Okay here it is:
This is from an AI run I was using to test out an AI personality mod I've been making (this doesn't affect the way ethics distribution works, just the AI personalities file is altered.)
I've picked up the Human Sol Force empire at the year 2315. Here are the faction distribution for them at this time:
View attachment 565649
As you can see, there is a strong Spirtualist faction, in what should be a Militarist, Xenophobic and Materialist empire. These governing factions are present, but their faction approval is really quite low for some. The reason why there is a high spiritualist faction is due to the this empire allying with a fanatic spiritualist / militarist empire to it's east. This also led to an increase in Xenophile attraction due to diplomatic relations, which is another large faction within the empire.
THE TEST:
So here's what I did, I ran the game for 10 years. I cancelled my federation to both remove the spiritualist and xenophile ethics, cancelled all the empires diplomatic action, I supressed both the spiritualist and xenophile factions, and promoted the Governing ethics factions of militarist, supremacy (xenophobe) and materialist factions.
Here are the results:
View attachment 565647
Now, as I mentioned in my previous post on this thread, whether this is quick enough of a change, or too expensive with influence to have an effect you could argue are fair points to be discussed about the system, or whether the factors that affect ethics shifts are too great, but is ethics shifting broken? The answer is no, as you can clearly see that the numbers being promoted have increased, and the numbers for those suppressed have decreased (albeit slowly)