Worldbuilding 203: Voting Systems

Greetings and scotoma! ...If you have that, either look for a doctor, take it very easy, or get into a dark room as a migraine is on its way. Anyway, as we all know, democracy is the absolutely worst government system that has ever been tried, except every other one is equally shit. Almost as if humans are bad at designing systems or that humans tend to exploit everything for personal gain 🤔 Anyway, only various ways for people to actually vote!

Voting is a system

Definition time! Long time readers will know I love this section.

A voting system is a method with a set of rules that takes a collection of votes of preference in a specific format and outputs a singular preference in the same, or occasionally different, format to represent the entire group’s preference.

What the tsan does ANY of that mean? The short answer is, it takes lots of votes and outputs a single vote. The thing to remember though is that votes, all kinds of votings, are preference stating. You prefer this party/candidate over these other ones and so on. The format part is because votes can come in many formats. You know, let’s get into the next section instead.

Voting format

When it comes to votes, they can come in many formats which depend entirely on the system of voting. But what they all have in common is that they always tell the preference you have. I won’t go into details of all kinds because they are so dependent on the actual different voting systems. But to give a quick rundown on various forms:

  • Single preference

  • Ranked preferences

  • Preference points distribution

  • Multiple preferences

Voting and people

Everyone gets a vote, right?

Children and teenagers don’t get to vote! Rightfully so, if you ask me, but that's besides the point. A society can in many ways decide who gets and who does not get the right to vote! And Women!? Bah, cannot give them the right to vote! Wait, we have; alright, it’s a good thing, but it wasn’t the case in the old days.

Women were the latest big one in most Western countries, and it came ridiculously late, if you ask me. But you know who couldn’t vote before women got their right to vote? People without land! 😱 Can you imagine it? People who didn’t own land being able to vote? Scandalous! Joking aside, I think you get the point, but in case you haven’t…

Democracy does not mean everyone gets to vote, only that the relevant units of the society get to have a vote. And I say units because while the West has said that its individuals, historically, you can say it has been families instead of people. In Rome and Greece, it was more often the patriarch, male leader of the family, that had the vote, and women, slaves, etc. did not. But at the same time, who, among my beloved readers, if only you could vote and you had a family of those who could not vote, would not talk with the family, even if you held all the power? 

As sexist as the phrase is, “Happy wife, happy life” exists for a reason. It is mostly a historical relic these days, but even when men did have the majority of the power, being too much against the wife in the family meant you would not have a happy time at home, and that has been true all throughout history. In my omega blogpost, I introduced the Laekwat, a frog-based species where Anne and I had lots of fun. Anyway, in it, they have it so only females can vote (you’ll see why if you read!), but it is not all females, it is the head of the family only. Though, the difference between the head of a family and not is a very short period of time.

Voting and fairness

One thing one has to fundamentally understand is that voting is not fair. Humanity has this intrinsic feeling of what is fair. It is varied, but most people generally don’t get too far from each other, even if preference for one's own favouritism always clouds one's mind. Anyway, people want things fair, and they want voting fair, and I am sorry to burst your bubble but ain’t gonna happen buddy. All you can get is “Good enough.”

Let me illustrate it. We’re going to do ranked choice voting, which means for your vote, you will rank how you view it. We’ll do COLOURS! What colours are best? For simplicity, we pick three, Purple, Green, and Orange. We will decide 2 very fair rules for this system; well, more properties because the details of how it is picked does not matter, only that these properties exist. The first one is unanimity. If everyone votes sensible Purple > Green > Orange, then naturally, the outcome should be that Purple > Green > Orange is the group ranked preference. Perfectly fair, right?

I think so, at least. The second one is wordier: “Independence of irrelevant alternatives.” What it means is that, let’s say everyone is again sensible and thinks that Purple is greater than Orange. The end preference should definitely be that Purple shall rank higher than Orange. Green might fly around depending on everyone's vote, it might get first place, second place, or third place, but Purple and Orange should not change relative to each other. Another one that seems fair, doesn’t it?

Well, tough shit. If you have this, you got a dictatorship, and I was the dictator all along! MUAHAHAHA! There are mathematical reasons and proofs for this that I will not bore you with, but you can look it up, right about here. The point is that from a voting system, Ranked Choice, and 2 extremely fair properties, we get a dictatorship, and honestly, that is kinda tsanned up. Notice this example only applied to ranked choice systems. But every, and I mean every, voting system can and will have–or more often than not, LACK–properties we consider extremely fair and a “must have.” There is no known voting system that has all we would want, and many combinations have mathematical proofs that they simply cannot exist. The example above is called Arrow’s Impossibility Theorem for the curious.

Voting systems

There are many of these, and I will only go through the most prominent in detail, and lastly give a run off of many that exist with links to learn more about them.

Plurality/First past the pole

This is among the most popular ones and is the simplest to understand. Everyone votes which one they prefer the most, and who/whatever gets the most wins. Seems incredibly simple, and it sure is simple. It is a perfectly adequate system when the choices are literally only two options naturally. “Should we adopt something or not?” is a common version of where two options are the natural state of things.

The problem with this voting system is that it is only good for when two options are the only options, so when more options are available, they will, at least when you can redo the choice over and over again, always result in the end that you only have 2 choices. Two parties, etc. It is also the system that has the highest possible level of dissatisfaction. Imagine you have 1000 people running for office, and we have 1000 voters. Everyone votes for themselves, except Anne, who votes for me. So I am happy, Anne is happy, I am the undisputed dictator once again. 998 people are very unhappy that they lost. So 99.8% of everyone is unhappy and didn’t get their winner.

Proportional Representation

This one has one thing in common with plurality: you only tell what your favourite preference is. The difference is that while plurality is to find A winner, proportional representation requires that there are many parts that can be won. Typically, in voting, there are seats in Riksdag, Parliament, Congress, etc. Without parts of a whole, you can’t really do proportional, now can you?

There are countless subversions, and then all differ by how you turn votes into seats. Almost all of these that are at least good will guarantee the whole seats you would get. By that, I mean that if party Purple gets 30% of all votes and there are 7 seats to be had, if all was perfect, Purple would get 2.1 seats, 0.3 x 7, but you can’t have fractions, so good systems will guarantee that you get at least the whole 2. How that 0.1 is dealt with depends entirely on the system itself. Some systems favour smaller parties, while others favour larger parties. 

In 🇸🇪, it is a bit complicated, but roughly speaking, and approximately true, you start with everyone having 0 seats. You check who has the most votes, and they get a seat. Now we divide the initial voter count by 3. Now we check again who has the larger number; they win a seat. And it continues on where the initial vote count a party gets is divided by a larger integer that corresponds to the number of seats they have. For the Sainte-laguë method, it is 1, 3, 5, 7, 9, …, in Sweden the initial one is replaced by 1.4 or 1.2, I don’t understand why, honestly. Some alternative methods to use are:

There are more methods of apportionment, as it is called. For entirely unbiased reasons, I tend to prefer this most of all.

Mixed member proportional

This one is, in a sense, a mix of both of the previous systems. If you are dead set on voting for a local representative that you know, this one is the best method, if you ask me. I find the obsession of having to vote for a specific person rather peculiar. Anyway, you get 1 ballot, but you are not casting 1 vote, you are voting for 2 things at the same time! What madness is this?

The madly kind that the maddest mad man from the mad clan McMad would be proud of. One portion of the ballot is to vote for a specific candidate of your choice. These candidates are generally associated with a specific party too, for this to work. The second part of the ballot is voting for a party! Like in proportional representation. I know, weird, huh?

So how do these interact? Well, you have to have MUCH larger districts than what Americans, the British, and whatever other Anglo Saxons that do plurality voting are used to. Think about, at least, 5 times as big. I think 6 hits the sweet spot of being able to be “proportional enough” and “local enough.” Imagine 6 districts that you’re probably used to being fused together into a single district. As a result, the district has 6 seats for the single district, but what about them? Half or less are given to local representation similar to plurality. This is less than or equal to half because otherwise the proportional part starts failing too hard. So 3 are given to that purpose, and we get 3 subdistricts. In these subdistricts, there can be any method to find the one winner, plurality as above is the most popular, unfortunately 🙄, but you can use any method that gives one single winner in each of the subdistricts. You get the three winners of local representation based on the first part of the ballot, assign them their seat, and we have 3 seats remaining. This is where you use the proportional representation to assign the last 3 seats according to whichever apportionment method of choice based on the party part of the ballot.

And that’s it, half or less of the seats are directly elected, the rest are assigned proportionally in an attempt to make both local and proportional. You be the judge if it's worth it.

Borda count

This one is a lot of fun! This is where we get into the REAL ranked choice voting! Well, kind of. You do rank all your preferred parties, candidates, whatever you have, which one do you like most, second, third, and all the way down. Some might allow you to stop prematurely. The difference is that each of the candidates are given points depending on how you rank them.

Let’s say you have n number of candidates… Well, shit, that is algebra. All right, let’s say 7 candidates. The one you rank first gets 6 points, the second one gets 5 points, and so on until the lowest one you rank gets 0 points. So far so good, and there is little more to this method. You sum up all the points, and whoever has the most points at the end is declared the winner. You can even use this to distribute seats by treating each point as a vote and do any of the apportionment above or that you like.

Run-off

Oh this is another fun one! The cheese eating surr… I don’t think I am allowed to finish that… Anyway, 🇫🇷 does this one and recently did it, too! You generally vote like you do in plurality for one person only, but you do it typically in 2 rounds, but it can be any number of rounds. So in the first round, you can have dozens of candidates, and you count it up and see who has gained the most votes.

Except you don’t declare who wins, you declare who passes on, and go onto the next round! Of course, the one with the most votes goes to the next round and the second one, but, like France, you can have many more move on. It can be so it is only the biggest loser that doesn't move on, but this is rarely done as the next one will be more efficient. In this voting system, once you reach the final round, whoever gets the most votes wins the entire election.

Instant Run-off

Despite the similarity in names, they are very different. Here, you only go voting once. And unlike in Run-off, you don’t vote for who you want like in plurality, you do like borda count and rank the order in which you prefer the candidates. And then the run-off can begin. 

It goes like this: count how many first choice votes every candidate got. If one candidate got more than 50% of all votes, they are the winner, and everything is over. But if there is no one like that, grab all the ballots that voted for the biggest loser as their first choice. That is the candidate that got the least votes. For all these ballots, you cross out the top winner and now treat their second choice as their preferred choice and dump the ballots into the piles of each candidate.

If there is STILL no one with more than 50%, you take the one with the least votes again and remove them, the ballots that were now in their ballot have this candidate crossed off and are redistributed to the remaining candidates according to who is their preferred candidate.

And the system keeps going like this until someone gets more than 50%, and at that point, they are declared the winner. This is why it is called “instant,” because it is like a Run-off except all rounds are done instantly, and you don’t have to wait.

Score Voting

This one is the weirdest of the bunch I am presenting because you don’t technically rank candidates or parties. You give them a rating on how much you like them relative to each other. You know the whole 5 star system of rating? Imagine that, but on your ballot, you see all the candidates, and you can give 3 candidates all 5 stars because you love them.

And the ones you really hate you can give 1 star only. And all the other candidates all get anything in between. It is important to notice here that while the ranked choice could never have 2 candidates be equal in value on your ballot, here, you can give any number of candidates the same rating!

The winner is determined by which candidate gets the highest average value of all the ratings given. Reminds me of that Black Mirror episode where social media ratings had gone wild, except now it is only politicians! Actually that gives me funny ideas about how politics could be done if politicians are actually rated.

Others

Those are by far not all the voting systems. There are countless more. Here is a large ass list of more:

These are not all of the voting systems, but they are the more famous ones after the ones I talked about. My favourite is Schulze.

Tactical voting

As I have stated, no voting system can ever be perfect. And perfect here refers to where it is totally fair and incentivises people to be honest about their preferences. And that last one is where we get here. Tactical voting is when you start lying about your preferences in order to get a suboptimal result that you consider better than other alternatives that you think are more likely to occur if you don’t do tactical voting. Like if you are a real heathen and really like Orange, but you know that Orange has no chance in winning, simply too few will vote for Orange. So you pick Pink instead, because Pink is much more popular and has a greater chance of actually winning than Orange, and you’d much rather have Pink than disgusting Green.

Some might call this a feature, I say it is a definite bug that is not good. Why would anyone consider it good that you have to settle for something you don’t like in order to avoid something? But it is inevitable to happen, especially when it is extremely obvious how the system works and how the result will shift. Plurality voting is extremely susceptible to this and is the primary reason why it keeps dragging to 2 parties. People start doing tactical voting for more popular candidates that they dislike less in order to have a chance to win anything, and eventually you get a position where the two parties are the only two that survived the endless tactical voting.

Every voting system is susceptible to this, but the rate at which people actually do tactical voting generally depends on how easy it is to see how one’s change in vote affects the outcome. The more obfuscated it is, the less people tend to do it. Another factor that comes in is how much difference their vote will make if changed. Certain voting systems diminishes the value of tactical voting by making it so that even if you do vote for your preferred candidate, and they lose big time, your vote is not lost but is then used for others.

There are many other ways to counteract tactical voting, which I think to any American voters would be obvious given the so-called “third party effect” and how it “spoils” elections and winners.

Summa Summarum

Voting is hard! It is not easy to decide which is the most fair system that you should use because each of those above have their drawbacks. If I went through them, we’d be here all day. So I won’t, but you can read up on it in the many links provided.

The main reason I think that plurality is so common is that it is easy to do, and ease is important At least before the advent of computers to do the heavy maths stuff for us. But Sweden and many other countries did take more computationally-heavy methods of apportionment despite lacking computers. So it is not out of the question for non-computer-having societies to pick others.

Ultimately, it is about compromises and what is “Good enough.” I will, in a later practicum, give my Commonwealth of Worlds, and in it, I will describe the voting systems I have settled for that are fixed there and my reasoning. Stay tuned for that! You keep reading, I’m getting a burger, bye! 🍔


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Copyright ©️ 2024 Vivian Sayan. Original ideas belong to the respective authors. Generic concepts such as voting and the various votings systems are copyrighted under Creative Commons with attribution, and any derivatives must also be Creative Commons. However, specific language or exact phrasing is individually copyrighted by the respective authors. Contact them for information on usage and questions if uncertain what falls under Creative Commons. We’re almost always happy to give permission. Please contact the authors through this website’s contact page.

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Vivian Sayan

Worldbuilder extraordinaire and writer of space opera. May include some mathemagic occasionally.

https://www.viviansayan.com
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