Comment by PaulDavisThe1st

> Satisfying the first assumption means "still monotonic".

Sorry, but I just don't agree. There are "qualifying tests" for jobs that I've done that just do not have any sort of monotonic relationship with job performance. I'm a firefighter (volunteer) - to become operational you need to be certified as either FF I or FF II, but neither of those provide anything more than a "yes, this person can learn the basic stuff required to do this". The question of how good a firefighter someone will be is almost orthogonal to their performance on the certification exams. Someone who gets 95% on their IFSAC FF II exam is in no way predicted to be a better firefighter than someone who got 78%.