Ignoring the rest of the thread, there are already some intensive studies done by players onto the genetics and i think it more or less conclusively proved that it was just a percentage chance and had nothing to do with careful breeding.
So it was just as likely to get a genius from 2 imbeciles as 2 geniuses....
However with patch 1.08 (and maybe 1.07 i forget) they seem to have increased these percentages based on the parents traits however i don't think it carries over in the DNA files to grandchildren etc as they only cover visual portraits.
Previously I don't think Paradox ever came out to confirm or deny any of this preferring not to crush the spirit of those who to liked to try breeding the ultimate ruler but even i have noticed the increased likelihood of parents passing on the traits. Is it too easy? Without elective probably not, a fair amount of first born etc aren't the ones that get the best stats but people can play how they want.
I have noticed that the genius children of genius parents seem to be the middle children. Sometimes later children but mostly middle.