I did a test of that in my current Deity-game. I got the ideology first.
In the next 15 turns the AIs chose different ideologies - even if I reloaded and chose the same. Ie I go Order twice and the swedes go Freedom the first time and Autocracy the second.
I'm gearing up for the mother of all wars, and I'm still considering Freedom for the happy faces. A buffer of 10ish just won't cut it, and Freedom gives the the most faces right? Bloody derail. Or is it Order?