Increasingly influential in our democracies, digital spaces’ closed algorithms are of growing regulatory interest. With this greater influence comes a greater need to characterize these algorithms’ inner mechanisms as well as their social consequences. We propose a faithful replica of Twitter user behaviors and explore various recommender systems that shape their online experiences. After having designed and calibrated our model using empirical interaction data collected by the Politoscope project, we show, from what is known of existing recommender systems, that they overexpose users to harmful, negative content. This overexposure, called algorithmic negativity bias, results from the positive feedback between human negativity bias and optimization of user engagement on online social networks.