hmm I always sort by highest stat numbers. Diplo and Martial preferred for most males. Then specific one intended as governors with Stewardship. Those unlucky ones not intended to breed with Learning.
Diplo and Intrigue for worthy females. Actually only Intrigue for females, but that too will not be important, as only the Dowager and Consort can be given Counsellor position.
Traits? I have experimented alot, yet has not seen the passing of traits (other than from both parents) but for the religion and culture..those two are VERY important and so easy to pass on..its dangerous not to take it seriously.
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Honestly, if your leader has any decent stats/traits, you should probably just tutor at least your heir yourself for more control... too many times I've seen that the courtier with better stats decides it's not good for my heir to be ambitious and stuff like that.
For breeding councillors, just go with the one with the highest score in the appropriate stat and the right educational trait.
Never try to reason the prejudice out of a man. It was not reasoned into him, and cannot be reasoned out. - Sydney Smith
Traits are the most important, because a teacher cannot bequeath a higher rank of trait than the one they possess. My emperor has something like 17 stewardship but is the lowest trait rank, so anyone he teaches can't get a better version of his trait, from what I've seen, so I don't use him to teach unless he's top tier. Usually one of my sons develops something really good, either diplomat martial or stewardship, so I always get them to tutor anyone down the line.
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You can find someone with good traits/ stats but they will be a s*** teacher if they are a measly underhanded rogue or naive appeaser. Their profession is by far the most important thing you want to look for, even if someone else has better stats but a weaker profession.
The clouds pass... the rain does its work and all individual beings flow into their forms." The Book of Changes