[shurtler]

Hey, the key assumption (the "identification" assumption) is in 2.4 of the paper you referred to. I do not have time to go through the notation, but it seems to be like a fairly standard "no unmeasured confounders" assumption - so you need to ASSUME that nothing influences both the treatment and the outcome you are interested in. Then, of course, you do not need to randomize, but can use observational data.

I know that Petersen and van der Laan are well-respected researchers in causality that know exactly what they are doing. E.g., Petersen has a course (I think at Berkeley) that uses causal graphs which were pioneered by Judea Pearl (see comments below). I can only second the recommendation to dig into his work.