Musical heirs.

Perhaps a Rotational Monarchy?

https://en.m.wikipedia.org/wiki/Monarchies_of_Malaysia#:~:text=The system originated in the,advised by his Royal Council.

Sounds a bit like Malaysia, where the “The Yang di-Pertuan Agong [the constitutional monarch] is elected by the Conference of Rulers, comprising the nine rulers of the Malay states, with the office de facto rotated between them, making Malaysia one of the world’s few elective monarchies.”

https://en.m.wikipedia.org/wiki/Yang_di-Pertuan_Agong

Look at historical examples like the Serene Republic of Venice.

Basically you have an oligopoly that controls the levers of power and elects one of their own to be the leader.

Also read up on selectorate theory. There’s a good book called The Dictator’s Handbook that goes into detail, and for a shorter way to consume this info you can watch the YouTube video Rules for Rulers which is based on the same book.

All governments are nested resources distribution streams. Resources flow up to the decision maker, which then distributes resources back down the chain to buy loyalty to maintain power. Regimes change when one side or the other experiences a major disruption.

Sounds like an aristocratic oligarchy to me.

Round-Robin Royalty

As a classification I think I would call it a Monarchic Oligarchy, or maybe a Cyclical Monarchic Oligarchy, but maybe as a more common term I would say something like the Council of Monarchy or something along those lines.

A recipe for frequent civil wars

Aristocracy

• https://en.m.wikipedia.org/wiki/Aristocracy

Could be a Plutocracy

• https://en.m.wikipedia.org/wiki/Plutocracy

Could be Nepotocracy

• https://en.m.wikipedia.org/wiki/Nepotocracy

Personally, I would avoid using the term oligarchy because it has become something of a trend term used as a negative label in US political culture and synonymous with Russian (self described) backwardness and corruption.

I would write in a nod to how humans usually dilute themselves in their political labels and oversimplified ideology. No one calls themselves what they are directly. Like I default assume every monarch believes in their own fantasy meritocracy.

The concept you described could hold parallels to the papal conclave and election process. I would use this as a loose framework to make the ideas relatable.

• https://en.m.wikipedia.org/wiki/Papal_conclave

It could also be a Magocracy depending on the fantasy.

Don’t have any extra suggestions, rotational monarchy that was mentioned in another comment sounds good to me.

Just wanted to say that I’m intrigued by your story setup :)

So a monarch that can’t appoint their own heir really isn’t much of a monarch. The point of being a monarch is not being beholden to any rules.

This is just an oligarchy with rules that don’t benefit 3/4th of the participants–which is as odd as it sounds.

After all, the point of 4-5 year terms in modern democracies is that you don’t have to wait your whole life to take over.

It’s an interesting concept, but coming to this arangement–and maintaining it in perpetuity–must have been an extremely extrordinary set of circumstances.

Is the monarch required to be sacrificed every so often? That would kinda mimic the Aztec Festival of Toxcatl, where an impersonator of the god was sacrificed every year after being treated like a god for the year.

I would call it a Dynasty.

Also consider asking at https://lemmy.world/c/worldbuilding !