Because it is the setting of my groups TT game, I have given a lot of thought to the methods by which covenants are governed in the Theban tribunal. It probably diverges somewhat drastically from other examples from the Order. I think in some they actually would elect a Despot, (Despot in the classic Byzantine definition, a absolute ruler) say at Hedyosmos and Polyaigos, while at Epidauros, Oikos Tou Eleous, and Favonius I imagine they are democratic, with Favonius going so far as to include mundanes as part of their covenant voting structure.
Other covenants, such as Erebos and Aegaea, may have a governing structure based on a oligarchy. Perhaps a ruling duumvirate or triumvirate, and the remaining magi or even mundanes being given a position as councilors or advisors. Somehow I imagine the Mercere covenant of Alexandria as having barely any government at all, rather being something of a bureaucrats heaven. Every person in their position doing their job with no one actually being the one in charge. Rather, I imagine they have a series of complicated laws, with one division being overseen by a separate division who makes certain that the rules and efficiency are being maintained; and in turn they are given the task of giving check and balance to yet another division. I see them as some sort of postal business with no one knowing quite who is in charge and it matters little to them. They do their job and they make certain those around them are doing their job, and everyone is happily moving along. Oddly everything works. (this may explain why they were so caught unawares by movement of Nicaean soldier onto their mundane soil, trapping them in their regio)
You can basically go through each of the Thebans covenants and do this, however I won't, maybe leave something to the imaginations of others.
So reading over the Covenant book, I came upon a story arc, which I am attempting to persuade my own group to use in our game. I was impressed with how hard the task would be for a entirely new group of magi to take charge of a covenant, in which the entire group of former magi had vanished. Loyalty would be horribly negative and the Gift could make things even worse for the magi. And while yes, they are magi, these people can only be dominated so much with fear or threats before they grow to loath their masters, or worse, revolt. Characters that are former residents of the Theban Tribunal would have a way of thinking, I reason, that would bring the experience of their former covenant's perspective of governing into the debate on how to rule the new covenant. However a interest complication would be if one or more of the magi were from outside of the Theban League. They would be less inclined to allow mundanes a voice and vote in the affairs of a covenant. Or perhaps not. Perhaps they came to the Theban precisely because they admire their methods of democracy.
So I wonder, have others gone to great lengths to describe the governing methods of their covenants? Have you simply taken the example and made a copy of it changing a couple of things, or have you gone to great lengths to make the ruling compact personal and unique to the characters? In some Tribunals it would not matter and I guess in Normandy and Black Forest they just accept the tradition of rule. But has anyone else experimented with this aspect of Ars Magica?