Does the increasing robotization of the workplace weaken labor unions? The dominant hypothesis in the automation literature is that robots weaken unions and, as a result, undermine worker voice in democratic politics. However, the leading task-based model of automation does not consider unions, and recent studies tend to focus on estimating average effects. We argue that the relationship between robotization and organized labor is heterogeneous. We integrate tasks and automation into a model of collective bargaining and worker mobilization. Our model illustrates that the impact of robots on unions does not reduce to a race of job displacement vs. productivity gains. Empirically, we use quantile instrumental variable regression and find that the impact of robotization on unionization significantly varies across 722 regional labor markets in the US. To explore mechanisms, we turn to a survey experiment that enables us to estimate whether beliefs about worker mobilization are sensitive to the bargaining environment.