Not sure if this report helps but here it goes:
Same turn I promoted a member of the 1st opposition party and also promoted a member of the 2nd opposition party.
Result = 3rd opposition party Influence increased by 4% (I lost 2% influence, 1st and 2nd party both lost 1%)
Most political actions I make ends up increasing the 3rd party Influence. Even with the 1st and 2nd party having a decent gravitas level advantage compared to the 3rd party.
Screen: https://imgur.com/a/yVN3suT
PS: I'm using the "@_influence_variables" pack posted in the OP, but I didn't edit any value.
Btw, does Influence have any effect in the Risk of civil war? Or just Loyalty?