> The value of an e.g. Princeton degree is that you're the sort of person that could get accepted into Princeton
This doesn't explain why a dropout (or even just someone with an acceptance letter but who never joined) isn't worth as much in the labor market as someone who finished the degree.
Why not? Those things also tell me what sort of person you are. If you took away that extra information and only told me which job applicants got accepted to Princeton and which didn't, then it would still be useful signal on its own.
