similarity and popularity biases, quantifying respectively the weight given to the most similar users and to the best rated items.

In particular, we derive a phase diagram of the model, where we observe three distinct phases: disorder, consensus, and polarization. In the last users spontaneously split into different groups, each focused on a single item. We identify, at the boundary between the disorder and polarization phases, a region where recommendations are nontrivially personalized without leading to filter bubbles.

Finally, we show that our model well reproduces the behavior of users on the online music platform last.fm. This analysis paves the way to a systematic analysis of recommendation algorithms by means of statistical physics methods and opens the possibility of devising less polarizing recommendation algorithms.

A. Bellina, C. Castellano, P. Pineau, G. Iannelli, G. De Marzo, Effect of collaborative-filtering-based recommendation algorithms on opinion polarization, Physical Review E 108 (2023) 054304, DOI: 10.1103/PhysRevE.108.054304.