  The prevalent perspective in quantitative research on opinion dynamics
flattens the landscape of the online political discourse into a traditional
left--right dichotomy. While this approach helps simplify the analysis and
modeling effort, it also neglects the intrinsic multidimensional richness of
ideologies. In this study, we analyze social interactions on Reddit, under the
lens of a multi-dimensional ideological framework: the political compass. We
examine over 8 million comments posted on the subreddits /r/PoliticalCompass
and /r/PoliticalCompassMemes during 2020--2022. By leveraging their
self-declarations, we disentangle the ideological dimensions of users into
economic (left--right) and social (libertarian--authoritarian) axes. In
addition, we characterize users by their demographic attributes (age, gender,
and affluence).
  We find significant homophily for interactions along the social axis of the
political compass and demographic attributes. Compared to a null model,
interactions among individuals of similar ideology surpass expectations by 6%.
In contrast, we uncover a significant heterophily along the economic axis:
left/right interactions exceed expectations by 10%. Furthermore, heterophilic
interactions are characterized by a higher language toxicity than homophilic
interactions, which hints at a conflictual discourse between every opposite
ideology. Our results help reconcile apparent contradictions in recent
literature, which found a superposition of homophilic and heterophilic
interactions in online political discussions. By disentangling such
interactions into the economic and social axes we pave the way for a deeper
understanding of opinion dynamics on social media.
