No actual suggestion about how to do this I see.
I am going to attempt this, but please keep in mind that I am an amateur.
To start, I believe there would need to be an interface addition in the intel section, specifically in the factions tab after clicking on the Perseans. A new diagram should be added somewhere on their faction page,
my first mockup of this is here, and yes I realize it can be confusing and needs alignment etc etc, but I think that it's still useful to understand at a glance how the mechanic would work or that diagram would look.
Each market name below a manager is considered as being controlled by that manager (please bare with me because it is not an AI player). The league convenes on the date listed on the center for some amount of time to render decisions, which appear in the center after. The color of a market name is that market's biggest trading partner in terms of net credit value of goods (perhaps including illegal ones) provided since the before the last league meeting was held. A manager's list of possible decisions includes sending an invasion fleet, sending commerce raiders, sending a planetary raid, and lowering or raising overall league reputation with a target faction.
The manager's biggest concern would be securing independence through power, so for this reason the primary factors affecting league decisions are who is committing hostile actions towards them, and who are their biggest trading partners. Occurrences of raids on League Planets, fleets, etc along with who the biggest trade partners are affect the numerical value of variables in equations that make league decisions happen. The way that this system promotes emergence is by allowing the player or NPC fleets to manipulate reputation a faction besides the ones in the fight or their allies has with another through fighting on the overmap, which I think would constitute
recirculating Starsector's own unpredictable events back into the Persean League's government. I think this has many significant implications, and perhaps modifying this system just a little bit more could result in an even greater level of potential emergence.
I do not have equations or statistics appropriate for this suggestion, and we are all busy people. I think that I could provide some eventually next month. This is my first attempt at a suggestion like this, so please give me some feedback, thanks.