We started out by listing some types of political systems. Monarchies, especially absolute monarchies, are quite common in European-centered medieval-style fantasy. Lesley suggested Theocracy, where the system is run by religious leaders. I mentioned that in The Left Hand of Darkness by Ursula LeGuin, she sets up two quite distinct systems, one a monarchy, and the other called a "commensality" which resembles a communist state. Erin mentioned that there was a form of communism in a book she read where there was a generation ship, where everything was shared and nothing inherited, and that the system worked until a religious group tried to control it. My Varin world has a rather mixed political system, where an underlying socialist system was hijacked by some powerful people and as a result the society is run by a single powerful monarch who is elected (indirectly - Heirs are elected) by the members of his Cabinet. That makes it a sort of monarchy/oligarchy with twisted democratic aspects.
Erin said, intriguingly, that people don't have the government they think they have.
When you are setting up a political system, it's interesting to ask who controls the money, and where they get it from. Does land ownership lead to wealth? Does business or corporate investment lead to wealth? How does money influence politics?
Misha talked about how she was working on a story where there were two neighboring nations and each one had a different political system. I think this is a really good idea, because in the real world there is quite a diversity of different coexisting systems.
We spoke for a bit about the system in George R. R. Martin's Game of Thrones, where the Lords of particular areas are subject to the Targarian kings. Then madness crops up and leads to serious tyranny (the mad king was going to blow up the capital so was killed by his own guard). At that point the legal right to rule came under dispute and led to further fracturing of power, and uprisings by low-level nobility. I think it's interesting to note that kings can layer over one another - the concept of the High King is probably familiar, but I don't see it quite as often these days as I remember hearing about it when I was younger. Also it's interesting to note where resistance comes from when a monarch is a maniacal tyrant (guards vs. rivals).
This made me think of a historical king of Ireland, Niall of the Nine Hostages, who was a High King over quite a portion of the British isles and even some areas of France in around 400CE, and maintained control over his subject kingdoms by taking their queens hostage (with the result that he's part of the bloodline of about 1 in 8 Irishmen).
N.K. Jemisin set up quite an interesting variation on the hereditary monarchy model in her novel The Killing Moon. In their system, which centered around worship of the moon goddess, the monarch upon his death would become the husband of the moon goddess, and thus the "king," so the living ruler of Gujaareh therefore bore the title of Prince.
Erin brought up the importance of women, and how it differs in different political systems. For example, marriages between the prince of one country and the princess of another were very important for peace, centered around the idea that when you (the prince) cared about your sister (the princess), you'd be less likely to attack a nation where she resided as the leader's wife. Women can also be an active, powerful influence in government, whether as queens and princesses or elected representatives of various varieties. We noted that the English monarchy is changing the rules of inheritance so women will have the place of their birth order in it, rather than being skipped over unless there are no male heirs. In our world, inheritance by primogeniture regardless of gender is becoming more common for monarchies.
We spoke a bit about the Emperor of Japan. Back at the very beginning of historical record, we see some Empresses, but this stopped over a thousand years ago. Historically, the Emperor was thought of as a deity, a status which was forcibly changed by the Americans after World War II. Even now his role as moral leader of the country is very important. Some years ago there was a failure of the rice crop, and Japan imported rice from Thailand - but nobody would eat it, until the Emperor went on television to eat Thai rice and vouch for it. That solved the problem.
There are lots of stories out there about changing types of government. Kings being overthrown. Oppressive systems crashing down. Successions and such. We clearly care about this stuff! Also, historically, governments change. French history involves a monarchy becoming a democracy and then becoming an empire for a while before becoming a democracy again.
Misha noted, quite importantly I think, that the character of a monarchy depends a lot on the personality of its monarch. Indeed, this may be one of the reasons why monarchies are so common in fiction, because they can be personalized, and change in government can be conveyed through the examination of a single person's experience.
I apologize if I missed or mischaracterized anything that went on in this discussion because of the long delay... you can always visit the video for details, because it's right here!