I agree that this Tweet was imperfectly phrased, and that it makes an unconvincing and strong claim about deterministic counterfactuals. I had anticipated that there would be responses such as this one, which are very reasonable, and I had already planned to add my thoughts on Twitter. I can no longer find the original tweet, it appears as if the author may have recognised that it could be misinterpreted and deleted it (?). Either way, thank you for giving me an opportunity to respond here instead, without being constrained to 140 characters!
When using causal models, you can either rely on an ontology with deterministic counterfactuals (as in the tweet) or one with stochastic counterfactuals (where every individual u has an outcome that is drawn randomly from their individual counterfactual distributions f_u(Y_u)(1) and f_u(Y_u)(0)). My understanding is that almost all the foundational results in causal inference are invariant to whether the causal model uses deterministic or stochastic counterfactuals, but that it is sometimes didactically useful to focus on deterministic variables, which are often easier to understand. Given that the results hold under either model, this simplification often appears justifiable, not least because it significantly reduces notational load.
I fully agree that treatment outcomes are highly situational and often unpredictable, that they depend on a large number of factors which are too complex to attempt to model explicitly and therefore best understood as “stochasticity”. But the crucial point I want to make, is that if we want to make decisions to optimize outcomes, it is necessary to find a structure to the randomness: If everything was fully random (without any structure), we could never have any rational reasons for preferring one treatment option over another.
Stochastic counterfactual distributions are ideally suited for representing the relevant kind of structure. If a person’s outcomes depend on a specific aspect of physiological complexity, there are some settings where this may be irrelevant to your decision making (such that it is acceptable to consider it “randomness” or “noise”), and other settings where causal reasoning will reveal that it needs to be tackled heads on in the analysis. Only with a causal model is possible to fully clarify the reasoning that optimises predicted outcome under intervention, and these causal models will use something like a counterfactual distribution to represent the structure that it imposes on the stochasticity.
I don’t think anyone in causal inference expects treatment response to be constant over time. When they talk about counterfactuals as “immutable personal characteristics”, I believe they are talking about a highly situational construct that is in some sense “known to God” and that represents what will happen to the patient if they take treatment at some specified time, but which is certainly not assumed to be stable over time. At the very least, the original Tweet should have given a time index to the counterfactuals.
The distinction between stochastic and deterministic counterfactuals is philosophically very interesting, and there may exist multiple rational ways to think about these constructs. I think it was a mistake for the original tweet to imply that causal inference depends on a “realism” about deterministic counterfactuals.