[Stormcrow]

It really depends on too many factors. But in general, any government of immortal elves will be as unchanging as they are. If we assume a generally good chance of continued life — that is, no constant wars to roil the population — then you would either have the government be static, or you would have constantly rotating positions. In the former case, if there's a king then the king will always be the king, etc., so there's no Game of Thrones-style court intrigue. Elves' ambitions would not tend toward the acquisition of limited resources like political power, because there's only so much of it to go around and those who have it can be expected to keep it forever.

If there are no fixed political positions, then I'd expect a very democratic, egalitarian society. No one expects to keep their position for very long, because there's no such thing as "very long" to immortal elves. And if you can't expect to keep political power for much time, it's not much of a draw to you to abuse it. So elves would just consider it a civic duty and do it. And everyone would do it, because eventually every elf will have had opportunities to serve.

So it depends greatly on what kind of society you're dealing with. A more interesting exercise might be to posit a society of elves, and then figure out what immortality would mean to that society.