Crossposting from my substack.

I figured I would crosspost to LessWrong since electoral systems seem like the type of thing rationalists would be interested in.

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. First I’ll discuss electoral systems for electing a single person, and then 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 choice.^[1] 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 (activism, interest groups, also they probably have higher turnout in elections).

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 think it’s important for a voting system to select for moderate candidates and am thus attracted to it. Whether and how much you prefer this depends in large part on your preference for consensus vs accountability democracy. Some reasons for my preference for moderates include that my candidate isn’t as good as the other candidate is bad (relative to a centrist candidate), that people are incentivized to undermine democracy when candidates get too extreme, and that extreme politics leads to political bias that makes it hard to think clearly.

I will also point out that the Condorcet criterion doesn’t go that 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 agree with me on preferring 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. 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.

IRV

In Instant-Runoff Voting (IRV), known colloquially as ranked-choice 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 IRV.

Two-round IRV (of some form) is just about strictly better than FPTP. The one downside, other than complexity, is that you can’t easily see the vote composition vote for each precinct like you can for FPTP, which makes it less secure—precinct vote analysis is one of the keys to election security—and more prone to mistaken implementation—see this case in California of a school board candidate accidentally seating the wrong candidate. Given that IRV has been used in real elections before, I don’t think this is fatal, but it’s something to keep in mind.

Tentatively, I think I’d consider two-round IRV 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, IRV, two-round IRV) 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 simplicity.^[2]

As with with IRV, 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 IRV.

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 that California case I talked about earlier), 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, and it’s probably my favorite system.

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 -10 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 to be good enough. I feel like in real life this system would elect the Condorcet winner when the standard left v. right election is a landslide (because the losing side would strategically vote for the centrist), but when the polling shows a close race it would be pretty unpredictable—how highly would left- or right-wing voters rank the centrist in that case?

You should also combine score voting with a top-four system to help with public knowledge.

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.

An example of highest median: just look across the 50% line to find the winner. In this case there is a tie between candidates A and B, which would be resolved in favor of A

Multi-Member Electoral Systems

Don’t Use A Non-Proportional System

A common multi-member electoral system is to have single-member electoral districts and use one of the previous electoral systems to elect them.

There might be some argument for using this method with an electoral system that elects a moderate/Condorcet winner. Even here though, I think if you want a moderate/Condorcet winner, you should just go with a proportional voting system instead, so the moderate ends up being the swing vote in the legislature.

Usually, however, people argue for non-proportional voting system using one of the two-party electoral systems because they don’t want their politics devolving into a bunch of small parties that make accountability democracy harder. But there is a better way.

You can force a proportional electoral system to elect larger parties by adding a threshold, a % of the vote a party must cross to get any seats. If you add a threshold, please use ranked voting so that people’s votes are not wasted if their preferred party doesn’t make the threshold. This is called Spare Vote, and works the same way as IRV does for single-seat elections, but instead of stopping at 1 candidate you stop once every remaining party is over the threshold.^[3] It comes with the same downsides of IRV—you probably can’t report results by precinct, and you should probably have two rounds if you set the threshold really high—but the downside to just throwing out votes that don’t make the threshold is even bigger than the downside to using FPTP because a lot of people are going to vote third-party in a proportional system.

High thresholds push a country away from consensus democracy and toward accountability democracy. High thresholds also force voters rather than politicians to form coalitions. For reasons I’ve discussed here and elsewhere, I thus generally prefer low thresholds, but it’s nice to have a single parameter to adjust. If you want a two-party system, for instance, you can raise the threshold to 34%³.

You might still favor single-member districts because you want seat share to go up faster-than-proportionally with vote share. Even then, though, you shouldn’t use single-member districts. The relationship between seat share and vote share in them is dependent on the weird geographic property of the partisan distribution of districts—the more swing districts there are, the larger majorities will be. (Also you have to deal with gerrymandering).

The better way to implement this greater-than-proportional relationship is to start with a two-party proportional voting system and then add some formula to give a boost to the winning party, like “a party gets an extra 1% seat share for every percent above 50% they get in vote share, up to 55%”. This yields a nice predictable relationship between vote share and seat share.

Now, onto the forms of proportional representation.

Closed list PR

Closed list-Proportional Representation (PR) is the simplest. Each party issues a list of candidates before the election, they’re allocated seats proportionally to how many votes they get in the election, and the top x from their list get seated (where x is the number of seats they were allocated).

The upside is that this system is simple and immune to gerrymandering or any other weirdness. There are three downsides I can see:

• It’s harder to mix this system with primaries if that’s what you want to do. I won’t discuss party candidate selection in this piece, but it’s worth noting.
• Scandals can’t be punished as precisely. People can’t vote against scandal-ridden candidates directly, they can only vote against the party as a whole.
• There are no representatives from swing districts to feel the heat.
  • An important reason that legislatures act moderately is that politicians from swing districts know that if they don’t vote moderately, they will lose their seats. You might see this phenomenon in party list PR with politicians low down on their party’s list, who know that if their party passes extreme stuff it will lose popularity and they will lose their seat. However, they don’t feel the pressure from voters examining their specific voting record and choosing candidates based on that.

One thing I don’t think is a downside is the fact that people don’t have a local representative. If the purpose of local representatives is that people can reach out to them, you can just have a bunch of non-voting local representatives. If the purpose of local representatives is that local constituencies have someone voting based on their interest, I would say that’s stupid and constituencies shouldn’t be given additional influence if they’re clustered geographically. If a constituency is big enough, national politicians should have to pander to it, either with a party of its own or through concessions from bigger parties.

Mixed Systems

Mixed systems are systems that have some district-level elections, but also some mechanism for ensuring that a party’s seat share is directly proportional to their vote share.

There are three methods I know of. There’s open-list PR, where seats by default come from the party list, but then candidates can guarantee a seat by getting a certain vote total in their district^[4]. There’s mixed-member proportional (MMP), where there are district seats usually elected in normal FPTP elections, as well as list seats given to make the party vote proportional and which are selected from a party list. And there’s dual-member proportional (DMP), where each district elects one member by normal FPTP, and then each district also has another rep which is chosen to make the national results proportional.

A lot of the properties of these systems depend a lot on implementation details. So let me make some broad comments about these systems:

• To the extent that a mixed system relies on list seats, it functions similarly to closed-list PR.
• To the extent that a mixed system sees candidates from different parties compete against each other in each district, it has the nice properties that closed-list PR lacks—scandals are directly precisely, politicians in swing districts are incentivized to moderate.
• To the extent that a mixed system sees candidates from the same party compete against each other in different districts (vying to get more votes in their respective districts), candidates have the incentive to moderate.
• To the extent that a mixed system sees candidates from the same party compete against each other in the same district, these systems function like primaries, love them or hate them.

And then more specific comments:

• If you have a separate party vote and person vote (like in open-list PR and some variants of MMP), combining it with spare vote is sort of annoying, because you probably want ranked voting both in the party vote and the person vote. This is why I prefer single-vote systems.
• Open-list PR is pretty simple, MMP is sort of in the middle, and DMP is pretty complicated. Open List PR is in place in a bunch of places, and MMP has been is in place in a few, notable Germany and New Zealand.

My favorite electoral system with low/no thresholds is closed-list PR, while with high thresholds it is probably MMP.

Multi-Member Districts

This bucket is of electoral systems that extend single-member electoral systems to multi-member. These systems have proportional results if everyone votes strictly by party line, and if not they function similarly to their single-vote counterparts. They are implemented in multi-member districts, preferably at size 3. Any fewer seats per district and the results become no longer meaningfully proportional, any more per district and public knowledge of candidates becomes very low.

The most notable of these systems is Single-Transferable-Vote (STV), which is the extension of IRV. Among the other systems are Schulze STV and CPO-STV, which are extensions of Condorcet ranked methods, and Proportional Approval vote, which is the extension of approval voting.

There’s lots to say about these systems:

• They avoid most of the downsides of the above systems
• They are the only systems that can handle a country where polarization is very low and people care more about individuals than parties.
  • Honestly though if a country gets to that point, voters are probably voting for people that don’t represent them very well on the issues, so I don’t think this is a good thing to encourage.
• They can handle some of the party candidate selection for you.
  • You still do need parties to nominate certain people though, as otherwise there are going to be way too many candidates and public knowledge of candidates will be really low. But parties can narrow it down to like 5 people and let voters select up to 3 instead of choosing 1 person. Whether this is a positive or negative, I’m not sure.
• You can’t combine them with thresholds, which means you don’t have this parameter to adjust to encourage bigger parties.
• 3 candidates per district is easy to gerrymander, so you need to ensure that lines are drawn impartially.
• They can’t report results by precinct.
• Even with 3 candidates per district, public knowledge of candidates takes a significant hit. When public knowledge of candidates is low, these systems lose many of their advantages over party-list PR.^[5]
• They’re very complicated, both to explain/implement and to some extent for voters to use. I’m pretty surprised that STV has actually been implemented in Ireland and Australia

Finally, I would be remiss not to mention Proportional Multi-Vote Representatives, a proposal I wrote about 5 years ago (wow I’ve been thinking about this stuff a long time). That piece is lower quality compared to this one, but not terrible.

Wow that was a long post. I hope you have a good overview of the pros and cons of different electoral systems, and that I was able to convince you of a few things.

1

1. ^{^}

   It’s not quite optimal, of course, because future citizens and foreigners and non-humans don’t vote

2. ^{^}

   Minimax selects the Condorcet winner if it exists but does not necessarily select a candidate in the Smith set

3. ^{^}

   There’s a different way of implementing it where you just remove all parties that don’t make the initial threshold and reallocate their votes. This however incentivizes parties to join forces if they are polling below the threshold, which defeats some of the point of thresholds, because then it is politicians (rather than voters) who are doing the coalition formation.

4. ^{^}

   Open-list PR usually isn’t regarded as a mixed system, but I think it fits well in the category

5. ^{^}

   Speculatively, I think they could be even worse than party-list PR. I think when people are voting for candidates and don’t know much about them, they are more likely to randomly vote for different candidates, rather than strictly relying on party labels which are better indicators of issue agreement.