The public is increasingly concerned about the practices of large technology companies with regards to privacy and many other issues. To force changes in these practices, there have been growing calls for “data strikes.” These new types of collective action would seek to create leverage for the public by starving business-critical models (e.g. recommender systems, ranking algorithms) of much-needed training data. However, little is known about how data strikes would work, let alone how effective they would be. Focusing on the important commercial domain of recommender systems, we simulate data strikes under a wide variety of conditions and explore how they can augment traditional boycotts. Our results suggest that data strikes can be effective and that users have more power in their relationship with technology companies than they do with other companies. However, our results also highlight important trade-offs and challenges that must be considered by potential organizers.