So lets see If I got this right
The Enoir Government is split up into:
The 3 members of the Triumvirate: they can be seen as making up the executive.
one spot is hereditary
one is by peerage vote among the four ruling vicarii.
and one is the 'The Festival Lord', but who in practice can be seen as the military representative to a greater or lesser degree. (barring the off chance that someone not a top-level fighter actually wins.)
while the books say that the high council votes on things, the Triumvirate still very clearly rule, if not to the extent of the electer counts or the dukes: so there is still obviously power within this office. so I'm going to go out on a limb and assume that they have something like A: a veto, B: they get to set agenda and choice whats gets to the floor for a vote, C: gets to choose who gets what spot in government or maybe even who gets an empty set in the high council. D: some combo of or all of the above.
there is also this line 'The Eonir consider their government to be the most democratic of the Elf realms, because decisions are usually made by council votes instead of royal decrees'
that is a telling usually: it means that the queen still has, and has at times used, her royal decree... its just that it's not often done for reasons that could be social, political or built-in limitations.
The High Council: the legislative branch
3-4 members of the Vicarii
Main houses members = N
this is the group that gets to vote on decrees, laws and major diplomatic and social events.
the Main house N is definitely the big question mark, but I guess we could look at it as 'how powerful does Boney want the Vicarii to be in Laurelorn? they already have a locked-down seat in the Triumvirate, so that's a lot of power right there.
but at the same time the outer wards are very clearly considered lesser to the sun ward: so they cant be near equal or more than the Main houses in numbers.
very powerful: N < 10 (the Vicarii make up a significant brunch of the Eonir government, and can be seen as the equivalent of empire dukes and markafs.)
Powerful: N < 15 (very powerful, around a third of the votes in both the high council and the Triumvirate)
significant: N< 20 ( a fair share of the votes, but its the seat on the Triumvirate that really gives them power)
Average: N< 25 (they are a voting block)
a little Weak: N < 30 ( they can turn a vote sometimes if they work together with others, but their power is from the seat at the big table, not this one.
Symbolic: N< 40 (they are basically one of the votes in this case.)
Insult: N> 40 (they have no real power here, and are just given a seat to remind them about it, if they didn't have the Triumvirate seat they wouldn't be able to contain their anger, and even then, its a sour point.)
The last, unsaid, group would be the Court: for lack of a better name.
The people that work for the crown, are part of the military, collect taxes, right up bills and laws and lobby everyone above them for the sack of the group or organization they represent: the elves part of the daily grind of running a nation.
Yes and no. Triumvirate is Royal and two prefects: one ruling vicarii, one Queen's Champion. But they aren't the Executive, they're the High Court. They only chime in if the High Council calls on them to do so, otherwise serving as quiet oversight.
The High Council can meet without them.
But if the High Council is deadlocked, or can't resolve some issue, then the Triumvirate rules and any ruling it makes is only up to it and final. No argument, no discussion.
The High Court is the legislative power
and the executive power, except when it doesn't work, which is when the Triumvirate step in.
The Senate meets once a year to discuss diplomacy with outsiders and the defense of Laurelon. Members are respected elders, rangers, scouts, warriors, priests, mages, etc. Emergency sessions can be called in a crisis. Member of the Senate have no practical political power, but come from all the Wards of Laurelon and can be of the second class of Elf. What they can do is suggest and present to the High Court actions or laws that need to be done, based on their practical, live, frontline experience.
The catch is that the High Court doesn't meet in some hidden room. They meet in a public amphitheater in the middle of Tor Lithanel, under a holy tree. And everyone is invited to watch them discus and decide.
This means that while in theory all the political power rests with the High Court, every member of it is subject to the judgement of anyone and everyone present. This being Elves, there are plenty of culturally appropriate ways to express themselves, if a particular member of the High Council is pushing an agenda the audience disagrees with.
So while in theory the High Court has all the power, in practice it's balanced among it's own members, the Triumvirate as judges who break up impasses, and the masses watching every session.
This being Warhammer, I've no doubt that if a particular Councilor decided to do something sufficiently abhorrent to their fellow elves, their own House mates would exile or duel them, if only to spare their House the embarrassment of having an Outsider clean up their mess. Since they are highly communal, I've little doubt if a particular shithead comes out of a Major House, that failure would reflect on all of them.
This being elves, said stain would mark them for centuries to come.
So while by Law the High Court has no peer, or check or balance on its power, in practice, it doesn't work out that way.
EDIT: As for the other Wards, they don't get a vote. Only their rulers, the vicarii do. And every vicarii, indeed every member of the High Court is Toriour. That's the high class of the Elves, those born in the capital, or back before the the colony was started. If you're not from the before times, or born in the city, you can't hold a spot on the High Court. End of discussion.