While searching older posts and conducting some testing regarding traits, I discovered that the public order ratio between Nobility and Middle/Lower Classes is heavily influential for most of the acquired Minister traits, some ancillaries and even general traits.
Having a higher ratio of P.O. favouring the nobility results in Lewdness traits, Morally Impaired, and ancillaries like Landscape Gardener, Mistress etc. Having a higher ratio favouring the Lower/Middle leads to Honest trait (amongst other positive ones), Jug Head etc.
A happy nobility ratio appears to be related with a general chance of gaining "Drunk" traits as well. It seems that when a certain amount of points is accumulated (I supposed it's the "value" on trigger_effects_tables) every character gets a random chance of spawning a bad trait based on trait_trigger_tables.
This would also explain why further in campaign acquired traits are way less common. As you develop (government and entertainment building chain), your public order increases for both sides. That being so, it's way more difficulty for putting a big ratio between Nobility and Lower Classes: a 1 for Nobility versus 2 for Lower P.O. is a difference of 100%. A difference between 10 for Nobility and 11 for Lower Classes is of 10%, diminishing dramatically the chance of acquiring a trait.
On the same note, Constitutional Monarchies have less traits that favour the middle classes, opposed to Absolute Monarchy, which leads to the snowballing issue.
Moreover, it seems that - for some obscure reason - higher Public Order for the Nobility seems to only lead to bad traits, which also provide a bonus for Nobility happiness... causing the good ole snowball of more bad traits!
Where is exactly this located on the db tables? trigger_effects_tables does explain some things, but not the P.O. effect. Is there some comprehensible guide on trait triggers? Did someone fixed this weird system by modding?