(The title I chose for this essay sounds like a high school teacher trying to interest their students in civics with a really strange hack of Dungeons & Dragons. 🙂 )
Great, you have a democracy! You get to vote! . . . what are you voting for?
If you’re in a representative democracy, which most of them tend to be in most contexts above a certain scale, then you’re voting for the people who will govern you. What name gets given to those people, though, is really up to your polity. The idea of elective monarchy came up back when we were discussing monarchical forms of government; it is possible to elect a king or queen, though usually the ones doing the voting in that case are an extremely limited set of elites, rather than the hoi polloi. The Roman Republic was governed by two consuls (and that’s unusual, dividing power between two people rather than having the buck stop with one). You can call your leader the Supreme Hand-Waver if you want — the name doesn’t define the office.
In modern practice, though, a limited set of terms tend to be used. And these actually do point a bit at the definition of the office.
There are a couple of interlinked concepts here. One is the head of state, i.e. the person who literally represents the state. Another is the head of government, i.e. the person who does the work of running the government. These two are sometimes embodied in the same person, but not always. Meanwhile, there’s also a potential division between the legislative branch of the government, which makes laws, and the executive branch of the government, which enforces those laws and does the actual governing. Again, some countries separate those functions, while others do not.
I bring this up because it’s partly responsible for the modern situation where some countries have presidents, some have prime ministers, and some have both. In a presidential system (like the U.S.), the president is generally both the head of state and head of government, and they lead the executive branch, while the legislature is separately elected. In a parliamentary system, like the Westminster system derived from Britain, the head of state may be a monarch (whose powers often become largely ceremonial), while the head of government is the prime minister. That latter person takes over many executive powers, but may come out of the legislative branch, i.e. be appointed or elected from parliament that itself may be elected, hereditary, or a mix. And then you have semi-parliamentary republics governed by both a president and a prime minister, with the former being the head of state (and sometimes largely ceremonial), and the latter heading up a cabinet that serves as the legislative branch. With many variants on exactly how all of this gets run, e.g. with who gets elected by the people vs. appointed by the head of state, and exactly what powers they have.
Modern-style democracy is a new enough thing that we’re honestly still experimenting with it. Not to say that there aren’t variants on monarchy, too — we covered some of those earlier this year — but in many ways, democratic republics seem to be more complicated. That doesn’t necessarily have to be a hurdle; when the national government is just a background note in a novel that focuses more on other aspects of society, you can easily toss in a comment or two about upcoming elections. (There’s graffiti in Pompeii touting one candidate or another, so this kind of thing was visible to the common citizen even when that citizen wasn’t allowed to vote.) But if you want to write the speculative equivalent of The West Wing, diving headfirst into the politics of your invented society, then suddenly the tangle of government branches and interlocking types of power becomes extremely pertinent.
Stepping back from that executive/leadership question and looking instead at the legislative branch . . . these days we’re almost evenly split between unicameral (60%) and bicameral (40%) legislatures, i.e. those which have only one house/chamber/assembly/call it what you will, and those which have two. (There’s also theoretically tricameralism, though no current examples exist, and most past ones actually consisted of two bodies who also had a special role when meeting together.) When there are two, they often have different selection processes and different responsibilities. In a previous essay I already mentioned some of the differences between the U.S. Senate and House of Representatives; in the U.K. you have the House of Lords (historically made up of bishops and hereditary peers, though changed in modern times) and the House of Commons (elected). One chamber is usually considered the “upper” of the two; the term “senate” is common here because its Latin root, senex, referred to old men, i.e. society’s theoretically wise elders.
So as with previous aspects of democracy, you rapidly see a smearing of the nice clear lines. Is the Parliament of the United Kingdom democratic in nature? Part of it is; part of it isn’t. How much power does the hereditary sovereign have over Parliament, and how much power does Parliament have over the sovereign? Depends on what year you’re looking at, with rather a lot of fighting (both political and literal warfare) over the answer to that question.
For fiction, then, you have something of a choice. The easier route is probably to base your government on one in the real world: choose a country and a time period that suits your purposes, looking at who holds what power, how they’re selected and dismissed, etc. The other is . . . well, to make something up, and hope it makes sense.
Except that “making sense” might honestly be optional. For a time in the medieval and Renaissance periods, here’s how the Republic of Florence governed itself: take the names of all guild members who are at least thirty years old. Put them into eight leather bags. Every two months, take those bags out, shake ’em up, and draw out names. They’ve got to be not related to each other and not in debt, and they can’t have served a recent term. You wind up with eight Priori and one Gonfaloniere of Justice, who promptly relocate to the governmental palace for the next two months to run Florence. While they’re there, they should consult with other elected councils — the Sixteen Gonfalonieri, the Twelve Buonomini, sometimes the Ten of War or Eight of Security or Six of Commerce or whatever else Florence felt like it needed at the time. When their term is up, kick them out and do it again.
This seems utterly absurd to us now. How can anything get done when the government changes six times a year and its members are chosen at random? And yet, they made it work for about three hundred years.
So honestly, anything you put into a novel could theoretically pass muster. Just have the characters complain about incompetent leaders, inefficient administration, nepotism, graft, and how much better things were in the old days, and the reader will believe it’s real.