In online debates individual arguments support or attack each other, leading to some subset of arguments being considered more relevant than others. However, in large discussions readers are often forced to sample a subset of the arguments being put forth. Since such sampling is rarely done in a principled manner, users may not read all the relevant arguments to get a full picture of the debate. This paper is interested in answering the question of how users should sample online conversations to selectively favour the currently justified or accepted positions in the debate. We apply techniques from argumentation theory and complex networks to build a model that predicts the probabilities of the normatively justified arguments given their location in online discussions. Our model shows that the proportion of replies that are supportive, the number of replies that comments receive, and the locations of un-replied comments all determine the probability that a comment is a justified argument. We show that when the degree distribution of the number of replies is homogeneous along the discussion, for acrimonious discussions, the distribution of justified arguments depends on the parity of the graph level. In supportive discussions the probability of having justified comments increases as one moves away from the root. For discussion trees that have a non-homogeneous in-degree distribution, for supportive discussions we observe the same behaviour as before, while for acrimonious discussions we cannot observe the same parity-based distribution. This is verified with data obtained from the online debating platform Kialo. By predicting the locations of the justified arguments in reply trees, we can suggest which arguments readers should sample to grasp the currently accepted opinions in such discussions. Our models have important implications for the design of future online debating platforms.
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