One other minor point on Bureacracy. If running the slavery civic and your capital goes into slave revolt you lose can lose alot of commerce and production in one turn compared to Free Speach where you still get the extra commerce to towns. Again a minor point.
Let me think about that, let a town-ed city have commerce b, capital with bureacracy a.
In free speech, expected commerce is (6/4)*b*n. (assume commerce goes from 4 to 6 for towns, doesn't matter that much)
Ok, is slave revolt an independent event (most importantly, can multiple happen in one turn?).
If yes, then it's 6/4*(1-p)*b*n, where p is the probability of a slave revolt, that is it is purely multiplicative. If it's not an independent event, then it's 6/4*b*(p*(n-1)+(1-p)*n) = 6/4*b*(n-p). Basically it effectively reduces your empire size by p, so at 100% probability, your empire would be one smaller.
For bureacracy, if it's an independent event, it would again be multiplicative, so you don't "lose" anything technically speaking in the long run.
If it's a one city event, it becomes
(1.5*a*((1-p)+p*(n-1)/n)+b*((1-p)*(n-1)+p*(n-1)/n*(n-2)) = (1.5*a+b*(n-1))-p*(1.5*a/n - b*2/n) = (1.5 a + b (n-1))*((n-p)/n)-b*p/n.
So if my math is right, which is a circumspect assumption at this point, if you're in bureacracy you lose an additional b*p/n, basically a non-capital city. I'll edit this later.