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Governments around the world are increasingly utilising online platforms and social media to engage with, and ascertain the opinions of, their citizens. Whilst policy makers could potentially benefit from such enormous feedback from society, they first face the challenge of making sense out of the large volumes of data produced. In this article, we show how the analysis of argumentative and dialogical structures allows for the principled identification of those issues that are central, controversial, or popular in an online corpus of debates. Although areas such as controversy mining work towards identifying issues that are a source of disagreement, by looking at the deeper argumentative structure, we show that a much richer understanding can be obtained. We provide results from using a pipeline of argument-mining techniques on the debate corpus, showing that the accuracy obtained is sufficient to automatically identify those issues that are key to the discussion, attracting proportionately more support than others, and those that are divisive, attracting proportionately more conflicting viewpoints. 2017 Copyright is held by the owner/author(s).