Single-Member Electoral Systems
This is the latest post in my constitutional design series. It is the quintessential topic of constitutional design, the one that everyone loves to talk about. I hope to show and have shown that constitutional design is far more than just electoral systems, but it’s obviously an important topic and worth discussing. In this first part, I’ll discuss electoral systems for electing a single person, and then in the second part I’ll discuss multi-member electoral systems for electing a legislature. But before that…
Social Choice Theory Background
Maximizing Societal Utility
If you want a prescription for who objectively “should” win an election given certain voter preferences, there’s basically two you could choose. The first is to define each voter as giving some utility to each candidate, and then choose the candidate that maximizes total societal utility.
If you’re a preference utilitarian and you view these utility values as direct measures of people’s preferences, this is of course the optimal choice1. But if you’re a hedonic utilitarian like I am, or if you view these utility functions as people’s political preferences which are separate from people’s real preferences in life, or if you don’t stand by a certain ethical theory and just want something vaguely democratic, I don’t think this method comes out looking amazing.
This method says that someone who hates one candidate and loves another should have more say in an election than someone whose preferences are milder. This might be desirable because not doing so can lead you to tyranny of the majority, where 51% of the population hogs all the resources and is happy while the other 49% is miserable. But on the other hand, I think people can get really passionate about politics in ways that don’t merit more say, like being terrified of immigrants that don’t actually hurt them. And besides, there are other methods in society for people with stronger preferences to have more of an effect (party candidate selection being the main one, but also activism, interest groups, higher turnout in elections, etc.).
So overall I’m kind of ambivalent on this prescription.
The Condorcet Criterion
The other prescription for who should win an election is to choose the Condorcet winner (called the “Condorcet Criterion” for a voting system). The Condorcet winner is a candidate that would defeat every other candidate in a 1-on-1 election. If a population is 40% left-wing/20% centrist/40% right-wing, the Condorcet winner is the centrist, assuming left and right-wing voters prefer the centrist to the opposite party. In this way, the Condorcet criterion is a way of encoding a preference for moderate candidates.
I will also point out that the Condorcet criterion doesn’t go maximally far in the direction of moderation. You might instead imagine electing the candidate that the fewest people really hate; that would be too far in my opinion. In the real world, the ideology model doesn’t hold that literally, so you can easily see a left- or right-wing candidate win in a 1-on-1 election with a centrist.
There isn’t always a Condorcet winner. Instead, you can have a Condorcet cycle, where A would beat B in a 1-on-1, B would beat C, and C would beat A—for example in an election where 1/3 of people prefer A>B>C, 1/3 prefer C>A>B, and 1/3 prefer B>C>A. I’m honestly not sure how often we should expect Condorcet cycles in practice. I don’t think it’s some crazy hypothetical; it’s quite imaginable for left-wing voters to prefer left-wing candidate (L) > traditional conservative “center-right” candidate (CR) > right-populist “far-right” candidate (FR), center-right voters to prefer CR>FR>L, and working-class voters to prefer FR>L>CR. Then again I would be surprised if it happened that often. Maybe 1 in 5 real-world elections feature Condorcet cycles?
Choosing the Condorcet winner (if it exists) is nice because it gets rid of all strategic voting. But you don’t have to prefer the Condorcet Criterion; I’ll try to go through the most notable electoral systems and discuss the pros and cons.
Single-Member Electoral Systems
Methods for Polarized Elections
This is the bucket of electoral systems you should choose if you like having a two-party system with politicians toward the extremes. Note that since politicians strategically moderate to win elections, none of these systems do as poorly at electing moderates as you might naively think, but still the politicians elected are usually well to the left or right of center.
FPTP
First-past-the-post (FPTP) is the simplest method for electing a single person: everyone votes for one person, and the person with the most votes gets elected. This system leads to the spoiler effect, where people voting for third parties are essentially throwing their vote away, and thus everyone is incentivized to vote for the two best-polling or most established parties.
Top-Two Runoff
You can expand upon FPTP by having a top-two runoff, where the two best-placing candidates in a first round of voting face each other in a one-on-one second round. This system allows people to vote more honestly during the first round instead of strategically coalescing around the two best polling candidates. In practice, you’re usually just going to get the same left vs. right election as you would in a regular FPTP election. There are three main differences from FPTP:
People are less likely to throw their vote away (abstaining, voting third party) in a runoff than under FPTP. This is because:
(a) they don’t have to rely on polling to know who the two front-runners are, and
(b) they feel like they have had the opportunity to vote honestly in the first round and so are happier to vote strategically in the second round
Sometimes, a runoff will allow a candidate not from one of the two main parties to gain enough traction to make the top-two when they wouldn’t have under FPTP.
You can use this system as a replacement for primaries.
RCV
In Ranked-Choice Voting (RCV), also known as Instant-Runoff voting or Alternative Vote, people rank their choices. At first all votes are allocated to people’s first choice; then, in successive rounds, the lowest-scoring candidate is eliminated, and each voter who had chosen this candidate has their vote reallocated to their next highest-ranked candidate. This is done until there is only one candidate remaining.
One downside is that people might have limited knowledge about all the candidates, which can lead to some voters giving poor rankings or not ranking everyone. To remedy this, you can have two rounds of voting, where the second round is a manual runoff for the top two contenders. Alternatively, you can do something like Alaska is doing, where there is a first round where everyone votes for one person, and then the top four placers make it to the second round which uses RCV.
Two-round RCV (of some form) is just about strictly better than FPTP. The main downside is really that it’s more complex. Tentatively, I think I’d consider two-round RCV to be the best system if you want polarized elections, but I think you can make the case for any of these systems (FPTP, FPTP+runoff, RCV, two-round RCV) and it wouldn’t be crazy.
Condorcet Ranked (Ordinal) Methods
The second bucket of electoral systems is ranked methods that explicitly pick out candidates from the winning Condorcet cycle, called the Smith set. Among these, the best for handling situations with no Condorcet winner is probably Ranked Pairs. The other system I think is notable is Minimax, which picks the candidate who does best in their worst 1-v-1 matchup, for its simplicity2.
As with with RCV, there can be limited public knowledge of candidates, which can lead to voters giving poor rankings or ballots that don’t rank everyone. The right way to deal with this is to do a top-4 system like what Alaska is doing with RCV.
The main downside is that these systems are quite complicated. How big of an issue is complexity? Well, in the real world, adopting a new electoral system is such a tall order that people are desperate for methods simple enough to explain to people. Once an electoral system is adopted, however, governments are quite good at following them to the letter. There have been some cases of mistabulations that have gotten resolved later on (like this case out of California), but in general I’d expect these cases to get much less frequent as an electoral system is widely adopted and used repeatedly.
These methods usually get dismissed for their complexity, and for most of them I get that. I feel like top-4+Minimax is simple enough to be worth seriously considering, though.
A Brief Note on Strategic Voting
These ranked Condorcet methods are the only ones that guarantee a Condorcet winner wins. An interesting result, however, is that almost all electoral systems should select the Condorcet winner (assuming one exists) if everyone is super strategic and public polling is good enough. This is easiest to see with an example from FPTP: if it’s a left vs. center vs. right and polling shows that the left would lose to the right in a 1-on-1, left-wing voters should all vote for the centrist so that the right-winger doesn’t take power. Here is a proof for score voting, a system I’ll talk about shortly.
In practice, people aren’t strategic enough and public polling isn’t good enough for this to hold. But it’s an interesting result, and can hold to some extent in some voting systems.
Rated (Cardinal) Methods
The last bucket of voting systems is rated methods, where people rate every candidate on the ballot, eg from 1 to 10.
Score and Approval Voting
Score voting is the simplest: have everyone rate the candidates, sum the ratings for each candidate, and then seat the candidate with the highest total rating. You can have a rating scale like 1 to 5 stars, or you can have a binary approve/disapprove, which is called Approval Voting. You can also combine score voting with a top-four system to help with public knowledge.
One other thing you have to figure out is what happens when a voter doesn’t vote on a candidate: you can count it as 1/5, 3/5, or maybe something in between. I think if you have a top-four system you should count it as 3/5 (“neither approve nor disapprove” for approval) or maybe even require voters to rate all 4 candidates for their vote to be counted. If you have more than 4 candidates though you should just count it as 1/5 or “disapprove”.
This system needs fewer strategic voters to elect the Condorcet winner by the above logic, but again this relies on public polling being good enough. I feel like in real life this system might elect the Condorcet winner it’s a standard left v. right election and polls show a landslide (because the losing side would strategically vote for the centrist). If polling shows a tight race, or if things are more complicated than left v. right, I feel like it would be pretty unpredictable. The hope is that people would be more honest in that case, since it’s not clear what the right strategy is, and thus you would get something close to the candidate satisfying total utility3. And idk, maybe. Or maybe they’d just give their candidate the max rating and every other candidate the min rating because they’re lazy and then you get FPTP.
STAR Voting
STAR is very similar, except instead of seating the candidate with the highest total score, it uses the total scores to narrow the field down to 2 candidates, and then seats the candidate which would win in a runoff (ie, the candidate which more voters rated higher than the other one). STAR has the (IMO) advantage of making it more likely the Condorcet winner wins, because they would win that final round. STAR stands for “Score Then Automatic Runoff”, but you should probably actually make it a manual runoff to help with public knowledge.
The biggest downside of STAR I can see is that it’s not cloneproof: if the winning candidate has a “clone” which has a very similar voting base, these two candidates will make the runoff and it will basically be score voting. Clones seem like a pretty gaping flaw if parties can nominate multiple people. You could try to mitigate it with some sort of “party only nominates one” rule, or with a threshold system where candidates need to have (eg) 10% of voters rate them highest in order to make the runoff, but even with them STAR seems liable to collapse into Score voting.
Highest Median
This is what the name suggests: choose the candidate with the highest median rating, with some secondary system for breaking ties (read about that here). This voting system lends itself to pretty pictures, which makes it fairly easy to explain (except for the tiebreaking procedure) even to someone who doesn’t know what a median is. Highest median is supposed to be more strategy resistant than score voting, but honestly it seems even more uncertain how it would work in real life. Like, in a standard left vs. center vs. right election, highest median should turn on if left/right-wing rank the centrist candidate higher than centrist voters rank the left or right-wing candidate, which seems highly uncertain.
Recommendations
My favorite electoral system if you have a really polarized political landscape and want to elect moderates is Minimax, while if you have a more complicated landscape it’s probably score voting. Score voting has the huge advantage of being far simpler, but I really worry that it wouldn’t select the Condorcet winner in a polarized environment.
If you enjoyed this, go read the second half of this post on multi-member electoral systems!
It’s not quite optimal, of course, because future citizens and foreigners and non-humans don’t vote
Minimax selects the Condorcet winner if it exists but does not necessarily select a candidate in the Smith set
Note that even if people were totally honest you wouldn’t get that, eg since everyone would rank their top choice 10/10, but not everyone achieves the same maximal utility from their top choice