The social web continues to explode, but existing online interaction tools (e.g. blogs, forums, news and media sites) tend to discourage debate, and may even facilitate low-quality argument and thinking. We are researching how to semantically represent, structure, evaluate and relate multiple argumentative viewpoints, integrated with linked data. We introduced a general model for argumentation and voting in the social web, providing an infrastructure for more open, flexible debates. Based on evolutionary game theory, we showed how actors/users can benefit from recognizing intentions and commitments of other actors/users, leading to a stable increase in cooperation compared to extant best strategies, with results published at Nature SR, IJCAI and AAMAS.