Book of Why, causal diagram 9.5 - how does that represent Kruskal's argument? In the Book of Why, Judea Pearl, there is the case of a Berkley admission gender discrimination paradox which was solved by Peter Bickel. The solution was done by searching for discrimination department-wise (conditioning on departments). However, Kruskal later showed a counterexample clarifying that conditioning on department was correct only if department and outcome (admission result) are unconfounded.
Kruskal hypothesized a department with the following admission criteria -

accept all in-state males and out-of-state females and reject all
out-of-state males and in-state females.

In the book, the causal diagram is provided in figure 9.5 as below -

My question is, how come the dependence of the criteria on State of Residence be depicted by drawing causal arrows from State of Residence to Department and Outcome respectively. To me it seems that, it is the function behind the arrow Department$\rightarrow$Outcome that is dependent on State of Residence and Gender. How is this causal diagram then an appropriate representation of Kruskal's argument?

Well, according to the rules of causal diagrams, you can only draw arrows from one node to another. You cannot draw an arrow from a node into an arrow. So the real question is this: are the arrows from State of Residence going into Department and Outcome both correct?

*

*State of Residence into Department. Different regions of the country have different problems, and it is not unreasonable to think that residents of New York City might be more inclined to go into finance (a hot item in NYC, or at least it was), and residents of North Dakota more inclined to go into petroleum engineering (quite a hot item there). So the idea of State of Residence influencing Department seems sound.


*State of Residence into Outcome. This is an accepted arrow by virtue of the discussion on page 313, where you quoted the most critical part. That is, this arrow partially models the blatant discrimination that Kruskal hypothesized. The arrow from Gender into Outcome models the other half of this discrimination.
