what about institute or provisional government of commonwhealth/minutemen? also, what other factions can you think of? anything will help me in my modding
I haven't played Fallout 4 yet, so I don't really know.
A couple of other minor factions I can think of:
The Boomers are tribals with a leader, who doesn't appear to be elected. Obviously Pearl isn't going to be a formidable fighter, so it's more likely that she stays in power because of wisdom, experience and respect.
The Powder Gangers aren't really a coherent faction. Whenever they took over the prison, the strongest people would have attracted followers, and they get what they want by force or intimidation. If you don't like it, you challenge them, or you leave to form a smaller splinter group
The Fiends are supposedly under control from Motor Runner, and it seems like this is done with the promise of drugs, due to his contact with the Khans. If you go against him he has the power to cut off your supply. The Fiends outside the vault seem only loosely affiliated with him, and he doesn't really seem to care what they do so long as they don't oppose him. They have their own minor leaders, who are probably just the ones strong enough or crazy enough to enforce their authority on those below them.
Westside and North Vegas both look like sort of anarcho-communist places. Small enough for those systems to actually work. They don't look like they have strong leaders, and everyone just sort of gets on with what they want to do. Problems and defence are handled by militias instead of a standing army, and major decisions are probably made as a group.
The Kings are just tribals with fancy clothes. Again, the King stays in charge because of the respect the Kings have for him. If he ever starts to make decisions that are too unpopular or abuse his power, the group will either fracture, or overthrow him.
There don't seem to be any true monarchies in the game, although the leadership of the Brotherhood does look like it quite often stays within the same families. Whether this is an official thing, if Elders can nominate their successors, or if it's just that the Maxsons happen to be good leadership material, combined with a family culture of raising their kids for command is never really explored.