Social scientific work on argumentation is yet to address the perennial tension between social cognition and social constructionism. Moreover, argumentation‐based qualitative analysis protocols are needed for interview and textual data. Nonetheless, argumentation models remain too complex to reflect everyday argumentation and are not necessarily reflective of underlying cognitive processes. This presents the need for further theorising social behaviour, with a view to formulating a model of argumentation that (a) is parsimonious, and (b) aligns with the literature on joint projects, due to the fact that in social cognition terms, argumentation is for doing. In this paper, we draw upon interdisciplinary literature on argumentation, noting convergences among different approaches. We then proceed to consider the socio‐cognitive bedding provided by Lay Epistemic Theory, to present our Minimal Model of Argumentation (MMA). In MMA, interlocutors are held to make claims concerning an issue of concern, and defend them using warrants, evidence and qualifiers. We end by providing empirical examples supporting the utility of our model in qualitative research.