One entrance exam idea I like is to have a lottery for N slots where the top test scorers have 90% chance of admission, but that decays by some curve until the

One entrance exam idea I like is to have a lottery for N slots where the top test scorers have 90% chance of admission, but that decays by some curve until the people in 3Nth place have 0% chance of admission. Adjust the curve to your liking. This might do a good job of fending off the parents that want to make their overachieving kids study a lot for the entrance exam, because it might all be for nothing.