In an increasingly polarized world, demagogues who reduce complexity down to simple arguments based on emotion are gaining in popularity. Are opinions and online discussions falling into demagoguery? In this work, we aim to provide computational tools to investigate this question and, by doing so, explore the nature and complexity of online discussions and their space of opinions, uncovering where each participant lies. More specifically, we present a modeling framework to construct latent representations of opinions in online discussions which are consistent with human judgements, as measured by online voting. If two opinions are close in the resulting latent space of opinions, it is because humans think they are similar. Our modeling framework is theoretically grounded and establishes a surprising connection between opinions and voting models and the sign-rank of a matrix. Moreover, it also provides a set of practical algorithms to both estimate the dimension of the latent space of opinions and infer where opinions expressed by the participants of an online discussion lie in this space. Experiments on a large dataset from Yahoo! News, Yahoo! Finance, Yahoo! Sports, and the Newsroom app suggest that unidimensional opinion models may often be unable to accurately represent online discussions, provide insights into human judgements and opinions, and show that our framework is able to circumvent language nuances such as sarcasm or humor by relying on human judgements instead of textual analysis.
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