Opinion aggregation on social media uses various mechanisms, such as "Likes" or thumbs-up/-down, which handle a single item at a time. In many domains (e.g., political discussion), we need to consider the relationships between different claims, and how they rebut one another through complex webs of arguments and counter-arguments. We study methods for aggregating opinions about such complex argument networks, the quality of the outcomes of different methods of opinion aggregation, and whether strategic agents can manipulate those outcomes.