[rwilson4]

In the hard sciences, it's often possible to isolate the phenomenon of interest away from any other influencing factors, e.g. in a laboratory. But many phenomena, like social interactions, or even agriculture, are difficult to isolate in this way. Randomization provides another way of "zooming in" on the treatment of interest.

In the example you gave, a test is going to have very low power because of the important factor with huge variance. If that factor is observed, you can create pairs of units with that factor identical within the pair, then randomly assign treatment to one unit in each pair.

[mjburgess]

The traits I was talking about are unobserved/unknown. As mechanisms become more complex from the genetic to cellular to social, powerlaws appear more often and the number of unobservables grows at least super-linearly. On these grounds I think that there really isn't any kind of social science possible.

[rwilson4]

This is a complex topic, but it's a bit simpler when outcomes are bounded, such as a binary outcome that either occurs or does not occur. In that case, the impact of any one factor is bounded.

In the scenario you're describing, this other factor drowns out any influence the treatment has on the outcome. You'll struggle to get a statistically significant result (low power) and the confidence interval on the treatment effect will include 0. This too can be a valuable finding: sometimes the answer is that the treatment is not particularly effective.

[RandomLensman]

Given the practical predictability of at least some (broadly) social phenomena and interventions (or in other areas with large "factor surfaces"), not sure why any kind of social science is impossible as such. Maybe some things are out of reach, but that would hold for other sciences, too.