Amenities are either totally broken or I simply don't understand how they work

To me the easiest way to understand amenities was this: They are exactly the same as Civ 5's +4 Happiness from Luxury Resources, except the +4 is split among your cities.
 
I understand that, but as I said, I am playing Always War, the only way to get rid of enemies is by total eliminations. Right now, USA and China have been eliminated from the game.

That said, there are cities that were not mine without war weariness such as Beijing and Washington (maybe due to them being capitals?), but also Chicago and Chengdu.

For all three city states, there are varying numbers for war weariness, Zanzibar, Yerevan and Kumasi. Weird
 
Is it proportional to pop?
Let's see

I could see some rough pattern for eliminated Nations:

Capitals no war weariness
population 1-5 war weariness 0
population 6- 10 war weariness -5
population 11 - ? war weariness -6

For Nations still at war like iwnw (Egypt), higher war weariness.

Now, could anyone confirm this?
 
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