Ranked voting

From Wikipedia, the free encyclopedia
Jump to navigation Jump to search

Ranked voting is any election 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. There are multiple ways in which the rankings can be counted to determine which candidate or candidates (or other outcome(s)) is or are elected (or adopted), and these different methods may produce different results from the same set of ballots. Ranked voting is different from 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]

Single Transferable Voting (STV) is categorized specifically as a voting system to resemble "proportional representation" through multiple constituencies rather than one. Since both STV and RCV hold similar processes, they are commonly used interchangeably. Those advocating for STV, argue that since candidates of different parties can be written on the ballot, rather than from just one, all members of government can be elected based upon their individual merits. [3] Voters also have the option to create connections with local candidates under STV, where constituencies can cover a smaller area, creating a local link, giving voters a choice of representatives to contact. [4]

A ranked voting system collects more information from voters than 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[5] 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.[6][7] Accordingly there is no consensus among academics or public servants as to the "best" electoral system.[8]

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][9] 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[edit]

There are different preferential voting systems, so it is sometimes difficult to distinguish between them.

Selection of the Condorcet winner is generally considered by psephologists as the ideal election outcome for a ranked system,[10] so "Condorcet efficiency" is important when evaluating different methods of preferential voting.[11] The Condorcet winner is the one that would win every two-way contest against every other alternative.[6]

Another criterion used to gauge the effectiveness of a preferential voting system is its ability to withstand manipulative voting strategies, when voters cast ballots that do not reflect their preferences in the hope of electing their first choice. This can be rated on at least two dimensions—the number of voters needed to game the system, and the sophistication of the strategy necessary.[11]

Instant-runoff voting[edit]

Sample ballot of ranked voting using column marks

Used in national elections in Australia, this system is said to simulate a series of runoff elections. If no candidate is the first choice of more than half of the voters, then all votes cast for the candidate with the lowest number of first choices are redistributed to the remaining candidates based on who is ranked next on each ballot. If this does not result in any candidate receiving a majority, further rounds of redistribution occur.[12][13]

This method is thought to be resistant to manipulative voting as the only strategies that work against it require voters to highly rank choices they actually want to see lose. At the same time, this system fails Condorcet criterion, meaning a candidate can win even if the voters preferred a different candidate, and fails the monotonicity criterion, where ranking a candidate higher can lessen the chances he or she will be elected and vice versa. Additionally, instant-runoff voting has a lower Condorcet efficiency than similar systems when there are more than four choices.[11]

Contingent Vote[edit]

Single transferable vote[edit]

Sample ballot of ranked voting using written names

This is one of the preferential voting systems most used by countries and states. (See table below in "Use by politics".) It is used for electing multi-member constituencies. Any candidates that achieve the number of votes required for election (the "quota") are elected and their surplus votes are redistributed to the voter's next choice candidate. Once this is done, if not all places have been filled then the candidate with the lowest number of votes is eliminated, and their votes are also redistributed to the voter's next choice. This whole process is repeated until all seats are filled. This method is also called the Hare-Clark system.[14]

When single transferable vote is used for single-winner elections, it becomes equivalent to instant-runoff voting.[15]


The term Single transferable vote is sometimes used synonymously with Ranked Choice Voting. Single Transferable Voting (STV) is categorized more clearly as a voting system designed to nearly resemble "proportional representation" through multiple constituencies rather than one. Under STV, a voter will cast a single ballot in a country or region which will elect multiple winners. Despite the difference, since both STV and RCV share similar process, in certain circumstances, they can be used interchangeably. [3]Similar to the process involved in RCV, if there are more running candidates than available spaces on any board, then the candidate with the fewest votes is eliminated and their votes are given to the candidate of which is the voter's back-up. Voters can also vote for members of different political parties on the same ballot, rather than of just one party. [16] Federal voting administers of the Republic of Ireland and Scotland in support of STV, argue that since candidates of different parties can be written on the ballot, all members of government can be elected based upon their individual merits. [3] Voters can also vote for an independent candidate and create connections with local candidates under STV, where constituencies are natural, covering a smaller area creating a local link, and gives voters a choice of representatives to talk to.[4]

Ranked Choice Voting (RCV)[edit]

Ranked Choice Voting is a electoral selection technique used to provide assurance and security for all voters by providing them the option to rank political candidates based upon personal preference: 1st, 2nd, 3rd, and so on, rather than indicating support for only one candidate.[17] A vote is given to the voter's first preference if permissible, however, if the chosen candidate drops out of the race or is eliminated, rather than being disposed of in a regular election, the vote is transferred to the back-up or second choice.[18]

IRV counting flowchart

[19]Process[edit]

  1. Voters rank the candidates by preference on their ballots (most preferred candidates followed by back up candidates).
  2. The candidate with the majority (more than 50%) of first choice votes (the number one spot on the ballot) wins the election outright.[20]

In the circumstance that there is no majority winner (no candidate receives more than 50% of the total votes), then the race is decided by an Instant-runoff which shows a comparison of the top two candidates head to head. [21]

Instant Runoff Process[edit]
  1. In the process of an Instant-runoff, if no candidate receives a majority of each voter's top choice, then the candidate with the fewest number of votes is eliminated from the race and voters.
  2. That being said, first preference votes for the eliminated candidate will have their votes count for the next choice.
  3. A new vote is counted adjusted using Instant-runoff to determine if any candidate wins an outright majority.
  4. This process is repeated with the second, third, and fourth choices until a candidate receives this voter majority.[22]

Instant Runoff Voting is similar to Single Transferable Voting in that with IRV, the goal is a majority representation of total votes in a district, rather than proportional representation of all voting blocks/districts.

Related Terminology[edit]

The term Instant-runoff is used in two contexts.

  1. As a synonym for Ranked Choice Voting
  2. As a description of Ranked Choice Voting processes specifically around voting circumstances where no voter holds such a majority. It is essentially a contingency process within another process- only used when necessary. (Used in single winner elections only)[23]

Condorcet method[edit]

Positional voting[edit]

Positional voting is a ranked voting electoral system in which the options receive points based on their rank position on each ballot and the option with the most points overall wins.[24] Plurality, anti-plurality, and Borda count are the three different methods in a positional voting. A candidate will receive a certain number of points based on the voter's ranking.[25]

Borda count[edit]

Borda is a positional system in which ballots are counted by assigning a point value to each place in each voter's ranking of the candidates, and the choice with the largest number of points overall is elected. This method is named after its inventor, French mathematician Jean-Charles de Borda.[6] Instead of selecting a Condorcet winner, this system may select a choice that reflects an average of the preferences of the constituency.[citation needed]

The Borda count does not exhibit independence of irrelevant alternatives[6] or independence of clones meaning the outcome it selects is dependent on the other choices present. In large scale elections, the Borda Count is only weakly manipulated by adding candidates, called clones, whose views are similar to the preferred candidate's, but in a small committee election it can more easily manipulated. An example of this strategy can be seen in Kiribati's 1991 presidential nomination contest.[26]

Path Voting (Schulze Method)[edit]

Examples[edit]

Some examples of RCV elections are shown below. The first table shows the process of RCV and the second demonstrates how Instant Runoff Voting plays a role in these elections. These examples have been taken from Ballotpedia and represents hypothetical situations to demonstrate a process and clarify a concept. [27]

Example 1:[edit]

Raw first-preference vote in political race
Candidate First-Preference Votes Percent outcome
Candidate A 475 46.34%
Candidate B 300 29.27%
Candidate C 175 17.07%
Candidate D 75 7.32%

Hypothetically speaking, there are four candidates running for a political election, the figure above shows the first preference votes based on each candidate and the accompanied percentages of total votes.

According to the results of the first election, no candidate received an outright majority, with the largest being candidate A with 46.34%. Based on Instant Runoff Election strategy, the candidate with the lowest total votes is to be eliminated, so in this case, candidate D is eliminated. As follows, the first-preference votes for the eliminated candidate are given to voter back-ups. For the sake of the example, assume that of the total 75 votes Candidate D received, Candidate A was listed as their second choice by 50 voters, and Candidate B was listed as a second preference by 25 of the voters. [28]

Example 2:[edit]

The second example will demonstrate how the concept of Instant Runoff is used to achieve a winner in a RCV system in the case that a majority is not initially secured.

Adjusted Vote in a political race
Candidate Adjusted first-preference votes Percentage
Candidate A 525 51.22%
Candidate B 325 31.71%
Candidate C 175 17.07%

According to the figure in example two, Candidate A received 51.22% of the votes among the second tally, therefore, winning the election. The process of Instant runoff as demonstrated above would hypothetically continue until a Candidate receives a majority of the voter population, regardless of the number of recounts it would take.

Pros and Cons of RCV[edit]

Pros[edit]

Advocates of Ranked Choice Voting argue that RCV promotes majority support: the voting process continues until the winner is selected using a majority of votes, thus gaining support and favor over a greater majority of people. [29]Subsequently, RCV provides more choice for voters over candidates they choose, potentially, minimizing tactical voting whereby a voter would support another candidate more strongly than their honest preference, for the purpose to prevent an undesirable outcome. [30] For candidates that run a negative campaigning strategy, verbally harming and demeaning their running-mates, they may see a decline in voter turn out due to this behavior that some voters might frown upon. Compared to running primary elections, in order to decrease the number of candidates running for a particular position, a ranked choice voting system may cost less to run due to the requirement of only one election, rather than multiple primaries or run-off elections to narrow down the field. [31]

Cons[edit]

Critics of a Ranked Choice Voting system argue that the concept and practice of Ranked Choice Voting is new and a subset of voters dislike change, possibly causing them to dislike the system and not participate. Among other arguments is the possibility that the ballots and counting processes will be more expensive and prone to user error. As such, RCV will either require a computerized counting system or a hand counting system which possibly could be more labor intensive than that of Cardinal Voting. While utilizing a computerized counting system, critics of Ranked Voting argue it is still necessary to hold on to the paper ballots so that election recounts can still be performed, minimizing error and holding a greater validity of results. [32] Concurrently, new, diverse voices will emerge by providing candidates a starting ground for those with a lack of name recognition. Critics add that previously, it would be difficult for women and people of color to share their voice because of this lack of name recognition that their challengers may have, providing a more equal and fair competition ground for all. [33]

The “Vetting Process”[edit]

Vetting is a thorough investigative process that a company, individual, or political entity utilizes before making decisions in going forward in a collaborative and joint partnership project or utilized before choosing candidates who may or may not appear on a voter ballot. [34] Within United States Primary elections, it is generally understood that voters will become informed about the candidates’ strengths, weaknesses, and character to an extent which can prepare them to make an informed decision when the General election comes around. If a Ranked Choice Voting process is implemented, some argue that the absence of Primary elections may affect the “Vetting Process” and require a different system to allow individuals to become a candidate in an election. [35]

Uniqueness of votes[edit]

If there are a large number of candidates, which is quite common in single transferable vote elections, then it is likely that many preference voting patterns will be unique to individual voters.[36][37] For example, in the 2002 Irish general election, the electronic votes were published for the Dublin North constituency.[38] There were 12 candidates and almost 44,000 votes cast. The most common pattern (for the three candidates from one party in a particular order) was chosen by only 800 voters, and more than 16,000 patterns were chosen by just one voter each.

The number of possible complete rankings with no ties is the factorial of the number of candidates, N; but if ties are allowed freely, it is equal to the corresponding ordered Bell number and is asymptotic to

[39]

In the case common to instant-runoff voting in which no ties are allowed, except for unranked candidates who are tied for last place on a ballot, the number of possible rankings for N candidates is precisely

[40]

Use by politics[edit]

Countries and regions[edit]

Country Years in use Type Notes
Australia 1918–present[41][42] Single transferable vote, instant-runoff voting From 1949, the single transferable vote method has been used for upper house legislative elections.[43] Instant-runoff voting is used for lower house elections.[44]
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,[45] 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.[43] This is no longer the case.[46]
Fiji[47] 1998–present Instant-runoff voting
Hong Kong 1998–present[48] Instant-runoff voting[49] Instant-runoff voting is only used in the 4 smallest of Hong Kong's 29 functional constituencies.[50] Officially called preferential elimination voting, the system is identical to the instant-runoff voting.[49]
Ireland 1922–present Single transferable vote[51] Single transferable vote is prescribed by Constitution or statute for all public elections.[51] 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.[51]
Malta[43] 1921–present Single transferable vote
Nauru 1968–present[43] Borda count Nauru uses the Dowdall system, a variant of the Borda count that behaves more like FPTP.[52][53]
New Zealand 2004–present[54] Single transferable vote[55] Instant-runoff voting is used in only some single-seat elections, such as district health boards as well as some city and district councils.[55]
Northern Ireland 1973–present[43] Single transferable vote[56] Used for local government, European Parliament and the regional legislature, but not elections to Westminster.
Papua New Guinea 2007–present[57] Instant-runoff voting[11] Between 1964 and 1975, Papua New Guinea used a system that allowed voters the option of ranking candidates.[43] Currently, voters can rank only their top three choices.[58]
Slovenia 2000–present[59] Borda count Only two seats, which are reserved for Hungarian and Italian minorities, are decided using a Borda count.[60]
Sri Lanka 1978–present Contingent vote and open list Contingent vote is used for presidential elections,[43] and open list for legislative elections.[61]
United States 2020 Limited instant-runoff voting In their 2020 primaries, the Democratic Party permitted voters who could not be physically present at the Iowa and Nevada caucus to early vote using a preferential ballot.
Zimbabwe[62] 1979–1985 Instant-runoff voting Was only used for white candidates

Federal provinces or states[edit]

Province/state Country Years in use Type Notes
Alaska[63] United States 2022 Instant-runoff voting Approved by Alaska voters in 2020 via ballot measure.
Alberta[43] Canada 1952–1954 Instant-runoff voting
Australian Capital Territory[43] Australia 1993–present Single transferable vote
British Columbia[43] Canada 1926–1955 Instant-runoff voting
Maine[64] 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.
Manitoba[43] Canada 1927–1936 Instant-runoff voting
New South Wales[43] 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. Full preferential voting for lower house since 1981.
North Carolina[65] 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[43] 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.[66] In the 2018 elections, the first ones conducted under the new legislation, the city of London used ranked balloting,[67] while the cities of Kingston and Cambridge held referendums on whether to adopt ranked ballots for the next municipal elections in 2022.[68]
Queensland[43] 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[43] 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[43] 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[43] 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[43] 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.

Municipalities[edit]

City/town Years in use Type Notes
Ann Arbor, MI[69] 1975 only Instant-runoff voting
Aspen, CO[70] 2009 only Instant-runoff voting
Berkeley, CA[71] 2010–present Instant-runoff voting
Burlington, VT[72][73][74] 2005–2010; 2021–present Instant-runoff voting Repealed for mayoral elections after the 2009 election; in 2021 a referendum reinstated it for the city council elections.
Cambridge, MA[75] 1941–present Single transferable vote
Hendersonville, NC[76] 2007–2013 Instant-runoff voting part of a statewide pilot program,[77] deauthorized in 2013[78]
London 2000–present[79] Supplementary vote[80]
London, Ontario[81] 2018 – present Instant-runoff voting
Memphis, TN[12] 2011–present Instant-runoff voting
Minneapolis, MN[82] 2009–present Instant-runoff voting
New York City, NY[83][84] 2021–present Instant-runoff voting Only applies to primaries and special elections for municipal offices
Oakland, CA[71] 2010–present Instant-runoff voting
Portland, ME[12] 2011–present Instant-runoff voting
San Francisco, CA 2004–present[85] Instant-runoff voting[12]
San Leandro, CA[71] 2010–present Instant-runoff voting
Santa Fe, NM 2018–present Instant-runoff voting
St. Paul, MN 2011–present[86] Instant-runoff voting[87]
Takoma Park, MD[88] 2006–present Instant-runoff voting
Telluride, CO[89] 2011–present Instant-runoff voting

International organizations[edit]

Organization Years in use Type Notes
European Union[90] option to use single transferable vote Member countries can use either party-list proportional representation (not a type of preferential voting)[citation needed] or single transferable vote to elect MEPs

Use outside of politics[edit]

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.[91]

See also[edit]

References[edit]

  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. ^ a b c "Single Transferable Vote". www.electoral-reform.org.uk. Retrieved 2020-11-30.
  4. ^ a b "How to conduct an election by the Single Transferable Vote 3rd Edition". www.electoral-reform.org.uk. Retrieved 2020-11-30.
  5. ^ Toplak, Jurij (2006). "The parliamentary election in Slovenia, October 2004". Electoral Studies. 25 (4): 825–831. doi:10.1016/j.electstud.2005.12.006.
  6. ^ a b c d Mankiw, Gregory (2012). Principles of Microeconomics (6th ed.). South-Western Cengage Learning. pp. 475–479. ISBN 978-0538453042.
  7. ^ 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.
  8. ^ "Electoral Systems in Europe: An Overview". Brussels: European Centre for Parliamentary Research and Documentation. October 2000. Retrieved November 7, 2019.
  9. ^ 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)
  10. ^ Saari, Donald (1995). Basic Geometry of Voting. Springer. p. 46. ISBN 9783540600640.
  11. ^ a b c d Grofman, Bernard; Feld, Scott L. (2004). "If you like the alternative vote (a.k.a. the instant runoff), then you ought to know about the Coombs rule" (PDF). Electoral Studies. 23 (4): 641–659. doi:10.1016/j.electstud.2003.08.001.
  12. ^ a b c d Bialik, Carl (May 14, 2011). "Latest Issue on the Ballot: How to Hold a Vote". Wall Street Journal. Retrieved June 29, 2012.
  13. ^ Bryden, Joan (October 19, 2016). "Is Trudeau jockeying to avoid fulfilling promise on electoral reform?". Toronto Star. The Canadian Press. Retrieved October 27, 2016.
  14. ^ "Glossary". ElectionGuide. International Foundation for Electoral Systems. Archived from the original on July 17, 2012.
  15. ^ "Q&A: Electoral reform and proportional representation". BBC. 2010-05-11. Retrieved May 13, 2010.
  16. ^ Affairs, The Department of Internal. "STV Information". www.stv.govt.nz. Retrieved 2020-11-30.
  17. ^ FairVote.org. "Ranked Choice Voting / Instant Runoff". FairVote. Retrieved 2020-10-20.
  18. ^ "New York City Voters Just Adopted Ranked-Choice Voting in Elections". Time. Retrieved 2020-12-01.
  19. ^ Santucci, Jack (2017-09-10). "Evidence of a Winning-cohesion Tradeoff under Multi-winner Ranked-choice Voting". dx.doi.org. doi:10.31235/osf.io/qjtwn. Retrieved 2020-10-20.
  20. ^ "Ranked-choice voting (RCV)". Ballotpedia. Retrieved 2020-10-20.
  21. ^ Press, PATRICK WHITTLE Associated. "Maine's ranked choice voting rules and procedures, explained". starherald.com. Retrieved 2020-11-30.
  22. ^ "Ranked-choice voting (RCV)". Ballotpedia. Retrieved 2020-10-20.
  23. ^ "Ranked-choice voting (RCV)". Ballotpedia. Retrieved 2020-10-20.
  24. ^ Saari, Donald G. (1995). Basic Geometry of Voting. Springer-Verlag. pp. 101–103. ISBN 3-540-60064-7.
  25. ^ Regenwetter, Michel; Tsetlin, Ilia (2004). "Approval voting and positional voting methods: Inference, relationship, examples". Social Choice and Welfare. 22 (3): 539–566. doi:10.1007/s00355-003-0232-z. ISSN 0176-1714. JSTOR 41106611. S2CID 16226738.
  26. ^ Reilly, Benjamin (2002). "Social Choice in the South Seas: Electoral Innovation and the Borda Count in the Pacific Island Countries". International Political Science Review, Vol 23, No. 4, 355–72
  27. ^ "Ranked-choice voting (RCV)". Ballotpedia. Retrieved 2020-10-27.
  28. ^ Walsh, Matt (2020-10-14). "Walsh '23: The promises and pitfalls of ranked-choice voting". Brown Daily Herald. Retrieved 2020-12-01.
  29. ^ "Is ranked-choice voting a better way to decide elections?". news.yahoo.com. Retrieved 2020-12-01.
  30. ^ Bol, Damien; Verthé, Tom (2019-09-30). "Strategic Voting Versus Sincere Voting". Oxford Research Encyclopedia of Politics. doi:10.1093/acrefore/9780190228637.001.0001 (inactive 2021-01-19). Retrieved 2020-12-01.CS1 maint: DOI inactive as of January 2021 (link)
  31. ^ "Pros and Cons of Instant Runoff (Ranked Choice) Voting". MyLO. 2017-12-22. Retrieved 2020-11-11.
  32. ^ "In Our View: Ranked-choice voting cons outweigh the pros". The Columbian. Retrieved 2020-11-11.
  33. ^ "Ranked Choice Voting Can Make Government Look More Like Us". www.wbur.org. Retrieved 2020-11-30.
  34. ^ Kopp, Carol M. "The Vetting Process Defined". Investopedia. Retrieved 2020-11-11.
  35. ^ "How to Create a Vetting Process for Candidates". www.indeed.com. Retrieved 2020-12-01.
  36. ^ Election database February 1, 2004
  37. ^ Irish Commission on Electronic Voting 2004
  38. ^ Dublin County Returning Officer complete table of votes cast Dublin North (zip file)
  39. ^ Wilf, Herbert S. (January 1994) [1990]. "Chapter 5: Analytic and asymptotic methods". generatingfunctionology (Second ed.). Academic Press. pp. 175–76. ISBN 0127519564. Retrieved 2006-08-06.
  40. ^ Sloane, N. J. A. (ed.). "Sequence A007526". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  41. ^ "Our electoral system". About Australia. Australian Department of Foreign Affairs and Trade. May 2008. Retrieved June 28, 2012.
  42. ^ Brent, Peter. Short History of Preferential Voting. Mumble Blog, The Australian. April 17, 2011.
  43. ^ a b c d e f g h i j k l m n o p q r Sawer, Marian (2001). Elections: Full, Free & Fair. Federation Press. pp. 93–95. ISBN 978-1862873957.
  44. ^ "Country Profile: Australia: Learn More". ElectionGuide. International Foundation for Electoral Systems. Retrieved November 7, 2019.
  45. ^ "Liberals vote overwhelmingly in favour of one-member, one-vote". Liberal.ca. 2 May 2009. Archived from the original on 4 May 2011. Retrieved 17 April 2011.
  46. ^ "Country Profile: Estonia: Learn More". ElectionGuide. International Foundation for Electoral Systems. Retrieved November 7, 2019.
  47. ^ "Section 54: Voting and other matters". Constitution of Fiji. International Constitutional Law Project. Retrieved June 29, 2012.
  48. ^ 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.
  49. ^ a b "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.
  50. ^ "Functional Constituency Elections". 2000 Legislative Council Elections. Hong Kong Electoral Affairs Commission. 2000. Retrieved June 29, 2012.
  51. ^ a b c Farrell, David; Synott, Richard (December 2017). "The electoral system". In Coakley, John; Gallagher, Michael (eds.). Politics in the Republic of Ireland. Routledge. ISBN 978-1-317-31269-7.
  52. ^ "Country Profile: Nauru: Learn More". ElectionGuide. International Foundation for Electoral Systems. Retrieved November 7, 2019.
  53. ^ 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.
  54. ^ "STV legislation, background and further information". New Zealand Department of Internal Affairs. Retrieved September 25, 2015.
  55. ^ a b "STV – It's Simple To Vote". New Zealand Department of Internal Affairs. 2010. Retrieved June 29, 2012.
  56. ^ "Voting systems in Northern Ireland". Electoral Office for Northern Ireland. Retrieved February 8, 2020.
  57. ^ Blackwell, Eoin (June 20, 2012). "Observers urge peaceful PNG election". The Sydney Morning Herald. Retrieved June 29, 2012.
  58. ^ "Voting". Electoral Commission of Papua New Guinea. 2011. Retrieved June 30, 2012.
  59. ^ "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.
  60. ^ "Country Profile: Slovenia: Learn More". ElectionGuide. International Foundation for Electoral Systems. Retrieved November 7, 2019.
  61. ^ "Country Profile: Sri Lanka: Learn More". ElectionGuide. International Foundation for Electoral Systems. Retrieved November 7, 2019.
  62. ^ "Negotiations". Administration and Cost of Elections Project. ACE Electoral Knowledge Network. Retrieved July 6, 2012.
  63. ^ "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.
  64. ^ Russell, Eric, "Mainers vote to keep ranked-choice voting, with supporters holding commanding lead". Portland Press Herald, June 12, 2018.
  65. ^ Joyce, Robert, "Instant Runoff Voting". University of North Carolina: School of Government, November 2013.
  66. ^ "Legislation passes allowing Ontario municipalities to use ranked ballots". The Globe and Mail, June 7, 2016.
  67. ^ "London, Ont., votes to become first Canadian city to use ranked ballots". CBC News Windsor, May 2, 2017.
  68. ^ Coyne, Andrew, "Election reform is coming to Canada — somewhere, somehow, and soon". National Post, October 6, 2017.
  69. ^ "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.
  70. ^ Urquhart, Janet (June 28, 2012). "Marks prevails in lawsuit over Aspen election ballots". The Aspen Times. Retrieved June 29, 2012.
  71. ^ a b c "Ranked-Choice Voting". Alameda County Registrar of Voters. Retrieved June 29, 2012.
  72. ^ McCrea, Lynne (March 3, 2010). "Burlington Voters Repeal Instant Runoff Voting". Vermont Public Radio. Retrieved November 7, 2019.
  73. ^ "Can Once-Maligned Ranked-Choice Voting Make a Comeback in Burlington?".
  74. ^ "Voters approve all Burlington ballot issues".
  75. ^ "Choice Voting in Cambridge". FairVote.
  76. ^ "New Voting Method for November 6, 2007: Hendersonville Pilots Instant Runoff Voting" (PDF). Henderson County Board of Elections. 2007. Retrieved June 29, 2012.
  77. ^ Harbin, John (April 8, 2011). "Hendersonville votes to keep instant runoff ballots". BlueRidgeNow.com. Times-News. Retrieved June 29, 2012.
  78. ^ Joyce, Robert (November 2013). "Instant Runoff Voting". Coates' Canons. Retrieved 2018-07-11. The 2013 General Assembly repealed all legislation authorizing instant runoff elections in North Carolina.
  79. ^ "London's elections: How the voting works". BBC. May 3, 2000. Retrieved June 29, 2012.
  80. ^ "Voting systems in the UK". Parliament of the United Kingdom. Retrieved June 29, 2012.
  81. ^ "Ranked ballots a reality for 1st time in Ontario municipal elections". CBC News. Retrieved 2018-10-12.
  82. ^ Gilbert, Curtis (November 2, 2009). "Instant runoff voting FAQ". Minnesota Public Radio. Retrieved June 29, 2012.
  83. ^ "Ranked Choice Voting | New York City Campaign Finance Board". www.nyccfb.info. Retrieved 2021-02-18.
  84. ^ Chung, Christine (2021-02-02). "Ranked Choice Voting Takes Backseat in New York City Debut". THE CITY. Retrieved 2021-02-18.
  85. ^ Poundstone, William (2009). Gaming the Vote: Why Elections Aren't Fair (And What We Can Do About It). Macmillan. p. 170. ISBN 978-0809048922.
  86. ^ Baran, Madeleine (November 7, 2011). "Election Day in St. Paul Tuesday". Minnesota Public Radio. Retrieved June 29, 2012.
  87. ^ "Ranked Voting Information". Ramsey County. Retrieved June 29, 2012.
  88. ^ "City of Takoma Park Election 2011". City Of Takoma Park. 2011. Retrieved June 29, 2012.
  89. ^ "Instant Runoff Voting Brochure". Town of Telluride. 2011. Retrieved June 29, 2012.
  90. ^ "Country Profile: European Union: Learn More". ElectionGuide. International Foundation for Electoral Systems. Retrieved November 7, 2019.
  91. ^ "Eurovision Song Contest voting system". European Broadcasting Union. Retrieved February 10, 2020.