The potential outcome frameworks (Rubin, 1974) and structural causal models (Pearl, 2009) have been proven to be equivalent (ibid.). Their formal equivalence is usually taken for granted, despite an ongoing debate about the benefits of either of the two frameworks in empirical sciences like epidemiology or economics. Markus (2021) has recently argued that the two frameworks are only weakly equivalent, albeit without reference to any formal notion of equivalence. The thesis defended in this poster is that the best available explication of the proof of equivalence of the two frameworks is in terms of 'equivalence as intertranslatability', a well-established and intuitive notion of equivalence that builds on inverse translations (Barrett and Halvorson, 2016). There is a growing literature on theoretical equivalence in the philosophy of physics that has developed and explicated several different conceptions of what 'theoretical equivalence' could mean (for an overview see Weatherall, 2019). Most of the authors start from their intuitions on which physical theories should be regarded as equivalent in some relevant sense. They then develop formal criteria of theoretical equivalence that conform to these intuitions. In arguing for 'equivalence as intertranslatability', I demonstrate why competing formal notions of equivalence, such as logical equivalence, categorical equivalence, and definitional equivalence, are unfit for explicating the equivalence between the potential outcome framework and structural causal models.

This poster extends the philosophical literature in two distinct ways. Firstly, the discussion on theoretical equivalence has mostly focused on examples from physics, with some exceptions; I will focus on two frameworks from the causal inference literature. The second contribution of this paper is a service to the empirical sciences engaged in causal inference. In clarifying the notion of equivalence relevant for this methodological discussion, I hope to assist empirical researchers in choosing the framework that best fits their research agenda.