Okay, suppose you have a two node system. One node is whether someone smokes, one node is whether there's tar in their lungs. The smoking node has a causal influence on the tar node, but there's also a random factor. Say if someone smokes they'll have tar in their lungs, otherwise there's only a 5% chance they do. This is only two nodes. To express this in the alternate approach, the tar node needs to be a deterministic function of other nodes, and an extra random node is required for this. It could be a "polluted atmosphere" node, value "yes" 5% of the time, and the tar node could be "yes" if either the smoking or polluted atmosphere nodes are "yes" (a deterministic function of its input nodes).
The smoking node has a causal influence on the tar node, but there's also a random factor.
I don't see how this is true of either approach.
Let X_smokes and X_tar be the random variables associated with your nodes. Under the first approach, if there are no other "exogenous" Y-nodes, then there is a function f_tar such that X_tar = f_tar(X_smokes). Doesn't that mean that whether you have tar is entirely a function of whether you smoke?
Maybe I'm mistaken about what it means for one random variable to be a function of another. We can underst...
Michael Nielsen has posted a long essay explaining his understanding of the Pearlean causal DAG model. I don't understand more than half, but that's much more than I got out of a few other papers. Strongly recommended for anyone interested in the topic.