Commentary & Analysis

What is Duverger’s Law?

By Eric Sanders & Aaron Hamlin

What is Duverger’s Law? How does it affect the number of political parties, and is it responsible for the US’s two-party system? In our latest video and podcast, CES directors Eric Sanders and Aaron Hamlin discuss just that.

You can choose to listen to the podcast in the following Youtube video or read the transcript below.


Eric Sanders: Eric serves on the board of directors at The Center for Election Science

Aaron Hamlin: Executive Director of The Center for Election Science


Eric: I’m Eric Sanders from The Center for Election Science. And I am very pleased to be here with our new executive director, Aaron Hamlin, in Washington, D.C., our nation’s capital. How ya doing, Aaron?

Aaron: Doing well, thank you.

Eric: Just before we get into the subject of today’s talk, I want to frame it by asking the sort of big picture question. And I’ve had people ask me this many times. I’ve debated with people over it. Why is it so hard in the United States for third party and independent candidates to win seats in government? It seems like we have almost no third party or independent politicians making laws for us. Why are we stuck with this defacto two-party system?

Aaron: I think probably the way to explain that or way to point to that effect is Duverger’s law. And Duverger’s law just says that the voting method plays a prime role in determining how many parties we’re going to wind up with.

Eric: Okay so, Duverger’s law. So who is Duverger? Is he a person?

Aaron: Yeah, he was a French scholar as well as attorney. Maurice Duverger. And he wrote a book in 1951 called Political Parties, which is where he first described his law.

Eric: So what is this law? Is this a law on the books in France or the United States Somewhere?

Aaron: It was an academic work. And it’s really, he’s pointing out a tendency of certain factors that are used to predict how many parties a system is going to wind up with.

Eric: And what are these factors that he says lead to the number of parties in a government?

Aaron: Sure. There are two factors. The first factor is the threshold necessary necessary to have a third party or independent get elected. And by definition when we’re using a single-winner method, you’re gonna need a high threshold. And so anytime you elect a single-winner office position, it’s gonna be pretty difficult to get past that first factor.

Eric: And the threshold meaning, basically, you need more votes than anyone else?

Aaron: Right, right, right.

Eric: Okay, and what’s the second?

Aaron: And so there’s that second factor. The second factor is really more of a psychological factor. So that feeling of being able to vote for whom you want regardless of whether you perceive them as being viable.

Eric: And so we have a two-party system in some cases because people don’t vote for candidates they genuinely want for some reason?

Aaron: Right, right. When we use Plurality, Plurality makes it so that, well, if you want a chance at determining who the winner is, then you’re going to start by looking at who’s in the lead. It doesn’t make sense if you’re wanting to determine the winner and you’re seeing someone that has one or two percent support. I mean, that candidate is unlikely to win.

Eric: Plurality, just to be clear, is single-choice voting where you’re legally forced to pick only one candidate, right?

Aaron: Right. It’s the bare minimum of information that you can provide. That’s our current method.

Eric: And you’re saying that voters, if not many voters, often don’t vote for the candidate they might most want because they think they might be wasting their vote if they do?

Aaron: Yeah, absolutely. And if voters had a way to be able to give a more accurate response, then you’d get a more accurate reflection of third parties and independents as far as what their support is.

Eric: Okay, so that makes sense to me. So what are some of the ways that third parties and independents could get more support? I mean, are we stuck in a two-party system? Did Duverger say that there were some solutions?

Aaron: Duverger said that Plurality will tend towards a two-party system. But he also said that using proportional methods will lead toward multi-party systems.

Eric: And do other countries use proportional methods? Does anyone use that?

Aaron: Yes, pretty much most places besides us.

Eric: Okay, but we are special. So that’s totally fine. And so we’re special in the United States we don’t want multi-winner elections. We want single winner elections. [laughing] So let’s say we keep our laws the same. We’re only going to pick one winner for all our elections for House and Senate and President and all these things. Is there any other way other than proportional voting methods that we could help third parties and independent candidates to have a more accurate level of representation?

Aaron: Sure, sure. And sticking with the framework of Duverger’s law, he had those two factors. That first factor deals with the high threshold. Single-winner methods, they can’t get past that. There’s no way around it. But you can get around that second factor, that factor, that psychological barrier that says whether or not you can choose an independent or third-party candidate that’s sort of up and coming. So if you want to be able to use a single-winner method and get past Duverger’s law to allow for multiple parties, you have to hit at that second factor.

Eric: So what can we do? What’s the American solution for overcoming that second factor?

Aaron: If you want to get past that second factor you have to use (and while in a single-winner framework)

Eric: Right

Aaron: You have to use a voting method that permits you to choose your honest favorite every single time. And so, but fortunately, even though that’s a very difficult criterion to achieve, there are methods that do pass that.

Eric: And I’m at the edge of my seat. I think you’re gonna tell me! Can you give me an example?

Aaron: The easiest example of a voting method that passes this (that is, it lets you choose your honest favorite no matter what) would be Approval Voting.

Eric: Okay, and Approval Voting, sometimes I’ve been saying multi-choice voting, lets you select as many candidates as you like. And then the candidate with the most approvals or selections wins, right?

Aaron: Right, right. It’s doing the same thing as Plurality. Only when you choose multiple candidates they don’t throw your vote away. They count it, just like normal.

Eric: Well that’s good because those overvote laws drive me crazy. Sometimes I wanna vote for more than one candidate. But that makes sense from the voter’s perspective. I know, great, yay, I get to express myself more fully. I get to say all the candidates I like. But how does that help third party and independent candidates have a chance at winning?

Aaron: When voters are allowed to choose as many candidates as you want, those third parties and independents get a more accurate reflection of support. Because, whereas before under Pluralty, a voter would look at them and say: “well, I like this candidates ideas, but I don’t want to throw my vote away. I wanna have a say in who wins.” Or even worse, they will see among the frontrunners and not even bother to look at other ideas because where’s the motivation to do it?

Eric: Right, why am I gonna waste my time, you know, going to your rallies or reading your campaign literature if I don’t even think you have a chance at winning anyway, right?

Aaron: Right, right. Whereas if you use a method that permits you to choose your honest favorite, then now you’re in a system where not only can you choose your honest favorite and get them a more accurate reflection of support, but you’re also incentivized to learn about new ideas.

Eric: Now it seems to me that one of the major problems here is the sort of self-fulfilling prophesy here of the frontrunners. The frontrunners being the only candidates that are worth paying attention to because why waste your time even considering for someone who can’t win? So did Duverger talk about how we can undue that vicious cycle?

Aaron: That goes right back into the second factor. So if you feel you’re going to be throwing away your vote, then those candidates have no opportunity to be able to grow.

Eric: Well, when I look at polls I see maybe the independent candidate I like has ten percent support, so I’m not going to vote for that person and throw my vote away.

Aaron: Right, right. And the reason for that (and ten percent for a third party or independent under Plurality is actually pretty high)

Eric: Yeah, it’s probably more like two! [laughing]

Aaron: Which is a little bit disturbing because it’s not like people disagree with all third party and independent ideas. It’s just that when you have a poll that is run in the same way that we do our voting method with our elections now, under Plurality you’re just not going to get a very accurate reflection. Whereas if you use another method, you’re gonna match that with the polling method.

Eric: Our current polls say who you’re planning to vote for in the upcoming election. That assumes that you’re only permitted to vote for one candidate, right? But are you suggesting that if we use polls under the Approval Voting framework and ask people who are the candidates you plan to vote for, then you’d have a much more accurate sense leading up to the election of overall support for the candidates? And it would sort of eliminate that frontrunner self-fulfilling prophesy, right?

Aaron: You’re right in that if you’re using Approval Voting for your voting method that it makes sense that you’re going to use Approval Voting for your polling method as well. A poll is designed to a predictor for what the election’s outcome is gonna be. And so you’re going to need to match the measurement. And so if you’re using Plurality Voting in your election, then that measurement needs to be the same when you’re using polling. And the same thing for Approval Voting. And with Approval Voting you’re still using that feedback with polling information. And so it’s still going to determine who you’re going to be looking at among the frontrunners. But one thing that’s completely different is that it doesn’t matter at all what the polls are when you’re choosing among your favorite candidates. So if you really like a candidate, it has no bearing how much support they have.

Eric: Right

Aaron: You choose that candidate to support their ideas. And there’s no disincentive to do so.

Eric: Right because you’re saying that there’s no negative repercussions for you as a voter ever for voting for or supporting all the candidates that you like on the ballot, unlike now, right?

Aaron: Right. Under Approval Voting if you have an honest favorite, you can always choose that honest favorite no matter what.

Eric: And say we switched to Approval Voting in New York State, would you say that independent and third party candidates maybe would start getting more media exposure, have access to debates? I mean, would it completely change the whole election cycle?

Aaron: It would. It would have an avalanche of secondary effects. Right now with when you have debates, the debate commissions, they have to use supposed objective criteria to decide who gets in those debates. And the big criterion that they often go with is polling information.

Eric: Ah, I see. I see. Yeah.

Aaron: And so if you’re using Plurality polling, then you’re getting a pittance of support whereas if you’re using Approval polling, then you get a more accurate reflection. And if you’re polling twenty or thirty percent, they can’t kick you out of the debates anymore.

Eric: Gotchya

Aaron: And importantly your ideas are represented. And you have more competition with discussion and ideas. Which, I mean, if you’re talking about democracy, you need that.

Eric: Well that sounds great. You know I have a lot of conversations with people and they’re fed up with the two-party system. You know, I’m just wondering, other than the voting method, is there any other reason why third party and independent candidates to really have a fair chance?

Aaron: Sure, there are other factors. And Duverger recognized this. Perhaps it’s a bit of a misnomer by calling it a law. Perhaps more of a tendency. But this wasn’t something that Duverger was ignorant to. So he recognized other factors such as ballot access issues, whether there is a good third party, whether people like the ideas of a third party. And also, there are other academics that looked at for instance the issues that were important to the electorate and how many dimensions those issues had. So if there were two big points or sides of an issue, then it would lead more towards two parties. But if it were three or more sides to a big issue that were really prominent, then it would lead more towards three or more parties.

Eric: That makes sense because it gives candidates a chance to differentiate themselves and splinter into various competitive factions, right?

Aaron: Right, right, right.

Eric: Alright, but if you had to distill Duverger’s law and you had some advice for say a Green Party supporter or a Libertarian Party supporter, someone came to you and said what can we do? What’s the real way to help third party and independent candidates? Would you say the voting method is the real place to start, that that’s the fundamental problem here?

Aaron: I would agree. Duverger was more accurate by saying that there were other factors involved. But he really hit the nail on the head by appreciating the voting method itself as the overall most important actor here.

Eric: Wow! Well that’s kind of mindblowing because I’ve had many conversations with people. And all the other topics you talked about are brought up, but rarely do I hear people say the voting method, the fact that we’re forced to pick one candidate is the fundamental reason why we have a two-party system. That sounds so simple, but I just don’t hear it that often. So I’m glad that you sort of elucidated that point.

Aaron: Yeah, I mean, we’re talking about the very way that we provide information for our voters to be calculated to determine a result. So if you’re hindered in being able to provide that information in the first place [laughing] it’s hard to imagine a situation that’s gonna be able to come up with an accurate reflection of what the electorate wants.

Eric: Right, right. And we look at all these sort of trickle-down problems and complain about those. But we don’t realize the underlying problem is the voting method itself, huh?

Aaron: Yeah, you’re really looking at the source when you’re looking at the voting method.

Eric: I like that! I like getting at the source. Well that’s good stuff. And who knows, maybe one day in our lifetimes we’ll pick a president using Approval Voting.

Aaron: That sounds awesome.

Eric: Maybe a third party candidate. [laughing] You never know. Thanks a lot, Aaron. It’s been a real pleasure.

Aaron: Thank you, Eric.


This podcast was brought to you by The Center for Election Science. You can find a transcript of this podcast and more of our work at our website, If you enjoyed this podcast, you can support us by donating on our webpage and by sharing our work on Facebook and Twitter. You can keep up to date and get involved by signing up on our mailing list from anywhere on our site. Until next time, thanks for listening.