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 leader, and then in the second part I’ll discuss multi-member electoral systems for electing a legislature. I hope to give you a good sense of the different types of systems out there, their pros and cons, and which ones are better or worse.
But before any of that, some social choice theory background is in order. What are we even looking for in an electoral system?
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.
There is one ethical philosophy, preference utilitarianism, which views this as close to the optimal choice1, assuming you view these utility functions as people’s true preferences. But if you don’t hold this stance, either because you’re not a philosophy nerd and just want something vaguely democratic, or because you have different ethical beliefs or ways of viewing democracy (like me2), I don’t think this method comes out looking all too 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 for electoral systems specifically, 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 it’s maybe not the right mindset here.
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 head-to-head 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 10 real-world elections feature Condorcet cycles?
I quite like the Condorcet Criterion. But you don’t necessarily have to share my preference; 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. I don’t recommend this though if you can avoid it, because of the case when two candidates from the same party make the runoff.
When it’s two candidates from the less popular side, eg, this is just a failure
When it’s two candidates from the more popular side, the more moderate candidate should win. I also see this as a failure - if you want a moderate candidate to win you should pick a different system, the fact that this system randomly picks a non-plurality moderate candidate 1/10 times is unintended
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.
Much of the stuff I said about top-2 applied to RCV as well:
People may be less likely not to vote for (ie rank) either of the top 2 candidates than under FPTP because they don’t have to rely on polling and are satisfied with their ability to vote for their top choice first
Sometimes, RCV will allow a candidate not from one of the two main parties to gain enough traction to be one of the final 2 candidates when they wouldn’t have under FPTP.
You can use this system as a replacement for primaries
The advantage of RCV over top-2 is that it can be more robust to having many candidates, eg it’s less likely to see two candidates from the less popular side make the runoff.
The main downside is “ballot exhaustion”: you never truly get 100% of voters to fill out their entire ballot. In practice, the main failure mode is that some people who vote eg Republican and generally prefer Republicans to Democrats don’t bother filling out any other Republicans besides their top choice. I’d also extend ballot exhaustion to include any time a voter’s full ranking isn’t as accurate as it would have been if they really thought long and hard about it, even if they did fill out most of their ballot. One reason for ballot exhaustion might be limited knowledge about all the candidates just because of how many there are. Another is just that some people are lazy and just mark their top choice.
To remedy this, you can have two rounds of voting, where the first round is RCV and the second round is a manual runoff for the top two contenders. Alternatively, you can do something like Alaska is doing, where in the first round everyone votes for just one candidate, 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. 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.
One last thing. I do think RCV can be more likely to select the Condorcet winner just based off vibes. As in: under RCV people are more likely to strategically upvote the Condorcet winner, and Condorcet winners are more likely to run, just because it seems like a thing the system is supposed to encourage (even when it doesn’t actually).
Condorcet Ranked (Ordinal) Methods
The second bucket of electoral systems is ranked methods that explicitly pick out the Condorcet winner with an algorithm, which is easy to do once you have everyone’s full ranking.
As with with RCV, ballot exhaustion can be an issue. The right way to deal with this is to do a top-4 system and mandate that people rank all 4 candidates in the second round. I do worry though that a Condorcet winner would not even be able to make the second round, like in a very polarized landscape you might need a decent amount of strategic voting to get them there. But there’s not really any way around this.
These ranked Condorcet methods differ in how they handle a situation where there is no Condorcet winner, their cycle-breaking method. Once you narrow it down to 4 candidates though, I find it unlikely that these systems would differ in practical cases of no Condorcet winner. The simplest and most intuitive approach is probably Minimax.
Condorcet ranked methods also tend to have minimal strategic voting. There’s a formal statement here:
Strategic voting in ranked Condorcet systems can only occur by manipulating the configuration so that there’s a cycle, and then exploiting the cycle-breaking method. In most sensible systems though, including Minimax, this is really tricky and I’d expect it not to happen at all in real elections. The one possibility I can see is that voters think they can manipulate the system and end up doing stupid things that lead to a worse result. Probably I just wouldn’t publicize the cycle-breaking procedure too widely and emphasize that it’s rare.
On complexity
The most cited drawback of these ranked Condorcet methods is that they are complicated. Honestly though, I think that’s overstated. Condorcet methods can be easily understood with a single chart: the head-to-head matchups. The winning candidate is just the candidate whose row is all green.
I think most of the public is intelligent enough to understand this chart. Some of the dumbest people in the world obsess over sports numbers, I feel like this is easier to understand than a lot of those. Understanding how the chart is produced - counting how many people rank candidate A above candidate B, vs. vice versa - is more complicated, but still not insane and not critical for understanding the method. And crucially, none of this is necessary for understanding how to use the method as a voter: the optimal strategy is the genuine one, to rank candidates in order of your preference.
I’ll have more to say about complexity at the end, but I do think these methods are too often dismissed.
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 0 to 10, or you can have a binary approve/disapprove, which is called Approval Voting.
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 behave irrationally in some other way, like giving their candidate the max rating and every other candidate the min rating because they’re lazy.
There’s one other failure mode of score voting that upon reflection seems quite bad. Let’s say you do score voting with a top-4 system to help with consolidation, and the public favors the left wing candidates 60:40 over the right wing candidates. Then imagine the runoff is two left-wing candidates polling relatively similarly, one right-wing candidate, and one irrelevant candidate that everyone knows is not going to win; this all seems like a very normal situation. But now, the voters for left-wing candidate A and left-wing candidate B are caught in a sort of prisoner’s dilemma with one another. If all candidate A voters “defect” by rating A 10/10 and B 0/10, while candidate B voters “cooperate” by rating B 10/10 and A 8/10 (and the other two candidates 0/10), then candidate A will win. But if they both “defect”, rating the other candidate 0/10, then all of a sudden the right-wing candidate will likely win. Now in the real world the numbers probably wouldn’t be quite as drastic, but still this seems like a very real dynamic.
One upshot of this dynamic is that score voting probably can’t replace party candidate selection (through primaries or some other means), so you shouldn’t have a top-4 system. But even with party candidate selection, I do worry that this would happen anyway, and it’s made me more reluctant about score voting.
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
The two best systems in my view are score voting and ranked condorcet methods. If you have free choice over which electoral system to adopt, I think there are solid arguments for both of them; for reasons I’ve discussed above I’d probably lean toward ranked Condorcet ranked methods just to get rid of all strategic voting when there’s a Condorcet winner.
I don’t usually go too far into the practical aspect of what you should actually advocate for in the real world, but let me do a bit of that here. In practice, 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.
My recommendation for what to advocate for when I initially wrote this piece was solidly score voting, because of its apparent simplicty. The more I thought about it though, I’m not sure simplicity actually works in its favor. Score voting is simple to describe, sure, but understanding why we’d expect it to work well - how it would lead to somewhere between the Condorcet and utilitarian winner - is actually very complicated.
And how do you sell politicians on why to adopt score voting? The first instinct I think is to say “people should be allowed to express their degree of preferences rather than just their top choice/ranking”. But the natural followup question, and the one that is actually really complicated to answer, is why people shouldn’t just rank their top choice 10/10 and all the rest of them 0/10. And the line about degree of preferences is also just not very compelling: who looks at politics and says “the underlying issue is that voters aren’t able to express degree of preference well”?
(I do think score voting is the obvious choice for primaries, as I discuss in this piece, and I think the degree of preference thing is more intuitive there.)
I think this complexity of justification, even when the system itself is not very complex, explains why score voting hasn’t been adopted basically anywhere. Approval voting, the binary version of score voting, has been adopted, and in those cases it’s been sold as a tool to promote positivity in politics. But that explanation is straight-up BS; limiting people’s choices to binary yes-no does nothing to encourage positivity if people are rational. I also just intuitively dislike approval voting. It does not sit right with me to have a system whose optimal strategy is a randomized one.
Ranked Condorcet systems also haven’t been adopted anywhere, probably on account of their apparent complexity. I do think though that they would probably be easier to adopt in real elections, and top-4+Minimax is the system I would advocate for IRL. I wrote another post for a wider audience advocating this system and the best terminology to use for it: “head-to-head” for Condorcet and “highest floor” for Minimax.
If you enjoyed this part, be sure to read the second part of this post, about electoral systems for electing a multi-member body like a legislature!
It’s not quite optimal, of course, because future citizens and foreigners and non-humans don’t vote
I’m a hedonic utilitarian, mostly. I’d also contend that these political preferences are different from people’s true preferences in life.
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
LOTS OF RAMBLING, sorry
Sorry for not writing out my fuller thoughts earlier. I did have it in the back of my mind, but clearly procrastinating was beneficial, as you've captured a lot of my thoughts in your edits. I certainly agree that ranked Condorcet methods are the best theoretically. Certainly there are some complexity concerns as you say, but I agree that it's an overcomable problem. With a strong publicity campaign, people can understand that the Condorcet winner is the one that beats every other candidate in a 1 on 1. Thanks for the great article, and I think we're much closer to on the same page now.
About score voting, I think you're mostly getting at my concerns with "understanding why we’d expect it to work well is actually very complicated". Put a little differently, I think an important aspect of a voting system is that a voter, if they're well researched and have clear views, feels confident in their vote and understands how their vote is impacting the results. This is the key benefit (despite basically everything else being terrible) of FPTP. FPTP almost always leads to just 2 parties and you vote for the better one. If you decide to throw your vote away, at least you probably did it knowingly. Now it's still the case that in primaries some candidates might win and some might lose, so voting for your favorite is not always best. However, the nature of the system makes this pretty intuitive. The one downside of RCV is that it makes this a bit less intuitive. However, it is basically exactly the same thing. And voters still seem to understand this pretty decently (many people who ranked Murkowski ahead of Chesbro clearly understood this in Alaska). And everything else about RCV is strictly superior to FPTP. In score voting, however, it is not at all clear how you should vote even with a strong understanding of all the candidates and your own preferences. Imagine an election in a 60-40 D district. Since it's a left-wing seat say we get 1 R and 2 Ds running. With one candidate all the R voters unite and give their candidate 10s and the 2 Ds 0s (I know they shouldn't but let's say they have no preference among the Ds). Say the Ds are split exactly 30-30 and the true preferences of the voters is 10 for their favorite and 8 for their second. So a poll comes out and shows a 540-540-400 race. Now supporters of the Ds can see that the Ds are far ahead and it may seem that they should vote 10-0-0 instead of 10-8-0. Whichever D has more of their supporters willing to "effectively lie" will then be the winner. Unless of course way too many people think this way and then even the R could win. The system works better if everyone expresses their true preferences out of 10. However, here the side defecting from that more gets to win. That seems quite problematic. I don't know if scenarios like this would actually occur. However, I do think people would feel betrayed that their own vote was "wrong" and thus directly led to an outcome they don't like in a way they don't with our current system (choosing to give Romney a 0 leading to Trump winning over Harris and Romney in a three way may be no worse than voting for Harris instead of Romney in a Dem primary then leading to a loss that would have been a win, but intuitively it feels different). Don't get me wrong, their are clear big advantages to score voting. Romney has no chance of ever winning a Dem primary, but maybe he could win this three way and save us from Trump. In fact, I've kind of talked myself into thinking some of my objections are illogical (the same things happens with primaries). However, I certainly hate the idea of not knowing who I should vote for, and I think a lot of people would feel similarly. And I think this is a legitimate problem for a voting system. If people don't feel like their vote is pushing in the direction they want it to, I think they will hate the system. Imagine how people would feel if a majority vote Republican, but the Dems win because they're more unified in giving all their candidates 10s.
Another problem is the incentives for the candidate are really bad as well. What should Harris tell people to give Romney? Certainly her own interests don't align well with the country's. For all these reasons, I think, despite the complexity, I definitely favor ranked condorcet methods over score voting. Versus ranked choice voting, I agree score voting is better for primaries, but I think Alaska's top 4 and then RCV I might prefer to score, not totally sure though. Top 4 and then ranked condorcet sounds great though.
Some ways I think RCV is good and you underestimate it a bit as an improvement (although you're certainly right that it's far from perfect:
1. Getting to vote for your favorite candidate is healthy. It's good if people can vote for a Green/Libertarian/Independet/etc without throwing their vote away. Less people will get discouraged and hate the system even if it doesn't change the results.
2. Scenarios like the Montana/Nebraska senate races are much easier. You don't have to clear the entire party or get a candidate to run on dropping out. All you have to do is get more first place votes. I'm confident Bodnar can do that against Bankhead.
3. The primary electorate is effectively much more moderate and much higher turnout. You often effectively hold the primary in the general. If Mills and Platner were on the same ballot in the general much better chances for Mills to win (of course this doesn't work if you still have partisan primaries, but this is largely defeating the purpose, it needs to be like Alaska)
4. It's really crazy when people win primaries with 25% of the vote. Look at the Maine Dem governor primary, would be a disaster with RCV
5. Related to that it allows people to stay in when they're not viable without affecting the race in primaries if you are having them. This has two benefits. One you don't get cases like Porter and Mahan playing spoilers. But secondly voters are smart and mostly consolidate. However, if they don't have to this can really change the dynamics and maybe someone like Mahan wouldn't collapse as people desperately try to consolidate. This can A give you more information about true preferences and B maybe even change who wins if it's a collective action problem.
6. I think the problem of ballot exhaustion is probably a bit less than people say. A surprising number of partisans do in fact vote for candidate A and then don't show up when B wins the primary for the general. I'd like some numbers on this, but I'd bet people are overestimating how many are exhausting because they're lazy and or don't understand and how many just legitimately don't want to vote for the other person.
7. Total unknowns aren't a problem, which they have the potential to be in either score or even ranked condorcet though less so.