Anders, what I meant is your Kim/Hillary example has a graph that looks like this:

A -> Y <- C -> A, and you want p(Y | do(a)). Your point is that your problem grows exponentially with the statespace of C.

Imagine instead that you had a much more complicated word example with a graph in Fig. 7 in the paper I linked (where a bunch of confounders are not observed and are arbitrarily complicated. In fact instead of x1, ..., x5, imagine it was a graph of length k: x1, ..., xk. And you want p(xk | do(xk-2)). Then my claim is the problem is not exponential size/time in the statespace of those confounders, OR in k, but in fact of constant size/time.

Although I am not entirely sure how to ask a prediction market for the right parameters directly... this is probably an open problem.