PurposeThe purpose of this paper is to apply Connolly’s (2003) concept of agonistic respect to develop a typology of agonistic/antagonistic discourses on Twitter. To develop the typology, this study examines 2,236 Tweets containing the hashtag #guncontrol and uses NodeXL (Smith et al., 2010) to create a network map from which the 75 most influential accounts are derived. Using constant-comparative analysis (Glaser and Strauss, 1967), the authors identify seven categories of discourse style based on Connoly’s (2001) notion of ressentiment and “good faith presentations” of opposing arguments: furtive/secretive, cravenly opportunistic, willfully ignorant, irrational sentimental, misunderstanding/misguided, contingently wrong and reciprocal inquiry. The typology provides a useful and unique way to operationalize agonistic democratic theory and serves as the possible basis for training a machine learning classifier to detect antagonistic discourses on social media platforms.Design/methodology/approachTo determine the level of agonism on Twitter, the authors examine tweets that employed the hashtag #guncontrol on March 12, 2018, one month after the shooting at the Marjory Stoneman Douglass High School in Parkland, Florida on February 14. The authors used the NodeXL excel add-on to collect and map 2,236 tweets. Using grounded theory/constant-comparative analysis (Glaser and Strauss, 1967), the authors develop a typology of seven types of discourses ordered from most antagonistic to most agonistic using Connolly’s (1993) concept of agonistic respect.FindingsAfter examining the top 75 most shared tweets and using constant-comparative analysis to look for patterns of similarity and dissimilarity, the authors identified seven different ways in which individuals present their opponents’ value positions on Twitter on the issue of gun control. The authors were guided by agonistic theory in the authors’ inquiry. The authors looked at how Twitter users expressed their opponent’s faith/value positions, how pluralistic the discourse space was in the comment threads and how much the “talk” was likely to elicit ressentiment from adversaries.Research limitations/implicationsBecause the authors intended to engage in theory building, the authors limited the analysis to a selected number of tweets on one particularly salient topic, on one day. The intent of this was to allow for a close reading of the tweets in that specific network for the purposes of creating a useful typology that can be applied to a broader range of cases/issues/platforms.Practical implicationsThe authors hope that typology could serve as a potential starting point for Twitter to think about how it could design its algorithms toward agonistic talk. The typology could be used as a classification scheme to differentiate agonistic from antagonistic threads. An algorithm could be trained to spot threads overwhelmingly populated by antagonistic discourse and instructed to insert posts from other threads that represent agonistic responses like “contingently wrong” or “reciprocal inquiry.” While generous presentations or deeper, more nuanced presentations of the opponent’s value position are not a panacea, they could serve to change the orientation by which users engage with policy issues.Social implicationsSocial media platforms like Twitter have up to now been left alone to make markets and establish profitability off of public sphere conversations. The result has been a lack of attention to how discourse on these platforms affects users mental well-being, community health and democratic viability. Recently, Twitter’s CEO has indicated a need to rethink the ways in which it promotes “healthy discourse.” The utilitarian presumption that, left to our own devices, we will trial and error our way to the collective good does not account for the importance of others in refining one’s preferences, arguments and world views. Without an “other” to vet ideas and lead us toward becoming wiser, we are left with a Wyly antagonism that moves discourse further and further away from agonistic respect and toward antagonistic virtual struggle. Platforms that allow antagonistic talk that breeds ressentiment run the risk of irrevocably damaging democracy through poisoning its public sphere.Originality/valueThis paper is unique in providing a typology/framework for thinking about the types of “political talk” that exists on Twitter. By using agonistic political theory as a framework, the authors are able to establish some guiding principles for “good political talk” that acknowledges the incommensurability of value positions on issues like gun control. The typology’s emphasis on agonistic respect, ressentiment and generosity in the presentation of alternative value positions provides a starting point from which to map and catalog discourse on Twitter more generally and offers a normative model for changing algorithmic design.