  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.
