  In the last decade, political debates have progressively shifted to social
media. Rhetorical devices employed by online actors and factions that operate
in these debating arenas can be captured and analysed to conduct a statistical
reading of societal controversies and their argumentation dynamics. In this
paper, we propose a five-step methodology, to extract, categorize and explore
the latent argumentation structures of online debates. Using Twitter data about
a "no-deal" Brexit, we focus on the expected effects in case of materialisation
of this event. First, we extract cause-effect claims contained in tweets using
RegEx that exploit verbs related to Creation, Destruction and Causation.
Second, we categorise extracted "no-deal" effects using a Structural Topic
Model estimated on unigrams and bigrams. Third, we select controversial effect
topics and explore within-topic argumentation differences between self-declared
partisan user factions. We hence type topics using estimated covariate effects
on topic propensities, then, using the topics correlation network, we study the
topological structure of the debate to identify coherent topical
constellations. Finally, we analyse the debate time dynamics and infer
lead/follow relations among factions. Results show that the proposed
methodology can be employed to perform a statistical rhetorics analysis of
debates, and map the architecture of controversies across time. In particular,
the "no-deal" Brexit debate is shown to have an assortative argumentation
structure heavily characterized by factional constellations of arguments, as
well as by polarized narrative frames invoked through verbs related to Creation
and Destruction. Our findings highlight the benefits of implementing a systemic
approach to the analysis of debates, which allows the unveiling of topical and
factional dependencies between arguments employed in online debates.
