Ranked voting

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Sample ballot of ranked voting using written numbers

Ranked voting is any election voting system in which voters use a ranked ballot to rank choices in a sequence on the ordinal scale: 1st, 2nd, 3rd, etc. There are multiple ways in which the rankings can be counted to determine which candidate (or candidates) is (or are) elected (and different methods may choose different winners from the same set of ballots). The other major branch of voting systems is cardinal voting, where candidates are independently rated, rather than ranked.[1]

The similar term "Ranked Choice Voting" (RCV) is used by the US organization FairVote to refer to the use of ranked ballots with specific counting methods: either instant-runoff voting for single-winner elections or single transferable vote for multi-winner elections. In some locations, the term "preferential voting" is used to refer to this combination of ballot type and counting method, while in other locations this term has various more-specialized meanings.[2]

A ranked voting system collects more information from voters compared to the single-mark ballots currently used in most governmental elections, many of which use First-Past-The-Post and Mixed-Member Proportional voting systems.

There are many types of ranked voting, with several used in governmental elections. Instant-runoff voting is used in Australian state and federal elections, in Ireland for its presidential elections, and by some jurisdictions in the United States, United Kingdom, and New Zealand. A type and classification of ranked voting is called the single transferable vote, which is used for national elections in Ireland and Malta, the Australian Senate, for regional and local elections in Northern Ireland, for all local elections in Scotland, and for some local elections in New Zealand and the United States. Borda count is used in Slovenia[3] and Nauru. Contingent vote and Supplementary vote are also used in a few locations. Condorcet methods are used by private organizations and minor parties, but currently are not used in governmental elections.

Arrow's impossibility theorem and Gibbard's theorem prove that all voting systems must make trade-offs between desirable properties, such as the preference between two candidates being unaffected by the popularity of a third candidate.[4][5] Accordingly there is no consensus among academics or public servants as to the "best" electoral system.[6]

Recently, an increasing number of authors, including David Farrell, Ian McAllister and Jurij Toplak, see preferentiality as one of the characteristics by which electoral systems can be evaluated.[2][7] According to this view, all electoral methods are preferential, but to different degrees and may even be classified according to their preferentiality.[2] By this logic, cardinal voting methods such as Score voting or STAR voting are also "preferential".

Types of ranked voting

See Category:Ranked voting methods.

Single-winner methods

In general, most ranked methods attempt to extend majority rule to elections with more than two candidates. Some ranked methods do this using some kind of runoff i.e. IRV and Condorcet methods, which explains why many of them pass the Condorcet loser criterion.

IRV is yhe most popular ranked method. It is an attempt to give voters in FPTP a chance to add support to new alternatives when their candidate is polling the worst in the race. This opens it to criticisms of limiting the Number of supportable candidates in various voting methods, as well as inducing odd Strategic voting.

The Borda count is an example of a Weighted positional method, not all of which aim for majority rule, in which points are given to candidates based on their rank. These are related to Cardinal methods.

Bucklin finds a majority winner by essentially looking for the median voter's preferred candidate. See Category:Graded Bucklin methods.

Smith-efficient Condorcet methods can be thought of as maximally combining compliance with the majority criterion in the two-candidate case with Independence of irrelevant alternatives.

Multi-winner methods

STV is the major ranked PR method, with there being several alternatives such as the Quota Borda system or the Expanding Approvals Rule. For ranked Block voting elections, any ranked single-winner method can be used by repeatedly electing the candidates at the top of its order of finish.


Activists and theorists that prefer other ballot systems make the following arguments against ranked voting:

Strength of preference

The first thing that should be mentioned is that ranked voting doesn't allow a voter to indicate weak preferences i.e. if a voter either slightly or strongly prefers one candidate over another. See rated ballot for information on this.

One criticism that can be made of ranked voting is that it creates a logical contradiction: if a voter ranks X>Y>Z, then the strength of their preference for X>Z must be stronger than their preference for X>Y or Y>Z, yet all 3 preferences are generally treated as equally strong in most ranked methods. This can most clearly be seen in many Condorcet methods: in the head-to-head matchups, the voter is considered to give 1 vote in all 3 matchups, rather than giving less of a vote in the X>Y and Y>Z matchups and more of a vote in the X>Z matchup. The Borda count resolves this issue if the point totals are kept the same i.e. a voter who gives 8 points to A, 7 to B, and 6 to C gives 1 point to A>B and 1 point to B>C, which adds up to equal the 2 points for A>C. This same criticism can be made for rated pairwise preference ballots as well, since they allow (but do not force) voters to exaggerate all of their pairwise preferences.

Approval voting (and some rated methods in general) can be thought of as a ranked method with constraints placed that fully resolve this contradiction: if an Approval ballot is thought of as a voter ranking one set of candidates equally 1st and above all others, then when a voter ranks an approved candidate above a disapproved candidate, they can't further indicate a preference between the disapproved candidates, thus ensuring that the strength of preference in each matchup is consistent with the strength in other matchups i.e. if they approve only X, then the strength of X>Y will be the same as X>Z, since the full preference is treated as X>Y=Z. In other words, from a pairwise counting perspective, if the voter gives 1 vote to X>Y, then they must give 0 votes to Y>Z, and when the number of votes given in both matchups is added up, this equals the 1 vote the voter gave to X>Z. If the voter's ranked preference is visualized as a beat-or-tie path from their 1st choice to their last choice, then the strength of their preference between any pair of candidates in the path will equal the strength of preference of each matchup between each pair of candidates starting from the first candidate of the pair vs the candidate sequentially after them, the candidate sequentially after them vs the candidate sequentially after the candidate sequentially after them, etc. all the way until the candidate sequentially before the second candidate in the pair vs the second candidate in the pair, added up. Another example would be a voter who approves A, B, and C, and disapproves of D, E, and F; this voter's Approval preference can be represented as A=B=C>D=E=F. If, for example, the B vs E matchup is analyzed, this voter is considered as giving 1 vote to B>E; this is equal to adding up the strength of their preference in the B vs C matchup (0 votes, because they ranked the two equally) plus their strength of preference in the C vs D matchup (1 vote, because they ranked C>D) plus the preference in the D vs E matchup (0 votes, because D=E). So, by starting at B and going sequentially one pair at a time down the beat-or-tie path that is the voter's ranked preference until you reach E, you can see that the strength of B>E is equal to the strength of the intervening matchups added up.

Score voting takes this a step further by allowing voters to vary their degree of approval; in some sense, this can be seen in the ranked context by first using the KP transform and then converting the resulting Approval ballots into ranked ballots as mentioned above. This allows voters to essentially "vote against themselves" in certain matchups or otherwise split their ballot up in such a way that only a fraction of it shows a preference between certain candidates, while the rest of the ballot is treated as indifferent between those candidates i.e. a voter giving 100% support to A, 70% to B, and 10% for C is treated as 10% of an A=B=C voter, 60% of an A=B voter, and 30% of an A voter, thus allowing them to have, for example, only 60% of their ballot showing preference for B>C, rather than 100%. Again, the same "the strength of X>Z is equal to X>Y plus Y>Z" beat-or-tie path consistency is achieved here; if analyzing the A vs C matchup, the voter gives 90% of their ballot to A>C and 10% to A=C, so they are in effect giving 0.9 votes to A>C. This equals the strength of the A vs B matchup (0.3 votes for A>B, since the voter gives 30% of their ballot to A>B and 70% to A=B) plus the B vs C matchup (60% or 0.6 votes for B>C, as mentioned above).


Most ranked voting methods can incentivize voters to strategically vote by ranking candidate Y above X even though the voter preferred X to Y (though the frequency and degree of incentive depend on the method). For this reason, it is claimed that Score voting is better, because it doesn't incentivize this, and thus may be even better at collecting ranked-preference information than most ranked methods.[8]

Majority rule as an approximation of utilitarianism

It is important to emphasize that majoritarianism and cardinal utilitarianism are not necessarily opposing principles. From a utilitarian perspective, majoritarianism can be considered an approximation of utilitarian principles under certain conservative assumptions. This is analogous to how most systems of ethics can be cast as varieties of utilitarianism with constraints on the utilities being used, even systems that are not utilitarian as such.


It is worth considering what a ranked method's "approval case" looks like. This is when, if equal rankings are permitted, all voters rank every candidate either 1st or last. Many ranked methods become Approval voting in their approval case i.e. the candidate with the most 1st choices wins (sometimes this depends on how equal-rankings are implemented); for example, all Smith-efficient Condorcet methods, Borda, IRV with whole votes equal-ranking, etc.


  1. Riker, William Harrison (1982). Liberalism against populism: a confrontation between the theory of democracy and the theory of social choice. Waveland Pr. pp. 29–30. ISBN 0881333670. OCLC 316034736. Ordinal utility is a measure of preferences in terms of rank orders—that is, first, second, etc. ... Cardinal utility is a measure of preferences on a scale of cardinal numbers, such as the scale from zero to one or the scale from one to ten.
  2. a b c Toplak, Jurij (2017). "Preferential Voting: Definition and Classification". Lex Localis – Journal of Local Self-Government. 15 (4): 737–761. doi:10.4335/15.4.737-761(2017).
  3. Toplak, Jurij (2006). "The parliamentary election in Slovenia, October 2004". Electoral Studies. 25 (4): 825–831. doi:10.1016/j.electstud.2005.12.006.
  4. Mankiw, Gregory (2012). Principles of Microeconomics (6th ed.). South-Western Cengage Learning. pp. 475–479. ISBN 978-0538453042.
  5. Hamlin, Aaron (October 6, 2012). "Interview with Dr. Kenneth Arrow". The Center for Election Science. Center for Election Science. CES: you mention that your theorem applies to preferential systems or ranking systems. ... But the system that you're just referring to, Approval Voting, falls within a class called cardinal systems. ... Dr. Arrow: And as I said, that in effect implies more information. ... I’m a little inclined to think that score systems where you categorize in maybe three or four classes probably (in spite of what I said about manipulation) is probably the best.
  6. "Electoral Systems in Europe: An Overview". Brussels: European Centre for Parliamentary Research and Documentation. October 2000. Retrieved November 7, 2019.
  7. Farrell, David M.; McAllister, Ian (2004-02-20). "Voter Satisfaction and Electoral Systems: Does Preferential Voting in Candidate-Centered Systems Make A Difference". Cite journal requires |journal= (help)
  8. "r/EndFPTP - Comment by u/MuaddibMcFly on "Score but for every pairwise matchup"". reddit. Retrieved 2020-05-14.