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If you want to do something for poorer students, pay a percentage of their tuition cost in direct proportion to their grades; a perfect GPA means free college.

This will cause GPAs to be subject to Goodhart's law even more than it is now. And GPA has flaws even without it; imagine a poor person being forced to choose between taking an easy class and certainly being able to afford college, or taking a class in which he can learn, and risking not getting an A and having to pay more for college. You can try to fix this by counting harder class more, but that can result in a situation where a student who takes a non-high-tier class and gets an A in it reduces his GPA by doing so.

Not to mention the possibility that a poor person got a bad GPA for external reasons related to poverty. Going hungry, being homeless, or not having an intact family, for instance, can hurt GPA

Then how about using SAT instead of GPA?
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You're right. It's important to think of ways in which policies can go wrong. I'll have to think about this more.
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That's easy to fix. Most colleges have core classes that everyone majoring in a certain subject has to take. The GPA can be based on this types of classes only. One can also add different weights for different types of classes.
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