Ranked voting, also known as ranked-choice voting or preferential voting, refers to any
voting system in which voters use a ranked (or preferential) ballot to select more than one candidate (or other alternative being voted on) and to rank these choices in a sequence on the ordinal scale of 1st, 2nd, 3rd, etc. Ranked voting is different from cardinal voting, where candidates are independently rated rather than ranked. The most important differences between ranked voting systems lie in the methods used to decide which candidate (or candidates) are elected from a given set of ballots. Some of the most significant methods are described below.
Another (more cosmetic) difference lies in the format of the ballot papers. Some jurisdictions require voters to rank all candidates; some limit the number who may be ranked; and some allow voters to rank as many as they see fit, with the rest being lumped together at the end. Other rules (sometimes entailed by the method of determining a winner) are imposed in different cases.
The subject of this article should not be confused with instant-runoff voting, a specific form of ranked voting to which the US organization FairVote has attached the name ‘ranked-choice voting’. Ranked voting is used in national or state elections in Australia, Ireland, two US states, New Zealand, Ireland, Malta, Slovenia and Nauru.
Theoretical properties of ranked votingEdit
The Condorcet criterionEdit
The theoretical study of ranked voting methods was initiated by the Marquis de Condorcet in the eighteenth century, and some of the concepts he developed still play a central role in the subject.
If there is a candidate who is preferred to every other candidate by the majority of voters in an election, then this candidate is known as the Condorcet winner. A voting method which always elects the Condorcet winner if there is one is said to be Condorcet consistent or (equivalently) to satisfy the Condorcet criterion. Methods with this property are known as Condorcet methods.
If there is no Condorcet winner in an election, then there must be a Condorcet cycle, which can be illustrated by an example. Suppose that there are 3 candidates, A, B and C, and 30 voters such that 10 vote C–B–A, 10 vote B–A–C, and 10 vote A–C–B. Then there is no Condorcet winner. In particular, we see that A cannot be a Condorcet winner because ⅔ of voters prefer B to A; but B cannot be a Condorcet winner because ⅔ prefer C to B; and C cannot be a Condorcet winner because ⅔ prefer A to C. But A cannot be a Condorcet winner... thus the search for a Condorcet winner takes us in circles without ever finding one.
A spatial model is a model of the electoral process developed by Duncan Black and extended by Anthony Downs. Every voter and every candidate is assumed to occupy a location in a space of opinions which may have one or more dimensions, and voters are assumed to prefer the closer of two candidates to the more distant. A political spectrum is a simple spatial model in one dimension.
The diagram shows a simple spatial model in one dimension which will be used to illustrate the voting methods later in this article. A’s supporters are assumed to vote A–B–C and C’s to vote C–B–A while B’s are split equally between having A and C as second preference. If there are 100 voters, then the ballots cast will be determined by voters’ and candidates’ positions in the spectrum according to the table shown.
Spatial models are important because they are a natural way of visualising voters’ opinions and because they lead to an important theorem, the median voter theorem, also due to Black. It asserts that for a wide class of spatial models – including all unidimensional models and all symmetric models in higher dimensions – a Condorcet winner is guaranteed to exist and to be the candidate closest to the median of the voter distribution.
If we apply these ideas to the diagram, we see that there is indeed a Condorcet winner – B – who is preferred to A by 64% and to C by 66%, and that the Condorcet winner is indeed the candidate closest to the median of the voter distribution.
Arrow's impossibility theorem casts a more pessimistic light on ranked voting. While the median voter theorem tells us that for many sets of voter preferences it is easy to devise a voting method which works perfectly, Arrow’s theorem says that it is impossible to devise a method which works perfectly in all cases.
Whether Arrow’s pessimism or Black’s optimism is closer to the truth of electoral behaviour is a matter which needs to be determined empirically. A number of studies, including a paper by Tideman and Plassman, suggest that simple spatial models of the type satisfying the median voter theorem give a close match to observed voter behaviour.
Principal ranked voting systemsEdit
The Borda count assigns a score to each candidate by adding a number of points awarded by each ballot. If there are m candidates, then the first-ranked candidate in a ballot receives m – 1 points, the second receives m – 2, and so on until the last-ranked candidate receives none. In the example B is elected with 130 of the total 300 points.
The Borda count is simple to implement but does not satisfy the Condorcet criterion. It has a particular weakness in that its result can be strongly influenced by the nomination of candidates who do not themselves stand any chance of being elected.
Other positional systemsEdit
Voting systems which award points in this way, but possibly using a different formula, are known as positional systems. Where the score vector (m – 1, m – 2,... ,0) corresponds to the Borda count, (1, ½, ⅓,... ,1/m ) defines the Dowdall system and (1, 0,... ,0) equates to FPTP.
Alternative vote / instant-runoff voting (IRV)Edit
|1st round||2nd round||3rd round|
IRV eliminates candidates in a series of rounds, emulating the effect of separate ballots on shrinking sets of candidates. The first round consists of the ballots as actually cast. The candidate with fewest first-place preferences is identified (in this case B) and deleted from the ballots for subsequent rounds. Thus in the second round the ballots express preferences between just 2 candidates (more generally m – 1). We stop at this point because A is identified as the winner on account of being the first preference of the majority of ballots; but if we constructed a third round A would be the sole candidate.
Elimination systems are relatively clumsy to implement, since each ballot needs to be re-examined on each round, rather than allowing computation from a simple table of derived statistics. IRV does not satisfy the Condorcet criterion. Unlike most ranked voting systems, it does not allow tied preferences except between a voter’s least preferred candidates.
Other elimination systemsEdit
Coombs' method is a simple modification of IRV in which the candidate eliminated in each round is the one with most last-place preferences rather than with fewest first-place preferences (so C rather than B is eliminated in the first round of the example and B is the winner). Coombs' method is not Condorcet-consistent but nonetheless satisfies the median voter theorem. It has the drawback that it relies particularly on voters’ last-place preferences which may be chosen with less care than their first places.
Baldwin’s and Nanson’s methods use more complicated elimination rules based on the Borda count. They are Condorcet-consistent.
The minimax system determines a result by constructing a results table in which there is an entry for every pair of distinct candidates showing how often the first is preferred to the second. Thus since 51 voters prefer A to C and 49 have the opposite preference, the (A,C) entry reads ‘51:49’. In each row we identify the least favourable (i.e. minimal) result for the first candidate (shown in bold), and the winning candidate is the one whose least favourable result is most favourable (i.e. maximal). In the example the winner is B, whose least favourable result is a win while the other candidates’ least favourable results are slightly different losses.
Determining the minimax winner from a set of ballots is a particularly simple operation. The method satisfies the Condorcet criterion, and can be seen as electing the Condorcet winner if there is one, and as electing the candidate who comes closest to being a Condorcet winner (under a simple metric) otherwise.
Llull's method / Copeland's methodEdit
Copeland's method (actually due to Ramon Llull) assigns each candidate a score derived from the results table as shown above for minimax. The score is simply the number of favourable results in the candidate’s row, i.e. the number of other candidates a particular candidate was preferred to by a majority of voters. The candidate with the highest score (in this case B) wins.
Copeland’s method is simple and Condorcet-consistent but has the drawback that for certain patterns of voter preferences with no Condorcet winner it will yield a tie however large the electorate. Its advocates therefore generally recommend its use in conjunction with a tie-break. Suitable rules for this purpose are minimax, IRV, and the Borda count, the last of which gives the Dasgupta-Maskin system.
A Condorcet completion elects the Condorcet winner if there is one, and otherwise falls back on a separate procedure for determining the result. If the Borda count is the fallback we get Black's method; if we use IRV we get Tideman’s ‘Condorcet-Hare’.
- The Kemeny-Young method is complex but Condorcet-consistent.
- Smith’s method reduces the set of candidates to the Smith set, which is a singleton comprising the Condorcet winner if there is one, and is otherwise usually smaller than the original set. It is normally advocated for use in conjuction with a tie-break, with IRV and minimax the commonest. It is computationally simple though not intuitive to most voters.
- The contingent vote is a 2-round version of IRV, and the supplementary vote is a restricted form of contingent vote.
- Bucklin's method exists in several forms, some of which are Condorcet-consistent.
- The ranked pairs method, Schulze method and Split cycle method are Condorcet-consistent methods of medium computational complexity based on analysing the cycle structure of ballots.
- Dodgson's method is famous chiefly for having been devised by Lewis Carroll. It is Condorcet-consistent but computationally complex.
- Single transferable vote (STV) is a multiwinner version of IRV.
Use by politicsEdit
Countries and regionsEdit
|Country||Years in use||Type||Notes|
|Australia||1918–present||Single transferable vote, instant-runoff voting||From 1949, the single transferable vote method has been used for upper house legislative elections. Instant-runoff voting is used for lower house elections.|
|Canada||Instant-runoff voting||Used in whole or in part to elect the leaders of the three largest federal political parties in Canada: the Liberal Party of Canada, the Conservative Party of Canada, and the New Democratic Party, albeit the New Democratic Party uses a mixture of IRV and exhaustive voting, allowing each member to choose one format or the other for their vote.|
|Estonia||1990–c. 2001||Single transferable vote||As of 2001, single transferable vote had been in use since 1990 to decide legislative elections. This is no longer the case.|
|Hong Kong||1998–present||Instant-runoff voting||Instant-runoff voting is only used in the 4 smallest of Hong Kong's 29 functional constituencies. Officially called preferential elimination voting, the system is identical to the instant-runoff voting.|
|Ireland||1922–present||Single transferable vote||Single transferable vote is prescribed by Constitution or statute for all public elections. In single-winner cases (presidential, most Dáil by-elections) this reduces to instant-runoff voting. Referendums to abolish STV for Dáil elections failed in 1958 and 1968.|
|Malta||1921–present||Single transferable vote|||
|Nauru||1968–present||Borda count||Nauru uses the Dowdall system, a variant of the Borda count that behaves more like FPTP.|
|New Zealand||2004–present||Single transferable vote||Instant-runoff voting is used in only some single-seat elections, such as district health boards as well as some city and district councils.|
|Northern Ireland||1973–present||Single transferable vote||Used for local government, European Parliament and the regional legislature, but not elections to Westminster.|
|Papua New Guinea||2007–present||Instant-runoff voting||Between 1964 and 1975, Papua New Guinea used a system that allowed voters the option of ranking candidates. Currently, voters can rank only their top three choices.|
|Slovenia||2000–present||Borda count||Only two seats, which are reserved for Hungarian and Italian minorities, are decided using a Borda count.|
|Sri Lanka||1978–present||Contingent vote and open list||Contingent vote is used for presidential elections, and open list for legislative elections.|
|United States||2020||Limited instant-runoff voting||In their 2020 primaries, several states used a form of instant run-off in Democratic Party primaries.|
|Zimbabwe||1979–1985||Instant-runoff voting||Was only used for white candidates|
Federal provinces or statesEdit
|Province/state||Country||Years in use||Type||Notes|
|Alaska||United States||2022||Instant-runoff voting||Approved by Alaska voters in 2020 via ballot measure.|
|Australian Capital Territory||Australia||1993–present||Single transferable vote|
|British Columbia||Canada||1926–1955||Instant-runoff voting|
|Maine||United States||2018–present||Instant-runoff voting||Originally approved by Maine voters as a 2016 ballot referendum to replace the First Past The Post system statewide, a 2017 state law sought to delay implementation of ranked-choice voting until 2021, to allow time for amending the state constitution. Supporters overrode the delay with a 2018 people's veto referendum that received a majority of votes, ensuring that ranked-choice voting would be used for future primary and federal elections.|
|New South Wales||Australia||1918–present||Single transferable vote (1918–1926, 1978–present), contingent vote (1926–1928), instant-runoff voting (1929–present)||Since 1978, NSW has used the single transferable vote method to decide upper house legislative elections only. Optional preferential voting for lower house since 1981. This means a voter can number all candidates with their preference, or stop at just one candidate.|
|North Carolina||United States||2006–2013||Instant-runoff voting||A state law in 2006 established instant-runoff voting for certain judicial elections, until a 2013 law repealed the practice.|
|Northern Territory||Australia||1980 only|
|Ontario||Canada||2018–present||Instant-runoff voting (municipal elections only)||In 2016, the provincial government passed Bill 181, the Municipal Elections Modernization Act, which permitted municipalities to adopt ranked balloting in municipal elections. In the 2018 elections, the first ones conducted under the new legislation, the city of London used ranked balloting, while the cities of Kingston and Cambridge held referendums on whether to adopt ranked ballots for the next municipal elections in 2022.|
|Queensland||Australia||1892–1942, 1962–present||Contingent vote (1892–1942), instant-runoff voting (1962–present)||Full preferential voting used 1962–1992 and since 2016.|
|South Australia||Australia||1929–present, 1982–present||Instant-runoff voting (1929–present), single transferable vote (1982–present)||Instant runoff for the lower house, single transferable for the upper house.|
|Tasmania||Australia||1907–present||Single transferable vote (1907–present), instant-runoff voting (1909–present)||Single transferable for the lower house, instant runoff for the upper house.|
|Victoria||Australia||1911–present||Instant-runoff voting (1911–present), single transferable vote (2006–present)||Prior to 1916, Victoria did not use any preferential voting method to decide upper house legislative elections. Instant runoff for the lower house, single transferable for the upper house. Full preferential voting for lower house since 1916.|
|Western Australia||Australia||1907–present||Instant-runoff voting (1907–present), single transferable vote (1989–present)||Instant runoff for the lower house, single transferable for the upper house. Full preferential voting for lower house since 1912.|
|Organization||Years in use||Type||Notes|
|European Union||option to use single transferable vote||Member countries can use either party-list proportional representation (not a type of preferential voting) or single transferable vote to elect MEPs|
Use outside of politicsEdit
The winner of the Eurovision Song Contest is selected by a positional voting system. The most recent system was implemented in the 2016 contest, and sees each participating country award two sets of 12, 10, 8–1 points to their 10 favourite songs: one set from their professional jury and the other from tele-voting.
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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.
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- J. Green-Armytage, T. N. Tideman and R. Cosman, ‘Statistical Evaluation of Voting Rules’ (2015).
- R. B. Darlington, ‘Are Condorcet and Minimax Voting Systems the Best?’ (v8, 2021).
- W. H. Holliday and E. Pacuit, ‘Split Cycle: A New Condorcet Consistent Voting Method Independent of Clones and Immune to Spoilers’ (2021).
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- The fact that Hong Kong began using preferential voting in 1998 can be seen from two sources:
- Minutes from a 1997 LegCo meeting include a proposal to use "preferential elimination voting" for the three smallest functional constituencies. See, "Legislative Council Bill (Minutes) 11 Sept 97". The Legislative Council Commission. Retrieved July 2, 2012.
- 1998 is the first year "preferential elimination voting" can be found in the Hong Kong yearbook. See, "The Electoral System: b. Functional Constituency". Hong Kong Yearbook 1998. Government Information Centre of Hong Kong. Retrieved July 2, 2012.
- "Chapter. 3, Functional Constituencies: The Preferential Elimination System of the 4 SFCs" (PDF). Guidelines on Election-related Activities in respect of the Legislative Council Election. Hong Kong Electoral Affairs Commission. Retrieved June 29, 2012.
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- "Country Profile: Nauru: Learn More". ElectionGuide. International Foundation for Electoral Systems. Retrieved November 7, 2019.
- Fraenkel, Jon; Grofman, Bernard (2014-04-03). "The Borda Count and its real-world alternatives: Comparing scoring rules in Nauru and Slovenia". Australian Journal of Political Science. 49 (2): 186–205. doi:10.1080/10361146.2014.900530. S2CID 153325225.
- "STV legislation, background and further information". New Zealand Department of Internal Affairs. Retrieved September 25, 2015.
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- "Voting". Electoral Commission of Papua New Guinea. 2011. Retrieved June 30, 2012.
- "Article 80: The National Assembly; Composition and Election" (PDF). Constitution of the Republic of Slovenia. United Nations Public Administration Network. pp. 47–48. Retrieved July 3, 2012.
- "Country Profile: Slovenia: Learn More". ElectionGuide. International Foundation for Electoral Systems. Retrieved November 7, 2019.
- "Country Profile: Sri Lanka: Learn More". ElectionGuide. International Foundation for Electoral Systems. Retrieved November 7, 2019.
- "Negotiations". Administration and Cost of Elections Project. ACE Electoral Knowledge Network. Retrieved July 6, 2012.
- "Alaska Becomes First In The Nation to Approve Top-4 Primary with Ranked Choice Voting". Independent Voter News. November 17, 2020. Retrieved November 17, 2020.
- Russell, Eric, "Mainers vote to keep ranked-choice voting, with supporters holding commanding lead". Portland Press Herald, June 12, 2018.
- Joyce, Robert, "Instant Runoff Voting". University of North Carolina: School of Government, November 2013.
- "Legislation passes allowing Ontario municipalities to use ranked ballots". The Globe and Mail, June 7, 2016.
- "London, Ont., votes to become first Canadian city to use ranked ballots". CBC News Windsor, May 2, 2017.
- Coyne, Andrew, "Election reform is coming to Canada – somewhere, somehow, and soon". National Post, October 6, 2017.
- "Instant Runoff Voting (IRV): History of Use in Ann Arbor". Green Party of Michigan. 1998. Archived from the original on February 8, 2012. Retrieved June 29, 2012.
- Urquhart, Janet (June 28, 2012). "Marks prevails in lawsuit over Aspen election ballots". The Aspen Times. Retrieved June 29, 2012.
- "Ranked-Choice Voting". Alameda County Registrar of Voters. Retrieved June 29, 2012.
- McCrea, Lynne (March 3, 2010). "Burlington Voters Repeal Instant Runoff Voting". Vermont Public Radio. Retrieved November 7, 2019.
- Lamdin, Courtney. "Can Once-Maligned Ranked-Choice Voting Make a Comeback in Burlington?". Seven Days.
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- "Choice Voting in Cambridge". FairVote.
- "New Voting Method for November 6, 2007: Hendersonville Pilots Instant Runoff Voting" (PDF). Henderson County Board of Elections. 2007. Retrieved June 29, 2012.
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The 2013 General Assembly repealed all legislation authorizing instant runoff elections in North Carolina.
- "London's elections: How the voting works". BBC. May 3, 2000. Retrieved June 29, 2012.
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- Poundstone, William (2009). Gaming the Vote: Why Elections Aren't Fair (And What We Can Do About It). Macmillan. p. 170. ISBN 978-0809048922.
- Baran, Madeleine (November 7, 2011). "Election Day in St. Paul Tuesday". Minnesota Public Radio. Retrieved June 29, 2012.
- "Ranked Voting Information". Ramsey County. Retrieved June 29, 2012.
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