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?