Uhm, is influence going to work this way?
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That seems to be the general idea.
Each colony costs X influence, where X increases with the total number of colonies
So to maintain an stable empire
your percentage of influence focused colonies must increase as you grow
your influence tech (or techs that reduce colony cost) must increase as you grow
so an empire with only influence focused colonies could still be unable to pay its influence costs, until it lost some colonies (Very unlikely situation, maybe if you were given a massive empire while you were still at low tech)
Your total Useful colonies would maximize when you are so large about 1/2 your empire was devoted to paying influence costs... any growth after that would Decrease your useful output