Y can consist of multiple variables, and then there would always be multiple ways, right?
Not necessarily. For instance if X has only one output, then there’s only one way for X to change things, even if the one output connects to multiple Ys.
I thought by indirect you meant that the path between X and Y was longer than 1.
Yes.
If some third cause is directly upstream from both, then I suppose it wouldn’t be uniquely defined whether changing X changes Y, since there could be directions in which to change the cause that change some subset of X and Y.
I’m not sure I get it, or at least if I get it I don’t agree.
Are you saying that if we’ve got X ← Z → Y and X → Y, then the effect of X on Y may not be well-defined, because it depends on whether the effect is through Z or not, as the Z → Y path becomes relevant when it is through Z?
Because if so I think I disagree. The effect of X on Y should only count the X → Y path, not the X ← Z → Y path, as the latter is a confounder rather than a true causal path.
Not necessarily. For instance if X has only one output, then there’s only one way for X to change things, even if the one output connects to multiple Ys.
Yes.
I’m not sure I get it, or at least if I get it I don’t agree.
Are you saying that if we’ve got X ← Z → Y and X → Y, then the effect of X on Y may not be well-defined, because it depends on whether the effect is through Z or not, as the Z → Y path becomes relevant when it is through Z?
Because if so I think I disagree. The effect of X on Y should only count the X → Y path, not the X ← Z → Y path, as the latter is a confounder rather than a true causal path.