Disagreements are pervasive in human communication. In this paper we investigate what makes disagreement constructive. To this end, we construct WikiDisputes, a corpus of 7425 Wikipedia Talk page conversations that contain content disputes, and define the task of predicting whether disagreements will be escalated to mediation by a moderator. We evaluate feature-based models with linguistic markers from previous work, and demonstrate that their performance is improved by using features that capture changes in linguistic markers throughout the conversations, as opposed to averaged values. We develop a variety of neural models and show that taking into account the structure of the conversation improves predictive accuracy, exceeding that of feature-based models. We assess our best neural model in terms of both predictive accuracy and uncertainty by evaluating its behaviour when it is only exposed to the beginning of the conversation, finding that model accuracy improves and uncertainty reduces as models are exposed to more information.