How to learn about voting methods

Materials for everyone, from complete beginners to experts

Unlike every other post on this blog, this one is designed to be accessible to people who have no prior knowledge of voting methods. If this is you, I suggest reading the articles in order (but you’re encouraged to poke around the sites I link to; there’s plenty of good stuff). More knowledgeable readers are encouraged to start at the first article whose content they don’t expect to be already familiar with; they may want to scroll down to level 2.

Level 1: Basics

Start with this basic orientation for questions like “What’s a voting method?” or “What do different ballots look like?” or “Why should we care about this?”

Next, learn the basics of how the most-discussed single-winner voting methods work:

• Plurality: This one’s so basic I won’t even give a link. Vote for one candidate. Whoever gets the most votes wins. Plurality is also known as First Past the Post (FPTP) and is the most commonly-used voting method in the United States. There is also a commonly-used variant with a top-two runoff.
• Approval Voting (where you can vote for any number of candidates)
• STAR Voting (score, then automatic runoff)
• Instant Runoff Voting (IRV)

Here’s a video on the basics of single-winner voting methods. It also covers Score Voting, which is like STAR Voting but without the runoff.

Terminology note: You’ll hear the phrase “Ranked Choice Voting” (or RCV for short) a lot. This is an umbrella term that refers to several different voting methods (this link is optional; you don’t need to read it at this stage) that use a ranked ballot. Instant Runoff Voting is the most commonly used form of RCV. The advocates of IRV typically refer to it as RCV without further clarification, but the advocates of other voting methods mostly prefer to use the more precise “IRV” label.

Note on advocacy organizations (links are optional): The links for Approval, STAR, and IRV go to the descriptions of the most notable organizations supporting these voting methods: The Center for Election Science (Approval Voting), the Equal Vote Coalition (STAR), and FairVote (IRV). Many of the links on this page go to articles from these organizations.

Currently, IRV is by far the most widely used, has the most traction and name recognition, and its campaigns receive the most funding. Approval Voting is only used by two cities (Fargo and St. Louis) and STAR isn’t used by any larger groups than some Oregonian political parties.

You should also learn about Condorcet winners, Condorcet voting methods, and Condorcet cycles. A Condorcet winner is a candidate who would defeat any other candidate head-to-head. A Condorcet voting method is a voting method that will always elect the Condorcet winner if there is one. Condorcet voting methods (usually) used ranked ballots, but Instant Runoff Voting is not a Condorcet method. A Condorcet cycle is a (rare) scenario in which there is no Condorcet winner due to candidate A defeating candidate B head-to-head, B defeating C, and C defeating A. Condorcet cycles aren’t actually that important (mainly because they’re so rare), but their existence means that there are a great many Condorcet voting methods that differ only in how they handle Condorcet cycles. Here’s an optional link explaining Condorcet cycles (the author calls them “Condorcet paradoxes”) if you’re curious. What I do recommend is reading this page on the Condorcet method called Ranked Robin, bearing in mind that all Condorcet methods are basically the same in practice.

Once you understand the basics of some single-winner voting methods, it’s time to learn about multi-winner voting methods and proportional representation (PR). I suggest starting with this video. Next, read up on these proportional voting methods:

• Party List methods
• Sequential Proportional Approval Voting
• Allocated Score (STAR-PR)
• Single Transferable Vote (STV, or the proportional form of Ranked Choice Voting — RCV advocates rarely use the STV label)

STV is the only notable proportional voting method that uses ranked ballots, but there are many other proportional voting methods that use Approval-style ballots or scoring ballots.

To round out level one, read this post on why adopting better voting methods is valuable.

Level 2: Analyzing and comparing voting methods

First, strategic voting: how voters can fill in their ballots to get the best results possible in their eyes, possibly by misrepresenting their preferences. Learn about:

1. Strategic voting under Approval Voting
2. Strategic voting under STAR Voting
3. The social benefits of strategic voting
4. Strategic straightforwardness
5. When strategic voting destroys a voting method
6. Three categories of strategic voting

4 through 6 are somewhat optional, but you should have at least a basic understanding of strategic voting. If you don’t understand how strategic voting works under a voting method, you don’t understand that voting method.

To get an intuition for how different voting methods perform in some interesting scenarios, read these articles about the center squeeze and the chicken dilemma.

A good way to assess how voting methods compare at electing winners who reflect the preferences of the electorate is with computer simulations. Start with this video on animated Yee Diagrams, then read about Voter Satisfaction Efficiency (VSE) for a more realistic and more quantitative model. (There is a more recent version of VSE, but the old version is currently more accessible so I suggest just reading that.)

Simulations can also be used to assess how voting method compare at incentivizing candidates. Read about Candidate Incentive Distributions.

Many people evaluate voting methods largely based on whether they satisfy certain mathematical criteria. I consider these pass/fail criteria to be virtually irrelevant, but it’s good to have basic familiarity with the most notable ones. Read more on pass/fail criteria and why we shouldn’t focus on them.

Finally, read these comparisons of different voting methods by the Equal Vote Coalition, FairVote, and the Center for Election Science. (The latter is horribly wrong about Condorcet methods, so read Equal RCV: The Political Case for Condorcet as well.) And read about how the 2023 Chicago mayoral election could have gone differently under different voting methods.

Level 3: More perspectives

Become familiar with the empirical research on the effects of RCV and other voting methods for which we have data.

1. Read New America’s report on RCV.
2. If diversity, racial justice, or gender equality is of interest to you, read this series on voting methods and diverse representation.
3. Read this article on RCV and Australian third parties, then read the follow-up for the 2022 election.
4. Neither Approval nor STAR has been used enough to yield a respectable amount of data, but you can read some case studies. Here are write-ups of the 2022 Fargo election (using Approval Voting) from the Center for Election Science and from FairVote. For STAR Voting, you can read about the Independent Party of Oregon’s primary for US President and Secretary of State.

Read about the importance of political parties (and maybe my response).

Read about the most basic impossibility results: Arrow’s theorem and the Gibbard-Satterthwaite theorem.

Learn about primary reform. Read Lee Drutman’s report and this post on Final Five.

You should also read about more voting methods:

• Borda Count
• Other Condorcet methods: Minimax, Smith//IRV, Smith//Score, Ranked Pairs, and Schulze (don’t worry if you fail to fully understand the last two).
• Various forms of non-proportional multi-winner block voting: Block Plurality, Block STAR Voting, and Preferential Block Voting (i.e. Block IRV). There is also Block Approval Voting, which is just like Block Plurality but without a limit on how many candidates you can vote for, and is used in Fargo. Basically nobody in the voting methods community thinks these are optimal (except maybe for primaries) since they’re non-proportional, but Block Plurality and Preferential Block Voting both get a lot of use.
• Semi-proportional voting methods: Cumulative Voting and Single Nontransferable Vote (SNTV). These voting methods can yield proportional representation but are reliant upon good voter strategy to do so; they’re worse than truly proportional voting methods but easier to implement and explain.
• Mixed Member Proportional (MMP)
• Other proportional forms of Approval Voting: Proportional Approval Voting and the Method of Equal Shares
• Other proportional forms of Score Voting: Sequentially Spent Score (SSS — note the sorted surplus handling variant), Score Cascading Vote, Sequential Monroe, Reweighted Range Voting, and Threshold Equal Approval (TEA). And maybe read the algorithm for Allocated Score again. Note that STAR-style runoffs can be added to any of these voting methods, either in all rounds or in the final round only.
• PLACE Voting
• Cascading Vote and Delegative Transfer Proportional methods

Read this report on redistricting reform.

Read stuff that I disagree with. My own opinion is that IRV is an improvement over Plurality but is somewhat worse than Approval Voting and substantially worse than STAR Voting and Condorcet, and my reading suggestions reflect this opinion. But it’s still worth considering the perspective of RCV advocates; maybe they’ll convince you that I’m wrong, and even if you agree with me it’s valuable to understand their arguments.

• FairVote’s comparison of IRV and Approval Voting
• Lee Drutman’s criticisms of Approval Voting (rebuttal)
• FairVote’s criticism of STAR Voting (rebuttal)
• FairVote’s argument for why IRV winners are better than Condorcet winners (rebuttal)

Want to read more arguments that I think are terrible? Check out the Center for Range Voting for angry ill-reasoned claims about IRV. This is very optional. (They also have some relatively good content, but you can generally get the good stuff from better sources instead.)

Read more about what we can accomplish by switching voting methods and what we should consider when choosing which voting method(s) to advocate for:

• The benefits of proportional representation
• The advantages of adopting less-used voting methods
• Estimating how much good we can do by switching voting methods and how cost-effective it is to advocate for that

(I wrote all of these linked articles and I’d prefer to link to stuff by other people as well, but I can’t think of other articles in this vein off the top of my head — excluding an exceptionally terrible one by the Center for Range Voting, at least.)

Further Reading

Places to find academic papers:

• Jack Santucci’s RCV library
• Library created by STAR supporters

Recommended blogs:

• Jameson Quinn’s
• Jack Santucci’s
• BTernaryTau’s
• Fruits and Votes — covers elections worldwide with a focus on the role of voting methods
• DemocracySOS (FairVote’s blog — I find the content repetitive, but I follow it to see what the RCV camp is thinking.)
• Thomas McIntee’s
• And, of course, this one

Other pro-RCV organizations:

• RCV Resource Center
• Sightline
• Rank the Vote

(There are also numerous state and local organizations that I won’t link to.)

Proportional voting methods that use Approval ballots and some pass/fail criteria that attempt to capture what it means for a voting method to be proportional in the context of an Approval ballot.

BTernaryTau’s list of voting methods simulations

This sequence on Maximal Lottery-Lotteries has conceptually interesting (not probably not practically relevant) content.

The MGGG Redistricting Lab studies redistricting and has some good comparisons between proportional representation and single-winner districts.

PhD thesis on the strategic manipulability of different voting methods

If you know any other resources that deserve to be linked here, post them in the comments. I do not intend to increase the length of levels 1 and 2 much (though I may replace some of the existing content with better, similar content if it gets pointed out to me). I do intend to expand level 3, especially the section with articles I disagree with. If you’re from FairVote and want to see something added/replaced there, let me know. I intend to greatly expand the “further reading” section over time, especially with more academic papers and links to other resources.