To what extent are democratic elections vulnerable to social media manipulation? The fractured state of research and evidence on this most important question facing democracy is reflected in the range of disagreement among experts. Facebook chief executive officer Mark Zuckerberg has repeatedly called on the U.S. government to regulate election manipulation through social media. But we cannot manage what we do not measure. Without an organized research agenda that informs policy, democracies will remain vulnerable to foreign and domestic attacks. Thankfully, social media's effects are, in our view, eminently measurable. Here, we advocate a research agenda for measuring social media manipulation of elections, highlight underutilized approaches to rigorous causal inference, and discuss political, legal, and ethical implications of undertaking such analysis. Consideration of this research agenda illuminates the need to overcome important trade-offs for public and corporate policy—for example, between election integrity and privacy. We have promising research tools, but they have not been applied to election manipulation, mainly because of a lack of access to data and lack of cooperation from the platforms (driven in part by public policy and political constraints).