Comparing Single-Winner Methods

Comparing Single-Winner Methods

There are many different ways to elect a single-seat office, such as a president, governor or mayor. The three most common methods in the United States are plurality voting (called “first past the post” voting); two-round runoffs, and ranked choice voting (also called “preferential voting” or “instant runoff voting”).

This page will compare various single-winner voting rules and systems, and demonstrate why ranked choice voting (RCV) is the best choice for government elections in the U.S. It’s been tested in our courts and literally thousands of meaningfully contested elections - it works and delivers fair outcomes. 

A voting “rule” is how the winner of a race is decided. This encompasses how people vote (e.g. choosing one candidate, ranking, scoring, etc.) and how these votes are translated into results. 

A voting “system” is the entire process of how someone gets elected, from start to finish. It can include a preliminary election like a primary, all the way up to the election that decides the overall winner, and includes the voting rules used throughout. Some voting systems have one stage, others have multiple stages. Different stages can also use different rules. 

RCV is a voting rule. It can be used at any stage of a voting system, such as in a primary election, a general election, or both. Approval Voting and STAR Voting are also voting rules. 

RCV alone can also be a system, that is, if the system consists of only one stage, and that stage uses RCV as the rule. Another example of a system is a two-round runoff. Therefore, when we compare RCV to a two-round runoff, we do so as a voting system (meaning, a one-stage RCV election compared to a two-round runoff). 

The chart below compares a mix of single-winner voting rules and systems. Of countless possible evaluation criteria, this chart focuses on those that most impact the voter experience and deliver outcomes that reflect the will of the voters. No criteria, however, is more important than voters accepting the system on its terms and using it.

There are countless possible evaluation criteria, so our chart is limited to those criteria which we believe are most significant in determining whether a voting method will lead to a positive voting experience and outcomes that reflect the will of the voters. Importantly, no criteria is more important than voters accepting the system on its terms and using it -- any system violating “later no harm” for electing one candidate is for that reason unsustainable.

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Well-tested in government elections

Has the method been tested in real, competitive elections for public office?  This attests to its viability for adoption and the degree to which it is a “known quantity” — without the potential for unintended consequences. 

RCV, two-round runoff, and plurality voting are the only methods that have been used extensively in competitive elections around the world. A wealth of evidence speaks to how these methods behave in real-world contexts.

Approval voting in its multi-winner form has been used in occasional municipal elections in the United States with mixed success. 

Condorcet methods, score, and STAR voting have never been used in a public election for government office, so any claims about their behavior in practice are unproven. Proposals to reform electoral systems with relatively untested methods face an additional political hurdle, because jurisdictions must agree to become “guinea pigs”, which carries some risk.

 

Resistance to Strategic Voting

 All methods are vulnerable to some form of strategic manipulation, but they differ in how strongly they incentivize strategic voting and how likely voters are to use the strategy. 

Four common types of strategic voting are: 

RCV is most resistant to strategic manipulation and immune to the most common strategies: bullet-voting and burying. It is immune to bullet-voting because it satisfies a criterion known as later-no-harm, which means that ranking an additional choice on the ballot doesn’t hurt the chances that an earlier choice will be elected. RCV is vulnerable to compromising in rare circumstances, according to James Green-Armytage's statistical analysis

Because of its non-monotonic nature, RCV could be vulnerable to the push-over strategy in certain cases, but that strategy is too risky and difficult to pull off in a political election because it requires denying support to a voter’s preferred candidate. Indeed, there is no evidence of voters employing a push-over strategy in real-world elections. As such, strategic voting is not a concern in jurisdictions and among voters that use RCV.

In contrast, strategic voting in plurality methods is quite common, as supporters of minor candidates often strategically "compromise" to vote for a front-runner.

Two-round runoff reduces much of the incentive to compromise, but not entirely, especially in crowded fields.

Approval and score voting are highly vulnerable to bullet-voting, compromising, and burying strategies.

STAR voting partially mitigates the bullet-voting incentives inherent to approval and score voting, but it is still somewhat vulnerable to the tactic. Additionally, STAR voting is vulnerable to burying, in which voters attempt to ensure a perceived strong competitor does not advance to the final round. 

Condorcet voting methods are vulnerable to burying and other strategies.

 

Resistance to “spoilers”

How well does the method prevent a minor candidate from causing a similar front-runner candidate to lose due to vote-splitting? Voting methods are resistant to “spoilers” if adding or removing candidates who are similar to front-runner candidates does not change the winner. Our spoiler analysis is closely related to the Independence of Irrelevant Alternatives criterion from Arrow’s Theorem and the Independence of Clones criterion

RCV is highly resistant to spoilers because it satisfies both the Independence of Irrelevant Alternatives and Independence of Clones criteria. In practice, RCV prevents spoilers because voters who vote for a minor candidate have the opportunity to mark a similar front-runner candidate as a backup choice. 

Plurality voting is highly vulnerable to spoiler candidates. 

Two-Round runoff is resistant to many but not all spoilers. For example, a spoiler effect could occur between the third-place candidate and a lower-place finisher with a similar platform, preventing either candidate from earning a place in the runoff.

Both approval voting and score voting are more resistant to spoilers than plurality voting because voters can give the front-runner they like best the top score to prevent them from being “spoiled.” However, the expectation that voters will behave in this fashion depends on three assumptions, which are not always true. 

First, voters need to know who the front-runners are, so they require access to accurate polling data in advance of the runoff. Second, there must only be two clear frontrunners; otherwise the question of how best to vote to avoid spoilers is further complicated. Third, voters must be comfortable insincerely giving a front-runner the same score as their actual favorite. If any of these assumptions are not true, the spoiler effect remains.

STAR voting is more resistant to spoilers than plurality voting, approval, or score voting but is still vulnerable to spoilers due to its susceptibility to strategic voting in the form of “burying”.

 

Majority cohesion

How well does the method reflect the will of cohesive political majorities? For democracy to flourish, voting methods must elect candidates preferred by a majority of voters. 

RCV is perfect in this regard: It satisfies the Mutual Majority Criterion, meaning politically cohesive majorities will always elect one of the options they support. 

Plurality voting only respects political cohesive majorities that are unanimous in favor of a single candidate, a weaker property known as the Majority Criterion. However, this system breaks down when the political majority is divided between multiple candidates.

Two-round runoff also satisfies the Majority Criterion but not the stricter Mutual Majority Criterion. This system guarantees the election of a candidate from the group supported by a majority of voters — but only if support is divided between two candidates at most. 

Approval, score, and STAR voting do not satisfy either criteria related to majority cohesion. These methods are vulnerable to the election of a candidate who lacks majority support.

Many Condorcet methods satisfy the Mutual Majority Criterion. Condorcet methods that violate it only do so in the rare case where no Condorcet winner exists.

 

Condorcet efficiency

How often does the method elect “beats-all” candidates, — those who would win head-to-head against every other candidate in the race, when such a candidate exists? Methods that always elect the “beats-all” winner when one exists meet the Condorcet Criterion.

Condorcet methods always elect the Condorcet winner (if they exist). Variation among Condorcet methods exists because the methods handle cases with no Condorcet winner differently. 

RCV doesn’t formally satisfy the Condorcet Criterion, but data from RCV elections suggest it nearly always elects Condorcet winners. Of about 400 RCV elections in the United States since 2004 for which full ranked-ballot data are available, the “beats-all” winner only lost one — a Condorcet efficiency rate of over 99% in practice.

Two-round runoff likely also performs relatively well in this regard, but slightly less than RCV. When RCV election data are used to simulate traditional runoffs between the top-two candidates, they usually elect the Condorcet winner. However, we have identified two elections in which RCV elected the Condorcet winner when a two-round runoff would not have done so. In these cases, the Condorcet winner was in third place after first preferences were counted and would not have earned a spot in the top-two runoff. 

Plurality, approval, score, and STAR voting fail the Condorcet Criterion, but they also fail a far weaker property known as the Condorcet Loser Criterion. While the Condorcet Criterion requires the “beats-all” winner to be elected, the Condorcet Loser criterion requires that a candidate who would lose to every other candidate not be elected. 

 

 

Simplicity of tabulation

How simple is the vote tabulation to conduct? 

Plurality, two-round runoff, and approval voting earn the best scores in this regard, as they only require incrementing candidates’ tallies by one vote at a time. 

Score and STAR voting are more complicated because they require incrementing candidate tallies from a range of scores, but the tally is ultimately still a simple sum.  

RCV and Condorcet methods are more complex than a simple arithmetic sum, and are therefore harder to explain and implement. All modern voting equipment is compatible with ranked-ballot tabulation, however, lowering the burden of complex counting processes. 

 

 

Descriptive representation

How well does the voting method promote the election of candidates who represent the electorate, in terms of gender, race, ethnicity, political identity, and other factors? 

RCV has demonstrably improved representation for women and people of color. Research shows that RCV leads to more women and candidates of color on the ballot and in office. Additionally, candidates of color tend to do well earning second- and third-choice votes during RCV elections that go to multiple rounds of tabulation, and RCV removes the “win penalty” that could otherwise occur when multiple candidates appealing to the same constituency compete against one another.

Plurality voting notoriously fails to elect women and people of color at a rate proportional to their share of the population.

While two-round runoff outperforms plurality voting in electing politically representative groups of public officials, little evidence finds that it improves election rates for women or people of color. In fact, turnout in runoff elections tends to decrease more for voters of color than for White voters; consequently, the decisive rounds are typically based on more predominantly White electorates. 

Approval, score, STAR, and Condorcet methods are untested in practice. No evidence shows these methods would improve the diversity of our elected representatives.

 

 

Compatibility with fair multi-winner elections

Does the method have an accepted version or analog method for multi-winner elections that ensures fair representation? Single-winner methods that have an analogous multi-winner method allow single-winner and multi-winner offices to appear on the same ballot in an intuitive and coherent way for the voter. 

RCV earns a top score in this area because its multiwinner form, proportional RCV (aka the Single Transferable Vote), is an accepted and well-tested method for ensuring proportional representation in multi-member districts. In jurisdictions that mix single- and multi-winner offices, RCV has the added benefit of simplicity: It offers a uniform voting experience that fills single-seat offices with majority-supported winners and allocates multi-winner seats proportionally. 

Plurality voting has a number of multi-winner analogs, but they are only semi-proportional at best. The most common multi-winner analog is at-large block voting, a method in which a cohesive majority can control every seat. Other methods used in the United States include limited voting and cumulative voting, both of which create semi-proportional outcomes but not true proportionality. 

A semi-proportional analog of two-round runoff in which the single non-transferable vote is used in both rounds is theoretically possible, but in practice it would not be a true proportional method.

While some advocates have proposed proportional analogs to Condorcet, approval, score, and STAR voting, they have seen scant or non-existent use and little study or advocacy. The only multi-winner elections using any of these methods is in Fargo, North Dakota. But its multi-winner approval method is a winner-take-all method rather than a proportional method.  

 

 

Resources

Austen-Smith, David, and Jeffrey Banks (1991). “Monotonicity in Electoral Systems”. American Political Science Review, Vol. 85, No. 2 (June): 531-537.

Brewer, Albert P. (1993). “First- and Second-Choice Votes in Alabama”. The Alabama Review, A Quarterly Review of Alabama History, Vol. 46 (April 1993): 83 - 94

Burgin, Maggie (1931). The Direct Primary System in Alabama. Masters thesis, University of Alabama.

Green-Armytage, James (n.d.). “A Survey of Basic Voting Methods”. Web page at http://fc.antioch.edu/~james_green-armytage/vm/survey.htm.

Green-Armytage, James (2008). “Strategic Voting and Strategic Nomination: Comparing seven election methods”. Unpublished manuscript, University of California at Santa Barbara. http://fc.antioch.edu/~james_green-armytage/vm/svn.pdf.

Nagel, Jack (2007). “The Burr Dilemma in Approval Voting”. Journal of Politics, Vol. 69, No. 1 (February): 43-58.

Robert, Henry M., William J. Evans, Daniel H. Honemann, Thomas J. Balch (2000). Robert's Rules of Order Newly Revised, 10th Edition. Cambridge, MA, Da Capo Press.

Tideman, Nicolaus (2006). Collective Decisions and Voting: The Potential for Public Choice.

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