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The precise mechanisms by which the information ecosystem polarizes society remain elusive. Focusing on political sorting in networks, we develop a computational model that examines how social network structure changes when individuals participate in information cascades, evaluate their behavior, and potentially rewire their connections to others as a result. Individuals follow proattitudinal information sources but are more likely to first hear and react to news shared by their social ties and only later evaluate these reactions by direct reference to the coverage of their preferred source. Reactions to news spread through the network via a complex contagion. Following a cascade, individuals who determine that their participation was driven by a subjectively "unimportant" story adjust their social ties to avoid being misled in the future. In our model, this dynamic leads social networks to politically sort when news outlets differentially report on the same topic, even when individuals do not know others' political identities. Observational follow network data collected on Twitter support this prediction: We find that individuals in more polarized information ecosystems lose cross-ideology social ties at a rate that is higher than predicted by chance. Importantly, our model reveals that these emergent polarized networks are less efficient at diffusing information: Individuals avoid what they believe to be "unimportant" news at the expense of missing out on subjectively "important" news far more frequently. This suggests that "echo chambers"—to the extent that they exist—may not echo so much as silence.