Just like how many companies have methods available to them to remove bad glassdoor reviews (or make fake 5-star reviews), this system is even more rife for abuse.
Credit scores seem to be pretty robust? Maybe this kind of system would work:
1. A third-party assigns everyone a hidden score, and gives them a cryptographic signing key.
2. They can sign off on one-time lookups to companies they apply to. Every time their credit score is looked up, it decreases to disincentivize "spray and pray".
3. Companies are incentivized to go directly to the third-party (to ensure truthiness), and not divulge the score to other companies (since they are in a competition).
4. The actual algorithms used to determine scores should stay hidden to avoid manipulation. However, how do you also ensure accuracy? Maybe have several dozen reputation companies, and apply Shapley values based on hiring decisions. To avoid correlation, you should only update a reputation's weight when the hiring decision didn't query it.
You also want colleges to signal to their applicants, not force them to also signal for their alumni. The two will naturally be correlated, but you can do better by specializing.
