So I was watching this: https://www.youtube.com/watch?v=rStL7niR7gs
About just how much of politics is just about maintaining power. Which made me begin to wonder, how would governments work if the leaders didn't have to worry about having approval, ruling solely through their individual might?
Let's imagine a scenario with dragons; dragons are extremely rare compared to humans, potentially immortal (though they are bound to get taken out after enough millennia) and can't cooperate except with their mate. They can't be poisoned, or otherwise killed through any means other than by another tougher dragon. They dislike subterfuge and given that they will only work with their mate, basically the only important factor in who wins a war is which mate pair is stronger.
They also extremely dislike other dragons generally, so no political structure is possible except one with 2 dragons at the top (or one if a smaller kingdom not worried about attracting other dragons notice)
Effectively the only thing that matters in this system is individual might
So with that in mind how does the government work?
Dragons really like having as much power as possible plus they will take all the gems and precious metals for themselves issuing fiat currency (or gold backed currency you can't legally trade for gold), or currency made of valuable material that isn't appealing to dragons. As thus dragons are incentivized to make the nation economically prosperous to build their hoard and it's not much of an empire if it's in anarchy so they do want their kingdom to thrive. They may take part in non-dragon warfare, but only occasionally in important battles. They can easily melt a castle or torch thousands of soldiers.
Dragons can shapeshift, taking human forms that are still as durable, so as to lie low and watch the humans discretely.
In addition: A third of dragons are pretty indifferent and won't be likely to take any part in all but the most important decisions, a third actually care about human welfare to some extent and another third are tyrants who demand worship, eat princesses the whole villainous shebang. This distribution is independent of power level.
You should expect dragons to get more wise and powerful with age, so the most powerful kingdoms ought to have better leadership than most.
Dragons attitudes to their underlings: All dragons will try to monitor their kingdom to some extent to ensure it's doing well and that they are properly respected and that nobody else is failing to act sufficiently humble. Indifferent dragons only start interfering if the kingdom starts to have major problems/people act uppity. Those underlings with the most power are those that seem to get results.
Friendlies like to spend lots of time in human forms, of course they always pose as important people since dragons can't tolerate anyone treating them as an equal or subordinate; they hate blatant suck ups however and will try to put people with impressive qualities in charge. They may even flirt with letting the government be semi democratic when it comes to things they don't strongly care about.
Tyrants will go publically in dragon form to be worshipped and are prone to randomly rampaging to eat people when it suits them. They are incredibly self absorbed and demand their whole kingdom glorify them. They can be easily manipulated by sycophants though their ability to see through flattery increases with age. Those in power will be those good at flattery and killing off opposition; the dragon likes picking people who seem powerful since having them suck up inflates their ego more. They are likely to never take human form as they find it insulting. They get more competent with age, or at least they stop repeating the dumb mistakes they've made in the past.
To some extent this question can somewhat apply to any situation where there are extremely powerful entities that don't work together, love power and are only in danger from each other.