Quantifying polarization: detection and analysis of opinion groups on the Gaza conflict in English-language Reddit discourse

Measuring digital polarization around geopolitical conflicts raises two methodological problems that are rarely addressed jointly: how to extract sociologically meaningful constructs from unstructured text at scale, and which representation of that text allows unsupervised methods to recover ideological structure. We study both on a corpus of 76,816 English-language Reddit comments on the Gaza conflict, collected from 18 subreddits over one year. Five discursive variables (political stance, sentiment, discourse tone, thematic frame and argument quality) are extracted with a large language model through zero-shot, rule-based prompting and validated against expert-coded ground truth. We then benchmark five clustering configurations that cross the feature space (validated discursive variables, dense semantic embeddings, or both) with the clustering architecture (standard k-means versus a robust mixed-data framework combining a Robust Generalized Gower distance with Fast k-medoids), and compare them through a Pairwise Separability Index that measures how distinguishable every pair of clusters is on the discursive variables. Embedding-based configurations conflate rhetorical register with political stance and fail to recover the ideological axis, a failure that persists when 90% rather than 50% of embedding variance is retained. Restricting the feature space to the validated variables is necessary but not sufficient: on the same variables, k-means yields an asymmetric partition that leaves one ideological bloc internally undifferentiated, whereas the robust mixed-data framework recovers a symmetric four-group structure. Substantively, the resulting partition reveals a bidimensional structure in which both the pro-Israel and the pro-Palestine blocs split into a non-hostile faction and a hostile, reactive one, so that ideological position and deliberative-affective register operate as distinct structuring dimensions of the debate.