Comparing Single-Winner Methods

Comparing Single-Winner Methods

There are many different ways to elect a single office, such as a president, governor or mayor. However, only three methods are widely used in the United Sates: Plurality voting (sometimes misleadingly named "first past the post" voting), two-round runoffs, and ranked choice voting (also called "preferential voting" or "instant runoff voting"). Other methods are too new to have been tested on a wide scale, or have not gained traction in the U.S. 

This chart compares the most widely discussed single-winner voting methods. There are countless possible evaluation criteria but this chart is limited to those which 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. 

 

Voting Systems Comparison Table

 
RCV
Plurality Voting
Two-Round Runoff
Approval Voting
Range Voting
STAR Voting
Condorcet Methods
Well-Tested in Government Elections
High
High
High
Low
Low
Low
Low
Resistance to Strategic Voting
High
Medium
Medium
Low
Low
Medium
Medium
Resistance to Spoilers
High
Low
Medium
Medium
Medium
Medium
High
Majority Cohesion
High
Low
Medium
Low
Low
Medium
High
Condorcet Efficiency
Medium
Low
Medium
Low
Low
Medium
High
Simplicity of Count
Low
High
High
High
Medium
Medium
Low
Promotes descriptive representation
Medium
Low
Low
Unknown
Unknown
Unknown
Unknown
Compatibility with Fair Multi-Winner Elections
High
Low
Medium
Medium
Medium
Medium
Medium

 

Resistance to Strategic Voting

How resistant is the method to efforts to manipulate the result? Every method is vulnerable to some form of strategic manipulation, but they differ in terms of how strongly the method incentivizes strategic voting and how likely voters are to use the strategy. 

Four common types of strategic voting are listed below: 

Ranked choice voting is the method most resistant to strategic manipulation. RCV is immune to the strategies with the highest likelihood of use: bullet-voting and burying. RCV 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 an earlier choice is elected. While RCV is vulnerable to compromising, the situations in which it is vulnerable are rare, measured to be "low" by James Green-Armytage's statistical analysis. Additionally, due to the non-monotonic nature of RCV, it could be vulnerable to the push-over strategy in certain edge cases, but that strategy is too risky and difficult to pull off in a political election. There is no evidence of voters employing a push-over strategy in real-world elections. This concurs with practical experience with RCV where strategic voting is not a concern among the jurisdictions and voters that use it.

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

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

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

STAR Voting partially mitigates the bullet-voting incentives present in approval and range voting, but still has some vulnerability to that tactic. Additionally, it is vulnerable to burying, in which voters may attempt to ensure a perceived strong competitor does not advance to the final round. 

Condorcet voting methods are vulnerable to a number of strategies, the burying strategy in particular.

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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? A voting method is 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

Ranked choice voting 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 strongly fails this test as it is highly vulnerable to spoiler candidates. 

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

Both approval and score voting are more resistant to spoilers than plurality, because under some assumptions, voters can score the front-runner they like best the top score on the ballot to prevent that candidate from being "spoiled." However, the expectation that voters will behave in this fashion depends on three assumptions, which are sometimes true but often not. First, voters need to know who the front-runners are, so they require access to accurate polling data in advance. Second, there must be no more than 2 clear front-runners, 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 honest favorite. Whenever any of these 3 assumptions are not true, the spoiler effect remains.

STAR voting is more resistant to spoilers than plurality, approval, or score voting, but can still be vulnerable to spoilers due to its susceptibility to strategic voting in the form of burying support for a strong candidate.

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Majority Cohesion

How well does the method reflect the will of cohesive political majorities? It is important for a voting method to elect a candidate preferred by a majority of voters. 

RCV is perfect in this regard, as 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, plurality voting notoriously breaks down when the political majority is divided between multiple candidates.

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

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

Many Condorcet methods satisfy the Mutual Majority Criterion, including the Schultze method. Condorcet methods which violate it only do so in the rare case of a majority rule cycle. 

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Condorcet Efficiency

How often does the method elect "beats-all winners," a candidate that would win head-to-head against every other candidate in the race, when such a candidate exists? A method that always elects the beats-all winner when one exists is said to meet the Condorcet Criterion.

Condorcet methods naturally always elect the Condorcet winner, if such a candidate exists. The variation among Condorcet methods exists because of different handling of cases in which there is no Condorcet winner. 

Ranked choice voting does not formally satisfy the Condorcet Criterion, but data from real RCV elections suggests it elects Condorcet candidates in nearly every election. As of this writing, there have been about 400 RCV elections held in the United States since 2004 for which full ranked ballot data is available, and the "beats-all" winner only lost one, for a Condorcet efficiency rate for RCV of over 99% in practice.

Two-round runoff likely also performs relatively well in this regard, but slightly less so than RCV. If that same ballot data from RCV elections is used to simulate a traditional runoff between the top-two candidates, it produces the same winner as RCV most of the time. We have identified two elections in which RCV elected the Condorcet winner when a two-round runoff would not have done so. These are cases in which the Condorcet winner was in third place after counting first preferences, and would not have earned a spot in a top-two runoff. 

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

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Simplicity of Count

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 each candidate's tally by 1 for each vote. 

Score and STAR voting are more complicated to count as they require incrementing each candidate's tally from a range of scores, but the tally is ultimately still a simple sum.  

Ranked choice voting and Condorcet methods use counts that 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, making a complex counting process less of a burden in the digital age than in the past. 

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Well-Tested in Government Elections

Has the method been tested in real, competitive, political elections? This matters both to it's political viability for adoption and the degree to which the voting system is a "known quantity" without the potential for “unintended consequences”. 

RCV, two-round runoff, and plurality voting are the only methods which have been used extensively for competitive elections around the world. There is a wealth of evidence to examine how these methods behave in real-world elections.

Approval voting in its multi-winner form has had a small number of municipal uses in the U.S. with mixed success. 

Condorcet methods, score, and STAR voting are not used for public governmental elections anywhere in the world, so any claims about how they will or will not behave in practice are largely unproven. Reforms that are not well-tested face an additional political hurdle, because jurisdictions must agree to become "guinea pigs" for methods without a substantial track record.

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Promotes descriptive representation

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

Ranked choice voting has demonstrably improved representation for women and people of color. Research has shown that RCV leads to more women and candidates of color on the ballot and winning office. Additionally, candidates of color tend to do well earning second- and third-choice votes during RCV elections which 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 diverse candidates to office in the U.S. 

While two-round runoff likely outperforms plurality voting in electing candidates whose political views match that of the electorate, there is little evidence 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, meaning the decisive round of the election is typically based on a whiter electorate. 

Approval, score, STAR, and Condorcet methods are untested in practice and there is no evidence that these methods would improve the diversity of our elected representatives.

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Compatibility with Fair Multi-Winner Elections

Does the method have an accepted version or analog method for multi-winner elections that ensures fair representation? Methods that have a natural generalization to the election of multiple candidates with proportional representation allow for single-member and multi-member offices to coexist on the same ballot in an intuitive and coherent way for the voter. 

Ranked choice voting earns a top score in this area because its multi-winner form, known as the Single Transferable Vote, is an accepted and well-tested method for ensuring proportional representation for multi-member districts. For jurisdictions with a mixture of single-winner and multi-winner elections, RCV offers the simplicity of using a uniform voting experience across the board, allowing single-seat offices to be filled with majority-supported winners and allocating multi-winner seats proportionally. 

Plurality voting has a number of multi-winner analogs, but they are semi-proportional at best. The most common multi-winner analog to single-winner plurality is at-large block voting, a method in which a cohesive majority can control every seat. Other methods used in the U.S. include Single Non-Transferable Vote and Cumulative Voting, both of which create semi-proportional outcomes rather than true proportionality. 

Similarly for two-round runoff, it is possible to imagine a kind of semi-proportional analog of Two-Round Runoff in which SNTV is used in both rounds, but not a true proportional method.

While there have been theoretical proposals for proportional analogs to Condorcet, approval, score, and STAR, they have seen scant or non-existent use and little study or advocacy. The only multi-winner elections using any of these methods is a form of multi-winner approval voting used in Fargo, ND which is a non-proportional method. 

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References

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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