How do you gain a Positive Management?

[Quillan]

One of the biggies is the size of your treasury. The "Wasteful" line of traits has triggers at 50k, 100k, and 150k denarii in the treasury at turn start (after the new turns income has been collected). So, if you've got more than 150,000 denarii in the treasury, each and every governor will check 3 times per turn to possibly pick up a point in that trait line.

[Darius]

Leaving your family members in a city with an academy or one of their higher tier versions, and youll find that not only do you tend to get the obviously helpful ancillary characters that increase your management and influence, but I also have noticed, and I'm sure it's not just me, that in a city with an academy or higher tends to grant your family members an occasionally beneficial trait as well. Another thing to do is to leave them in a town with a temple that is dedicated to "law", they will get some nice traits and the priest ancillary and depending on how well developed the temple is a few more ancillaries later on. Try to avoid having a large surplus of funds, and keep your governor's away from temples that promote "war" as they will always end up as "the wrathful" and keep them away from the "wine" temples and such as they tend to get anything from lewd to raging alcaholic type traits.

[tai4ji2x]

in vanilla RTW, academies DO NOT have any effect on traits. this is proven if you look at the relevant file in the data folder.