Commentary & Analysis Voting Methods

An Assessment Of Six Single-Winner Voting Methods


There are lots of single-winner voting methods out there. Yet, we’ve focused on advocating for approval voting at The Center for Election Science (CES). So why is that?

As a starting point, it’s important to think about what makes a voting method good. You’ll see the factors from that article applied in this essay. The voting methods selected for inclusion are ones that have activity within the reform space or have been featured in academia.

Here are the six voting methods we’ll be assessing:

  • Plurality Voting (Choose one candidate, the candidate with the most votes wins)
  • Condorcet Methods (Rank candidates, the candidate beating everyone head-to-head, inferred through these rankings, wins—if that candidate exists)
  • Ranked-Choice Voting (Rank candidates, use rankings to simulate sequential runoffs across rounds until the winner has the majority of the remaining 1st-choice rankings)
  • Range Voting (Score candidates, highest scored candidate wins)
  • Novel Cardinal Methods, with STAR focus (Score candidates, a top-two runoff is simulated through comparing these candidates’ paired scores to determine the winner)
  • Approval Voting (Choose all approved candidates, the candidate with the most votes wins)

Methods for Assessment

These factors were chosen because they were seen as identifying the basic properties we want to see in voting methods, both in them doing their fundamental job and their ability to be utilized at scale.

While there is an inherent level of subjectivity to this assessment, there was an objective basis in data for each of these factors. This is explained in the overview of each factor. Each method was scored for each factor on a scale from 0 to 10. To maximize the sensitivity of our assessment, the scores are anchored with the worst and best method within each category getting a 0 and 10, respectively. This means that each method is assessed relative to the other options.

Here are the six assessment factors we’ll be applying:

1. Simplicity

This includes how easy it is for the voter to fill out the ballot, in terms of both mental effort and risk of spoiling the ballot so that it won’t be counted. Simplicity is important because it increases the transparency and trust of the voting method. This can be especially important during times of government mistrust and even mistrust of the election process. That mistrust from lack of simplicity can also trigger repeal efforts.

Simplicity was broken down into two parts: (1) voter ballot completion and (2) understanding the calculation. Depending on the expression element used by the voting method, working memory demands on the voter can increase drastically as the number of candidates increases—particularly with ranking methods. This applies to a much lesser degree with scoring methods and far less so with approval-style ballots. You can demonstrate this difference in effort for yourself. Just imagine filling out different ballot types for a “best movie” contest with movies you’ve seen before. You can consider different numbers of movies on the ballot as well.

For the calculation complexity, there are multiple ways to measure this, which are factored into each simplicity score:

  • The ease and fidelity of being able to explain a voting method and having it explained back to you.
  • How long it takes to explain all the steps of a process.
  • How long it takes to fill out a ballot.
  • How many lines of code it would take to program a process.
  • How long it takes to do the calculation correctly by hand with minimal mistakes.

2. Ease of Administration

The ease of administration component assesses how well a voting method fares with key elements of administration. Ease of administration is important because it tells us how easy it is to implement and carry out a method along with all its logistics. Complex administration can cause a voting method to take longer to be implemented, and it can cause issues with other core components of an election.

Ease of administration looks at:

  • whether special software is needed,
  • how much space the ballot design requires,
  • risk-limiting auditability,
  • and whether the method requires all the ballot data to be centralized to count (precinct summability).

3. Elects a Good Winner

Our starting premise for this factor is that a good winner is one that maximizes happiness among the voters. If a voting method cannot elect a good winner from a field, then it has failed its most basic job. Electing bad winners means worse spending policies, worse regulation and laws, and worse leadership.

Computer Simulations

A winner may vary depending on the use and impact of tactical voting. One component of winner selection was measured by considering two computer simulations done independently of another.

These simulations create imaginary distributions of voters according to perceived reasonable parameters with agents of the model behaving under certain sets of rules. Voter happiness is then measured with each outcome. They can also simulate factors like voter ignorance, tactical voting, and different election scenarios.

The first was done by mathematician Warren D. Smith in 2000 and the second was done by then-PhD-candidate (since graduated) Jameson Quinn. Figures for both approaches shown in order below place electorate happiness on the x-axis.

Comparing Single-Winner Voting Methods Chart
Warren D. Smith’s Bayesian Regret simulation
Voter Satisfaction Chart
Jameson Quinn’s voter satisfaction efficiency (VSE) simulation

(Note that while both simulations were performed by former CES board members, they were done independently of CES and not by CES.)

Simulations have their pros and cons. On the positive end, they can draw from countless simulated elections, more than could be drawn from practically. The simulations also allow direct comparisons between methods. These models are helpful, but they’re only as helpful as the assumptions within the model. That’s one reason why it’s wise to look at different models done independently.

Polling Data

This article also used polling studies that compare against control measures to assess winner selection accuracy. These include polls of the 2016 US Presidential elections and the 2020 US Democratic Primary (one earlier and one later in the election). Though control measures weren’t taken, there’s a lot of data to be gleaned from studies that compared voting methods in the 2007 (1) (2) and 2012 French Presidential elections. Another study—which didn’t compare against any other voting methods or control measures—also looked at the 2020 Democratic Primary, using only ranked-choice voting.

Real-World Election Data

One may ask, “Why not use more actual election data with alternative voting methods?” The answer is we would, but data from actual elections alone often do not provide the information necessary to assess outcomes. Additional control measures are needed to see whether the result was actually desirable and if not, how far off the outcome was. We may sometimes, however, make inferential assessments with ranking data or with elections that had head-to-head polling comparisons done alongside the election.

Another challenge here with gathering actual election data is that sometimes election scenarios are just not interesting. Some factors in the real world may disincentivize candidates to run, and thereby create simpler elections—factors like restrictive ballot access or marginalization stemming from the voting method. This can mean elections don’t have enough candidates competing at once or that the elections are not that close. This can overestimate a voting method’s merit in the real world by giving it “easy” election problems, particularly when an alternate voting method gives the same winner as the choose-one method would.

Another reason we can’t solely rely on real-world elections is that not every voting method has had the opportunity to see the light of government elections. And even for voting methods that have seen government elections, those uses don’t provide the opportunity for those same voters to vote under other methods simultaneously, nor do they typically provide a control measure. Without this extra measurement step—which can be done alongside actual elections—it’s impossible to make a direct comparison between the methods’ winner selection.

4. Represents Candidates’ Support Accurately

This factor looks at whether the overall candidate support aligns with voters’ true opinions. That alignment is not always the case as a voting method may not capture the information needed to measure candidate support, or the voting method may not use the data intelligently.

This accuracy is important so that candidates with new ideas are incentivized to run without being unfairly marginalized. Properly capturing candidates’ support means good ideas are more likely to be fairly heard. Further, even if a candidate loses, if their ideas have traction, those ideas could be co-opted by the winner. Candidates can also use that traction to build up their campaign or party for future elections.

This analysis of candidate support accuracy looks at the discrepancy among all candidates between each voting method’s measure compared to a control measure. A control measure would, for example, ask respondents their honest desire for a candidate to be elected regardless of viability. The only data that allows this comparison are the previously mentioned 2016 Presidential election study and the 2020 Democratic Primary polling. The 2016 excerpt contrasting normalized results from different voting methods and the honest assessment measure is shown below. The short and long columns refer to a four-person and nine-person candidate list, respectively.

Voting Methods Comparison in 2016 Election

5. Tractability

Tractability looks at whether the method is likely to catch on or face obstacles spreading to government elections. This factor is important because even if a voting method performs well, that is of little value if it’s unlikely to go anywhere or takes greater effort relative to other options.

Tractability is evaluated here by looking at the academic underpinning, ballot initiative track record, and feasibility. These factors can influence how seriously the public is likely to take a voting method, the method’s base rate of success, and a method’s practicality for implementation. Importantly, tractability is not the same as momentum—which can be influenced merely by money and a longer timeline. The scope within tractability is limited to government use as most voting methods have seen organizational and intra-party use, including repeals.

6. Overall Assessment

The overall assessment looks at the big picture. Here, we decide whether it makes sense to go forward with this method using a combination of all the previous factors combined. A method performing badly on any one factor counts substantially against it within the overall assessment. It is not merely an average but rather a consideration of the totality of all the factors. This overall assessment is necessary because, at the end of the day, we have to decide how to allocate limited resources.

Voting Methods

Now we’ll assess the voting methods using the factors from the previous section.

1. Plurality Voting

Plurality Voting Ballot


Plurality voting is the most common of the voting methods and is used almost uniformly throughout our elections. It’s also called first-past-the-post. We tend to call it the choose-one voting method because the name is more descriptive and sounds less technical. This method is considered so bad among reformers and academics that it’s the go-to target for those focused on voting method reform.

Simplicity (10)

The choose-one voting method is simple. Pick one option and the option with the most votes wins. This makes it easy for the voter to fill out the ballot. The ballot directions are also straightforward.

The only way to spoil a ballot is to choose too many candidates, which does happen in a fraction of cases. Figuring out the calculation is easy. It’s just adding the vote totals or taking each candidate’s percentage of total votes.

Administration (10)

The administration for this method is easy, too. All voting machines are already set up for this and this method is easy to count by hand. The ballot design is—or should be—easy (we’ve seen unforced errors on behalf of administrators not due to the voting method itself). There’s only one markable bubble to fill out per candidate, which cuts down on ballot space.

The choose-one method is also precinct summable, which makes logistics for counting easier as you don’t have to transport the ballots to one place. Risk-limiting auditing of ballot data is also straightforward due to the simple type of data.

Winner Selection (0)

The choose-one voting method is abysmal at selecting a winner. It’s the worst of the voting methods in this regard. This is because of its tendency to provoke vote-splitting among similar candidates, the incentive it creates to vote against one’s favorite, and the complete lack of information that the voter is permitted to provide.

The choose-one method can collapse even with the introduction of a weak candidate who happens to overlap with one of the frontrunner candidates. Consider any election when a third-party candidate doesn’t win yet changes the outcome. We can only be really confident that the winner is good when that candidate has more than 50% of the vote—an absolute majority. Of course, a candidate receiving an absolute majority is far from guaranteed (also note that no method can guarantee a majority, even with a simulated or direct runoff).

Because the choose-one method is so limited, it also lacks the ability to consistently choose good winners even with voters being honest. Even in this best-case scenario, this method performs terribly at picking winners, risking collapse even with minimal candidate competition.

Candidate Support Accuracy (0)

The choose-one method does not do well in the accuracy department. This is most likely due to the incentive for voters to vote against their interests and the fact that so little information is captured on the ballot. The way other methods perform that are better on these properties gives evidence for this explanation. The method’s only saving grace is that it at least uses all the—albeit little—information that it gathers. The reflection of candidates’ support under the choose-one voting method often shows little resemblance to their actual support.

Tractability (10)

The choose-one voting method’s only safety net for tractability is the status-quo bias resulting from it being so ubiquitous. It takes friction just to move away from the method. It may be, however, that over a (very) long timeline that virtually no one uses this method. It’s just a matter of when reformers are able to replace it. But for the time being, it is the system to replace.

Overall (0)

A voting method is good for nothing if it can’t select a good winner or properly gauge candidates’ support. This choose-one voting method earns a zero score based on these factors alone.

Being simple and easy to administer are its only redeeming qualities. That so many reformers appropriately rail against it places a serious question of whether it should be as common as it is.

2. Condorcet Methods

Condorcet Matrix


Condorcet methods have been around awhile. The method was developed by Marquis de Condorcet, a French academic from the 1700s. Technically, a Condorcet voting method is a class of ranking methods that will always select the candidate who can beat everyone else head-to-head—a Condorcet winner.

All the different Condorcet methods select this winner when it’s available. What differentiates Condorcet methods is how they select a winner when there is no candidate who can beat all others head-to-head (an event called a cycle or Condorcet paradox).

Simplicity (0)

Condorcet voting has the voter rank their choices from most to least favorite. That information is then used to simulate pairwise comparisons between every possible candidate pairing. This is often displayed in a Condorcet matrix (shown above). There are multiple Condorcet methods such as Schulze, Ranked Pairs, Minimax, Nanson, Kemeny–Young, Dodgson, and Copeland.

Copeland is probably among the easiest as it looks at who has the most pairwise victories—called a Copeland score. Still, this can easily result in ties when there isn’t a Condorcet winner. Another method, Dodgson, eliminates candidates based on rankings which are transformed as points similar to another voting method, Borda Count. This repeats until a Condorcet winner is present. Other Condorcet methods compare margins of victory to determine the winner.

Any ranking method—Condorcet methods included—can be more complicated with longer candidate lists. A voter can spoil a ballot if they ranked the same candidate repeatedly or if the voter ranked multiple candidates the same, though some Condorcet methods allow for different candidates to be ranked the same.

From the brief calculation summaries, one can imagine how easily voters could get confused, particularly with more complicated Condorcet methods.

Administration (0)

Administration for a Condorcet method is more challenging. It would require special software to calculate and is not easily counted by hand. In some cases, hand counts would be extremely difficult and not at all practical.

The ballot design will get more complicated as the number of candidates increases, as is true for any ranking method. It’s possible to simplify the ballot by truncating the choices, but this can cause valuable data to be lost. With multiple marks available next to each candidate, this can take up substantially more ballot space.

Condorcet methods are not easily precinct summable and in some cases must just simply be counted in a central location. Special approaches would also need to be developed for risk-limiting auditing.

Winner Selection (6)

Because Condorcet methods will always pick a Condorcet winner when there is one, Condorcet methods tend to pick good winners in simpler and even moderately complex elections. Condorcet winners also tend to be—but are not always—the candidate that maximizes happiness for voters. To prove this to yourself, imagine two voters with a slight preference in the same direction and a third voter with a heavy preference in the opposite direction. The majority prefers one outcome whereas the other outcome maximizes utility. Part of why the Condorcet method performs well may be due to its use of all the ballot data and the information it provides.

Still, there are the usual limitations with any ranking data as there is no clear satisfaction delineation between rankings. Where voters’ satisfaction begins and ends from ranking to ranking is invisible. This is true for the degree of satisfaction as well. Because of this, Condorcet voting method winners are sometimes not the same candidates that maximize voter happiness.

Performance can suffer from tactical voting, but this can be tough to pull off for the average voter because of the complexity. Tactical voting could still take place, however, if voters turn to a sophisticated source for advice.

Candidate Support Accuracy (7)

Candidate support accuracy is likely to be reasonable because of the amount of data captured. Candidate support will have to be displayed as a Condorcet matrix, which takes more effort to read and understand. That said, the pairwise comparison information is rich, which is helpful.

Copeland scores (number of pairwise wins) may help to demonstrate order within a Condorcet matrix. The inherent issues with using ranking data to capture candidates’ support still remain, however.

Tractability (0)

Other than being used in some groups—which tend to be more sophisticated users—complexity and administrative hurdles would halt its use for public elections. This has likely been the largest barrier keeping Condorcet methods from being used more widely. Condorcet methods are commonly discussed in the academic literature and have a long history there, but it’s obscure in the public eye. There is no movement for this method in government elections, and there is no clear path forward.

Overall (2)

Condorcet methods do a reasonable job selecting winners and highlighting candidate support. But there is an exceptionally high complexity cost to be paid, and administration will be a challenge. These technical barriers likely play as much a role as any for its lack of use outside of sophisticated groups despite hundreds of years of the world being aware of the method.

3. Ranked Choice Voting (RCV)

Ranked Choice Voting Ballot
[Image source:]


Ranked-choice voting (RCV) is likely the most well-known of the alternative voting methods. It has a longer history, being referenced (unfavorably) by Condorcet in the 1700s and also by Nanson in the 1800s. A professor in the late 1800s also noticed that a multi-winner method, single transferable vote, could be applied to single-winner elections. Following this, the method saw government use in Australia and quasi-use in other countries. It’s since seen a surge in the United States with a particular bump in popularity over recent decades.

RCV is known by many names depending on its moment in time and location. These include the Hare method, alternative vote, Ware method, and instant runoff voting. Its more recent use of the name RCV is the result of a rebranding to make it more palatable to voters during US campaigns. This “ranked-choice voting” name has drawn confusion as there are many ranking methods besides RCV that operate very differently. The name RCV is used here because at this point it’s better recognized by this name in the US.

This assessment does not refer to single transferable vote, a proportional, multi-winner voting method that uses similar calculation features. These are not the same voting method, and this is an article on single-winner methods.

Simplicity (2)

RCV requires voters to rank their preferences. Voters cannot rank multiple candidates the same, and it can be more mentally demanding to rank a longer candidate list. While voters may choose not to rank all the candidates, this can produce an inferior result as it captures less data.

The calculation of RCV uses the ranking data to simulate sequential runoffs. First, one looks to see if any candidate has more than 50% of the first-choice preferences. If yes, then this is the winner. If not, then eliminate the candidate with the fewest first-choice preferences and transfer those votes to the next-choice preference of those ballots, and now treat the next-choice preference as a first-choice preference. Again, see if any candidate has more than 50% of the first-choice preferences of the remaining ballots (some ballots may be exhausted and no longer be in the counting). If a candidate has greater than 50%, that candidate wins. If not, repeat this process until a candidate passes the 50% threshold of the remaining ballots.

Understanding the calculation above can be complicated. It takes a while to explain precisely, and it can be difficult to follow in elections with many candidates. In practice, an election with many candidates can take numerous rounds.

Administration (3)

RCV requires special—and often expensive—software to calculate because of its complexity. In the future, this may become less of an issue as more voting machines get upgraded, but right now it is costly for places that have older machines. This has caused significant delays in implementation for some cities, though it’s possible some cities have purposefully dragged their feet. Sante Fe, New Mexico is one such example.

RCV elections can technically be counted by hand, but it becomes quite complicated with many candidates and drastically increases the time. Even using voting machines, there have often been significant delays of several days to over a week before results were available.

Contributing to the logistical challenges is that RCV requires all the ballot data to be centralized and complete before counting can even begin. This can cause delays starting the count.

RCV can take up significant ballot space, particularly if voters are permitted to rank all the candidates. Some cities using RCV limit voters’ rankings as a practical matter. Even with a truncated ranking that has voters provide less information—say three or five rankings—this still occupies a significant amount of ballot space.

Procedures have been developed to allow for risk-limiting audits of RCV elections.  While it takes more work than with approval or plurality voting, it’s still doable.

Winner Selection (4.5)

RCV is able to mitigate some of the vote splitting that can occur when multiple, similar candidates run. Unfortunately, however, it can still eliminate good candidates. This is because first-choice votes can split causing strong candidates—including Condorcet winners—with fewer first-choice rankings to get eliminated. The 2009 Burlington, Vermont election saw exactly this scenario, and RCV chose the wrong winner.

RCV can also behave oddly when there are many candidates within a close election—as it did in the Burlington election. This includes candidates sometimes being hurt by receiving better rankings and helped by receiving lower rankings—called nonmonotonicity. RCV can also sometimes cause individual voters a worse outcome when they rank their favorite candidate as first. RCV’s complexity can hide these downfalls from being more transparent, so we’ve written about them in more depth.

While RCV does let voters provide significant information, because the algorithm looks at only a section of the rankings at any one point, it can disregard useful data. This, in tandem with the vote-splitting of first-choice preferences causing candidates to be eliminated early, is what compromises the method’s ability to select strong winners in tough elections. That said, the method is able to easily handle simpler elections such as would-be “spoiler” candidates who generate little support overall.

One of Maine’s 2018 congressional elections provided such an example. Independent candidate Tiffany Bond had fewer than 6% of the votes and was eliminated under RCV. She had most of her votes transferred to Democrat Jared Golden. Without this transfer under RCV, Republican incumbent Bruce Poliquin would have won merely due to Bond’s presence.

The tactics under RCV can be complicated for the average voter. While sometimes voting honestly can cause the electorate a worse outcome, the electorate as a whole benefits—on average—when voters are more honest. Like complicated Condorcet methods, one way more challenging tactics can be leveraged may be by having a sophisticated source provide tactical voting advice. This may be the voter’s preferred political party, for instance.

Like all other ranking methods, the failure of RCV data to take into account degrees or even thresholds of satisfaction creates an issue. This limitation of ranking data interferes with the method’s ability to determine better winners.

Candidate Support Accuracy (2)

RCV’s dismissal of ballot data unfortunately means that it fails to capture much of candidates’ support. When a candidate is eliminated, it no longer has an opportunity to capture support from transferred ballots of later-eliminated candidates. And voters who prioritize candidates who are not eliminated do not have the voters’ next-choice preferences revealed. That’s additional support that candidates never receive. The inherent nature of ranking methods also poses limits on the accuracy of candidates’ support.

Consequently, RCV’s support for alternative candidates beyond the winner often appears little better than under the standard choose-one method. This was shown during the US Democratic primaries in 2020 both earlier and later in the election. This was also shown with data collected for the 2016 US presidential election. This can distort not only the amount of support candidates have overall, but it can also distort candidates’ order of support relative to other candidates.

Tractability (7)

Despite being quite complicated and suffering in performance, RCV has some qualities going for it that help it with current tractability. Having been around and in use for government elections for over a hundred years and being part of the academic literature certainly helps.

RCV has been implemented across Australia and in roughly two dozen cities and a state in the US. The city of London, Ontario in Canada used RCV for the first time in 2018.

This familiarity—despite the complexity and performance drawbacks—has spurred advocacy funding for organizations to push it forward. Over recent decades, these organizations in the US have seen tens of millions of dollars in funding, which have undoubtedly helped their traction.

One caveat here is that supporters who have gotten behind this bandwagon have done so largely without knowledge of alternatives. There is still a lot of space for reform—in the US and elsewhere— as most places still use the choose-one method. But RCV may not always continue to be the go-to alternative as other alternatives show viability. That landscape may change citizens’ preferences as they realize there is more than one way to move away from the current choose-one voting method.

Another long-term tractability issue is repeal risk, which has already happened in multiple cities including Burlington, VT; Ann Arbor, MI; Cary, NC; Aspen, CO; Pierce County, WA; and Sunnyvale, CA. Often the rhetoric for RCV repeal focuses on either anomalies or method complexity. That said, some countries like Australia have kept RCV around for quite some time.

RCV has also seen implementation failures. Aside from cases where it has failed to gather enough signatures to get on the ballot, it has had voters overwhelmingly oppose passing each failed RCV initiative. Over 60% of voters opposed an RCV ballot measure in Alaska’s statewide ballot in 2002; Glendale, Arizona in 2008; Fort Collins, Colorado in 2011; Duluth, Minnesota in 2015; and in a country-wide loss in the UK.

This means that, within the US, RCV has either been repealed or failed to pass in a third of total cases with successful implementations in the other two-thirds. Another factor to consider with RCV’s tractability is that it’s had well over a hundred years to expand, tens of millions of US dollars spent over the last decade, and it’s only just now gotten to this point.

Overall (3.5)

Among alternative voting methods, RCV has familiarity going for it. And it does do better than the status quo by performing some mitigation with vote-splitting. But besting the worst voting method isn’t something to get too excited over when virtually any other alternative voting method can do the same. Even while performing marginally better than the status quo, it still fails to capture meaningful support from the remaining candidates. And this mild-to-moderate increase in performance comes at a high complexity cost.

There’s also the fiscal cost of new voting machines, which has played a deciding role in some cities saying no to RCV from the beginning. At CES, we saw this play out first hand in Fargo and St. Louis after they refused to consider it due to this cost. That may not be the case, however, for cities or states with robust budgets or that already have taken on the cost of modern voting machines.

Overall, RCV offers a nontrivial improvement in winner selection, even as it mostly fails to capture candidates’ general support. But there is a high price tag to pay for this improvement—in both complexity and dollars. That’s a big factor as other alternatives best RCV’s performance without the complexity or logistical challenges.

4. Range Voting

Range Voting Ballot


Range voting is a cardinal/scoring/grading method and is one of the more highly expressive voting methods. This method has also taken its place in the literature in various forms. It was heavily advocated for by mathematician Warren D. Smith through The Center for Range Voting, which he co-founded alongside Jan Kok, an electrical and software engineer. The method is also sometimes called score voting but often referred to as range voting in academic literature.

Range voting is commonly seen on the internet and versions of it are used in places like IMDB. You’re essentially using it to see the “best” product when you sort by rating on Amazon. Probably the most commonly seen use of range voting is with the Olympics.

Range voting’s governmental use goes back to Renaissance Venice and a crude version used in Ancient Sparta. It’s failed to show use more recently, however, and has no organization effectively championing its use for government elections.

Simplicity (7)

Range voting has the voter assess each candidate on a scale, say 0 to 5, inclusive, with higher numbers meaning better and lower numbers meaning worse. The scale itself could range by quite a lot from say three intervals—0 to 2—up to 101 intervals, which would be 0 to 100. (Having only two intervals would be the equivalent of approval voting—0 to 1.) These scores are then totaled. Often, for simplicity, candidates that aren’t scored on a voter’s ballot are given a zero score.

Scoring on a scale is a task that varies in complexity relative to other expression styles depending on the number of candidates on the ballot. For instance, ranking three candidates may be slightly easier than scoring three candidates. But scoring 15 candidates is much easier than ranking 15 candidates. We would expect voters to be more likely to provide the scores and thus more information for longer candidate lists—though perhaps not scoring every candidate. 

One mental shortcut to scoring for the voter may be to identify the most and least favorite candidates and give them the most extreme scores. Then place the remainder candidates either at those same extreme ends or find appropriate scores in between. Voters could also choose to evaluate candidates independent of one another.

The calculation for range voting is just adding all the scores. Averaging scores would give an equivalent result. It’s also difficult to spoil a range voting ballot since voters can give multiple candidates the same score. It is possible to spoil a ballot by giving multiple scores per candidate.

Some voters may be tempted to just give the middle score when unsure. To address less useful scores, the ballot should provide an even number of options so there is no middle option. It’s also helpful to have the range of scores include zero so that scoring isn’t confused with ranking.

Administration (6)

Range voting can be counted easily enough by hand, though it takes longer than plurality voting or approval voting. Machines should be able to do this quite easily, but it may not be as shovel-ready as other approaches like approval voting. That’s because no other existing voting method used in government resembles range voting. While no machines are explicitly designed for range voting, the simplicity of the method may make its calculation easier for machines than other voting methods.

The ballot design is straightforward. But because there are multiple selections next to each candidate, it will take up more space relative to other methods. If a 0-3 scale is used, then that’s four intervals next to each candidate. That can take up some ballot space, though the number of selection options per candidate never grows even as the candidate list grows—unlike ranking methods, which can quickly take up increasingly more space.

Range vote is easily precinct summable, so tabulation is logistically easy with ballot data in separate locations. Because of the simple type of tallying involved in range voting, risk-limiting auditing should be straightforward.

Winner Selection (10)

Range voting is excellent at selecting the winner that maximizes happiness for the most number of voters. We see it consistently scoring well in the simulations as well as with polling data comparing different voting methods referenced earlier.

Range voting is both highly expressive and uses all the ballot data in a sensible way, which contributes to why it does such a good job selecting winners. Range voting is quite resilient to vote-splitting and voters can always give maximum support to their favorite candidates.

Like all methods, range voting does have its anomalies. One such anomaly is the grading paradox, which is when the range voting winner does not pick the Condorcet winner. This is because the winner that maximizes happiness for the most people is not necessarily the winner who beats everyone head-to-head.

Imagine one voter with a heavy preference for a slightly less popular option while many others only have a small preference for a slightly more popular option and you can get the idea of how that could be. If we’re more concerned with maximizing happiness, however, then the paradox creates less of an issue.

Like any voting method, there is the potential for tactical voting with range voting. There, tactical voting would be to only use extreme scores. But we can again refer to the modeling shown earlier. Even under heavy tactical voting, range voting performs well. And in practice, there are cases when it can make sense to use in-between scores on candidates. Plus, it’s reasonable to expect some mix of tactical and honest voting in practice.

While there may be some tactical incentive to use more extreme scores in particular circumstances, polling data from a larger sample did not show tactical voting as being as prevalent as one might expect.

Candidate Support Accuracy (10)

Range voting is also excellent at measuring candidates’ support. Again, this is due to the combination of both being highly expressive and using all the information voters provide. This type of data shows the order of preferences as well as degree.

One way we see the accuracy of candidates’ support is through polling that takes an honest control measure of voters’ attitudes towards candidates. In one study conducted by The Center for Election Science and The Paris School of Economics, we saw much more use of the scale than one would expect, so it compared quite well with control measures.

Tractability (5)

Although this method performs very well, the slightly higher complexity could present an issue. It does mean a different ballot design and could face some obstacles with existing voting machine infrastructure. Still, these obstacles with voting machines are shorter hurdles than other methods face or have faced.

People are also generally familiar with settings that use scoring elements like Amazon and Yelp reviews. And most people have seen events in the Olympics like gymnastics and diving where range voting is used by judges. This may in some ways compensate for its lack of modern use in government or more widespread use in major organizations.

There are no active campaigns for range voting or even recent attempts. Nor is there any current financing for future campaigns. Range voting may be most tractable in places with modern voting machines and voters who are not bothered by the novelty or small jump in complexity. Like any new voting method, it will surely have to establish a proof of concept within a city and secure an organized backing before it can move forward.

Given the track record of advocacy campaigns for the more complex and novel cardinal method of STAR voting, range voting’s tractability is expected to be at least marginally better than that.

Overall (7)

While excellent in both winner selection and gauging candidates’ support, range voting has real barriers. The lack of use in modern elections, potential obstacles with voting machines, and different ballot design all present barriers. Lack of advocacy also hurts its cause.

It’s worth noting that range voting does provide a nice feel for voters because it’s so highly expressive, and this could be persuasive in getting it adopted in its first locations. In practice, however, it’s challenging to lead with range voting when a simpler cardinal method—approval voting—is also an option, and it performs quite nearly as well. It may be challenging for this approach to gain traction until voters are used to accepting other new voting methods that are easier to implement.

In the meantime, range voting is an excellent voting method option for organizations to help it gain popularity as it is a relatively simple method that performs very well overall.

5. Novel Cardinal Methods (STAR Voting Focus)

STAR Voting Ballot


Many novel cardinal methods have been developed in recent years. These methods tend to use scoring data while also taking that data to provide pairwise comparisons. Sometimes they also do complex rounds and eliminations. These methods tend to perform at least as well as range or approval voting from the start—which is quite good. But they then add additional operations that transform scores to pairwise comparisons to increase their performance an inch more.

Examples of these methods—and there are many—include majority choice approval, majority approval voting, 3-2-1 voting, and STAR voting. It’s quite straightforward to create a new method as it just involves identifying the expression element and how you want to calculate that information. Many of the novel approaches mix and match scoring (the hallmark of cardinal methods) and implied ranking elements.

As an example, imagine a hybrid of Condorcet and range voting, which we’ll call Condorcet range voting. Voters score each candidate. Those scores are translated to pairwise comparisons to identify the Condorcet winner. If there is no Condorcet winner among these pairwise comparisons, then take the range-voting winner with the highest score. As you see, one can come up with new voting methods all day long taking different elements of scoring and pairwise comparisons, and they will all technically perform well and capture candidates’ support.

This section from here on will focus on STAR voting because it’s received more attention relative to other novel cardinal methods. STAR was developed by tech/transportation entrepreneur Mark Frohnmayer from Portland, Oregon. The method stands for score, then automatic runoff. The stated premise by the creator was to have a voting method where votes were able to equally cancel each other out through an “equally weighted vote”—though virtually every cardinal method already does this.

Simplicity (3.5)

STAR has voters score the candidates. Those scores are then used to determine pairwise comparisons between the top two candidates. The majority preferred between these two is the winner. (Again, recall that no voting method guarantees a majority, and explicit or simulated runoffs do not change this.)

Like range voting, this takes more concentration for the voter to assign each candidate a score. This is also information that voters aren’t used to seeing on other election ballots.

As with range voting, the voter can choose to anchor scores at the extremes and then fill in scores in between with the remaining candidate. Or voters can assess candidates independently.

Like range voting, it’s difficult to spoil a ballot since voters can give multiple candidates the same score. It is possible, however, to spoil a ballot by giving multiple scores per candidate. Many of the other technical issues of range-style ballots are addressed by the same remedies used to address range voting.

This is similar to RCV though not as bad since there are always only two rounds with STAR. Still, the simulated runoff component does add complexity. There is also a transformation of data—from scores to pairwise rankings—that adds another layer. This may be challenging for average voters to understand. And it could be challenging for some average voters to successfully understand the calculation process as written within the ballot directions.

Administration (4)

There is quite some effort in performing a STAR voting hand count, particularly as the number of voters increases. The first portion is equivalent to a range voting count, which takes longer than plurality since you’re taking additional data from each candidate. With STAR, however, you have to look at the entire ballot stack again and focus on the scores from the top two scoring candidates. Now between those candidates, you begin a tally between who scored higher within each ballot. The candidate who is preferred more between the pairwise comparisons of these two candidates is the winner.

In practice, voting machines will be used for elections. This can create obstacles and fiscal impact for cities without modern voting machines. The logistics here create an obstacle as specialized code needs to be written and approved for STAR to be used on even modern voting machines. Like RCV elections, the calculation process could also cause delays with results.

The ballot design—like range voting—is mostly straightforward. Again, however, because there are multiple selections, this will take up extra space depending on the range of the intervals being used. But it does not increase in ballot complexity with longer candidate lists in the same way that ranking methods do.

Although range voting is easily precinct summable, the tabulation and transformation step in STAR voting complicates this. Technically, it is possible—in the same way a Condorcet method calculation is precinct summable if there is a clear Condorcet winner. But this requires keeping a Condorcet matrix tally at each precinct level. In practice, precinct summability may prove challenging.

No risk-limiting auditing system exists for STAR. This may be easier to develop than an RCV risk-limiting audit, however, due to the type of raw data. Still, this remains to be seen.

Winner Selection (10)

STAR is expected to do at least as well as range voting in selecting a good winner, which is quite good.

Part of the rationale for STAR’s development was to address a perceived risk of tactical voting by range voting. But even in the presence of heavy tactical voting with range voting—using only extreme scores and equivalent to approval voting—range voting still performs very well. And we saw that, in practice, many voters who used range voting tended to be rather honest. Using the intermediary grades was supposed to be what made STAR stand out. But if range voting already has voters using these intermediary grades, then STAR’s advantage isn’t materialized.

To the degree that normal range voting voters are more tactical, STAR could make up for that with a tiny improvement. Still, we’re not seeing these extreme range voting tactics in practice, so this creates doubt over any meaningful improvement. And even if tactical voting is present under range voting, the additional complexity added by STAR still appears to add only trivial if any real improvement both according to Quinn’s simulation shown earlier and separate independent analysis.

The lackluster improvement over simpler methods is not especially surprising given the method’s origin. A look at existing research such as the French studies referenced earlier—which existed before STAR was developed—would have also given this insight.

Candidate Support Accuracy (10)

Overall candidate support under STAR voting is likely to be largely indistinguishable from traditional range voting. Range voting, as a base in itself, performs excellently. STAR should perform no worse than this.

Tractability (2)

The commonality of these novel cardinal methods is that none of them have been formally studied in academia, and STAR voting is no exception. Given its lack of use as well, familiarity presents a major issue.

STAR voting’s largest issue is that it quests to move a tiny bit nearer to ideal winner selection at any cost to complexity or practicality—despite easier alternatives being available that perform nearly identically. Even if STAR does find some success, there may be issues with repeal, similar to the obstacles that RCV faced due to its complexity.

STAR has attempted and failed—albeit not by a lot—on one ballot initiative so far in Lane County, WA, which holds the city of Eugene. The measure failed despite not having to fight any organized opposition. County voters were also not oppositional to ballot measures in general. Voters had passed more than 60% of its ballot initiatives over the decade leading up to the STAR initiative. A separate ballot initiative for STAR voting also failed to gather enough valid signatures. STAR likely has an uphill battle given that cities have much simpler or more familiar alternatives.

It may be that STAR eventually finds success in a highly progressive area where practical concerns are less of an issue. Or it may find some limited success within intraparty or intraorganizational elections—a fate similar to novel Condorcet methods. But this raises questions about any hopes it may have for broader application. It’s unlikely to share much of that support from other areas where voters are more wary about testing out such novel alternative voting methods.

Overall (4)

STAR suffers from a lack of familiarity, track record, and academic grounding. While it likely performs excellently at selecting winners—as virtually any cardinal method would—it does so at the cost of practicality. In light of other options such as score and approval voting, there seems to be very little reason to move towards STAR voting. Its place at the moment may just be within organizations that have a high tolerance for complexity. STAR may eventually find a city willing to take on its extra challenges, but the method is far less likely to spread the way other strong voting methods with lower complexity would.

The additional complexity cost with STAR voting has heavily diminishing returns for winner-selection compared to switching to simpler methods that also perform very well. It’s challenging to make a strong case for STAR when easier methods like range voting and approval voting are clear alternatives.

6. Approval Voting

Approval Voting Ballot


Approval voting has had incidental use for electing the Pope and up until 1920 in Greece elections before they moved to proportional representation. But it wasn’t identified more formally and academically until later in the 1970s where it was independently documented by several academics at once. The more outspoken advocate among the academics, Dr. Steven Brams, unsuccessfully attempted to have state legislatures adopt it directly. He was, however, able to persuade organizations to adopt it and push it forward in academic research.

Approval voting is generally considered to be a solid method among voting theorists and is easily the simplest of all the alternative voting methods. But only in recent years has it seen adoption in governmental elections via ballot initiative.

Simplicity (10)

Approval voting has the voter choose as many candidates as they approve of. That is, the voter would be satisfied with any of the candidates they chose. The candidate with the most votes (equivalent to the highest approval percentage) wins.

Because of its simplicity, approval voting is especially functional with long candidate lists. In contrast, scoring systems and especially ranking systems demand a lot more voter concentration with longer candidate lists. It is slightly more involved to assess which candidates to approve compared to the choose-one voting method, but that’s the cost of providing useful information.

Approval voting may also be the only voting method where a voter can’t spoil their ballot—that is, make their ballot uncountable. It’s simply impossible for a voter to choose too few or too many candidates. 

Administration (10)

Any voting machine can run an election using approval voting. No special software is required as all machines already work in elections allowing voters to select multiple candidates. Hand counts are also especially easy and are the quickest to do of any alternative voting method.

Ballot design is especially simple just as long as the directions make it clear to the voter that they can choose more than one candidate. Because there is only one open mark next to each candidate—the same as with a choose-one ballot—an approval voting ballot uses no more space than a usual ballot.

Because approval voting uses such simple data, it’s possible to sum the ballots at the precinct level. Central tabulation is not necessary. This also avoids any delays with counting. The simple tally method also makes risk-limiting audits straightforward. In fact, the only challenge to administration is that it is ever-so-slightly different than the current approach.

Winner Selection (9)

Approval voting does very well at electing strong winners. It does this by addressing vote splitting, always allowing voters to support their honest favorite, and using all the voter data at once. Approval voting tends to elect Condorcet winners when they exist and winners that maximize voter happiness.

As shown by the modeling and polling references earlier, Approval voting typically does better in choosing winners than ranking methods. One reason for this may be that the voter can decide the threshold between approval and non-approval. This threshold is absent in ranking methods. Approval voting’s only rival in winner selection is other cardinal methods, which require the voter to provide more information on each candidate.

One critique of approval voting is that all or nearly all voters will just choose only one candidate. This critique is complicated in that polling data indicates many voters do only choose one candidate. And they can do this in a way that makes sense such as when they only like one candidate and that candidate only has one clear competitor. But it’s vital that voters have the option to choose more than one candidate when they need it. Sometimes voters desperately need to hedge their bets against bad candidates or to support multiple similar candidates and not split their vote.

A minority of voters who choose multiple candidates can still make all the difference, as was shown in one of the earlier referenced French election polls that chose Bayrou as the winner over Sarkozy. This makes sense as you consider the margin of victory in many typical competitive elections.

Candidate Support Accuracy (9)

Approval voting does quite a good job measuring candidate support. This is the result of getting good information to begin with and using all that information. As seen in our 2016 US presidential election study and the 2020 primary studies, approval voting better captured candidates’ support when compared to a control group.

Another reason for this accuracy is that approval voting always allows voters to support their honest favorite candidates without negative consequences. This means that third parties, independents, and newcomers with fresh ideas—often neglected by other voting methods—show their true support with approval voting.

Tractability (8)

Approval voting had been stumbled upon in the past, likely due to its simplicity. Upon its modern discovery, its initial push did not have the advantages of a formal organization advocating for it. But after The Center for Election Science came forward, government use began quickly landing Fargo, ND as the first implementation. This win came immediately after funding was present. While this phase is still early, it appears to be moving rapidly. Its first win was by a 63.5% landslide facing little opposition, and its second campaign in St. Louis is on track as of this writing.

Unlike other alternative methods, approval voting’s simplicity may be one of its biggest assets for tractability. Complexity was one of the big talking points that caused methods like ranked-choice voting to be repealed. But to say approval voting is too complicated would be to claim that voters cannot do simple addition—a claim that even the most dubious of politicians would have trouble making.

One surmountable obstacle approval voting may face is the prevalence of voters who choose only one candidate. While approval voting only requires a fraction of voters to support multiple candidates to function, that fact is often lost by those opposing the method. To inoculate against this argument and guard against erroneous repeal, advocates will need to continue studying case examples to compare approval voting against alternatives as well as control measures.

Simplicity is no doubt a benefit for approval voting’s tractability. Add to that the fact that any voting machine can already use approval voting. The only barriers to implementation are cases when state law requires the use of a choose-one method—which effectively bars any alternative voting method.

Currently, as a matter of practicality, approval voting will likely need ballot initiatives to get it implemented. But this could change as its use catches on. After more exposure, more open-minded legislators may be open to persuasion from lobbying or simply instituting the method themselves. If the method reaches a tipping point, we could see a flash of use due to its incredible ease of implementation.

Overall (10)

Approval voting performs an exceptional balance of both selecting a strong winner and capturing each candidates’ support while at the same time being remarkably simple. That is an especially hard balance to reach, and no other voting comes nearly as close.

The method is seamless to implement and comes at no added costs or complexity. Arguably, the method is simpler than the choose-one method as the voter cannot spoil their ballot, though voters may need to consider each candidate more carefully.

While the method is newer to use for government elections, its first early win suggests it will be a competitive alternative to the status quo. Its main drawback is that it did not have organized support earlier causing it to be late out of the gate relative to other reform efforts. With proper funding, however, approval voting could easily catch up due to its many positive qualities.

In the meantime, approval voting faces its biggest momentum challenge—which is funding. The other leading reform—ranked-choice voting—outspends approval voting more than 10-to-1 in the US with advocacy organizations either explicitly advancing RCV or pushing it as an ancillary part of their mission. The funding discrepancy in combination with the decades-long-head-start that RCV has had to gain the public’s attention are approval voting’s biggest relative barriers.

But funding and awareness are factors that can change—unlike other factors like voting method performance and complexity, which are where approval voting excels.


A voting method is not good merely because it chooses a winner. Any voting method can do that. If choosing winners were our only metric, then our current choose-one voting method would be the best; it has chosen many winners.

Of course, a voting method must choose a good winner. And it must also do a good job capturing all the candidates’ support. This ability to capture candidates’ support is where RCV fails most substantially, aside from its complexity.

A voting method must also be practical. If the method is needlessly complicated and adds only trivial or even negative value for this complexity cost, then it becomes a poor choice. This was the ultimate issue for STAR voting, Condorcet methods, and—to a lesser extent—range voting.

Are these evaluations set in stone? No. As time passes, the landscape may change. More cities may open up to new methods as additional alternative voting methods are adopted. New information may also come into play, helping to adjust or fine-tune these assessments.

This assessment also overlaps with the assessment of other voting theorists. For one, it has a clear loser. One of these methods scored a zero on winner selection, capturing candidates’ support, and its overall assessment. That method is our current choose-one voting method, plurality voting.

Also, like those other voting theorists, we’ve selected a clear winner among our options: approval voting. Approval voting excels at its job in both selecting a winner and capturing candidates’ support. And it does all this in a simple way that makes it immensely practical. It does not get perfect 10’s across the board, but no method can do that. If that were the case, then our quest to choose which alternative voting method to advocate for would have been much easier.

Comparing Voting Methods - Chart

0 = Terrible; 10 = Excellent