H AVING THE L AST WORD :U NDERSTANDING H OW TO S AMPLE D ISCUSSIONS O NLINE APREPRINT Gioia Boschi Department of Mathematics King’s College London Strand, London WC2R 2LS gioia.boschi@kcl.ac.uk Anthony P. Young Department of Informatics King’s College London Strand, London WC2R 2LS peter.young@kcl.ac.uk Sagar Joglekar Department of Informatics King’s College London Strand, London WC2R 2LS sagar.joglekar@kcl.ac.uk Chiara Cammarota Department of Mathematics King’s College London Strand, London WC2R 2LS chiara.cammarota@kcl.ac.uk Nishanth Sastry Department of Informatics King’s College London Strand, London WC2R 2LS nishanth.sastry@kcl.ac.uk June 11, 2019 ABSTRACT In online debates, as in offline ones, individual utterances or arguments support or attack each other, leading to some subset of arguments winning (potentially from different sides of the debate). However, online conversations are much larger in scale than offline ones, with often hundreds of thousands of users weighing in, and so, readers are often forced to sample a subset of the arguments or arguments being put forth. Since such sampling is rarely done in a principled manner, users may not get all the relevant “winning” arguments to get a full picture of the debate from a sample. This paper is interested in answering the question of how users should sample online conversations to selectively favour winning arguments. We apply techniques from argumentation theory and complex networks to build a model that predicts the probabilities of the normatively winning arguments given their location in idealised online discussions. Online discussions are modeled as reply networks where nodes represent the comments exchanged and directed edges represent replies that can either be supporting or attacking. Our model shows that the proportion of replies that are supporting in the network, the network’s in-degree distribution and the locations of unrebutted arguments (“the last words”) all determine the behaviour of the probability that a comment is a winning argument given its location. This is also verified with data scraped from the online debating platform Kialo. In predicting the locations of the winning arguments in reply networks, we can therefore suggest which arguments a reader should sample and read if he or she would like to grasp the winning opinions in such discussions. Our models have important implications for the design of future online discussion platforms. Keywords Argumentation Theory, Online Discussions, Probabilistic Analysis, Graph Sampling, Kialo 1 Introduction 1.1 Background and Research Question The Internet has enabled large scale discussions on all sorts of topics, ranging from important news events to comments on user-posted videos, and they often have consequences in the offline world (e.g. [1, 2, 3, 4, 5, 6]). Early examples of arXiv:1906.04148v1 [cs.SI] 10 Jun 2019