Conviction, persuasion, and cross-cutting exposure: a Bayesian model of deliberation in online political debates

Abstract

Online debate platforms offer a window into whether exposure to diverse crowds changes how people reason: they capture political preferences, the perceived quality of arguments, and the ideological diversity of the audience. Drawing on theories of deliberative democracy and cross-cutting exposure, I develop a Bayesian logistic regression model that decomposes voting behaviour in online debates into three components: conviction (agreement between a user's prior beliefs and a debate's stance), persuasiveness (perceived argument quality), and cross-cutting exposure (the ideological diversity of a debate's prior voters). I apply this framework to the Debate.org dataset: approximately 341k votes across 78k debates on 48 socio-political topics. As the platform provides no predefined topic labels, I infer topic and stance from debate text using large language models. I test whether a more ideologically diverse prior audience weakens a voter's conviction, a central claim from the cross-cutting exposure literature. Persuasiveness is the strongest and most consistent predictor of vote choice, never outweighed by conviction, though conviction remains a credible predictor on several topics tied to personal freedoms. Cross-cutting exposure moderates conviction on 4 of 47 topics, though these results are sensitive to topic classification and sparse coverage, with implications for the design of deliberative platforms.