Ranked Voting
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Ranked Voting
Sample ballot of ranked voting using written numbers

Ranked voting, also called ranked-choice voting, is an election voting system in which voters rank choices in a hierarchy on the ordinal scale (ordinal voting systems): 1st, 2nd, 3rd, etc. In some areas, ranked-choice voting is called preferential voting, but in other places this term has various more-specialized meanings.[1] The other major branch of voting systems is cardinal voting, where candidates are independently rated rather than ranked relative to each other.[2]

In a ranked-choice voting system, voters always have more than two options, and this leads to preferential ballots collecting more information from voters than single-mark ballots used in First-Past-The-Post, Mixed-Member Proportional, etc.

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.[3][4] There is, accordingly, no consensus among academics or public servants as to the "best" electoral system.[5]

There are many types of preferential voting, with several used in governmental elections. Instant-runoff voting is employed in Australian state and federal elections, in Ireland[6] 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[6] and Nauru. Contingent vote and Supplementary vote are also used in a few locations. Condorcet methods have found more use among private organizations and minor parties.

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.[1][7] According to this view, all electoral methods are preferential, but to different degrees and may even be classified according to their preferentiality.[1] By this logic, cardinal voting methods like Score voting or STAR voting are also "preferential".

## Different types of systems

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,[8] so "Condorcet efficiency" is important when evaluating different methods of preferential voting.[9] The Condorcet winner is the one that would win every two-way contest against every other alternative.[3]

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.[9]

### Instant-runoff voting

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.[10][11]

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.[9]

### Single transferable vote

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.[12]

When STV is used for single-winner elections, it becomes equivalent to IRV.[13]

### Positional voting

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.[14]

#### Borda count

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.[3] Instead of selecting a Condorcet winner, this system may select a choice that reflects an average of the preferences of the constituency.[]

This system suffers from the fact that the outcome it selects is dependent on the other choices present.[clarification needed] That is, the Borda count does not exhibit independence of irrelevant alternatives[3] or independence of clones. The Borda count can be easily manipulated by adding candidates, called clones, whose views are similar to the preferred candidate's. An example of this strategy can be seen in Kiribati's 1991 presidential nomination contest.[15]

## Uniqueness of votes

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.[16][17] For example, in the 2002 Irish general election, the electronic votes were published for the Dublin North constituency.[18] 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

${\displaystyle {\frac {N!}{2(\ln 2)^{N+1}}}}$[19]

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

${\displaystyle \sum _{n=1}^{N-1}{\frac {N!}{n!}}=\lfloor (e-1)N!-1\rfloor =\mathrm {floor} \left((e-1)N!-1\right)}$[20]

## Use by politics

### Countries and regions

Country Years in use Type Notes
Australia 1918-present[21][22] Single transferable vote, instant-runoff voting From 1949, the single transferable vote method has been used for upper house legislative elections.[23] Instant-runoff voting is used for lower house elections.[24]
Czech Republic[25] ? Contingent vote only used to decide lower house legislative elections
Estonia 1990-c. 2001 Single transferable vote As of 2001, single transferable vote had been in use since 1990 to decide legislative elections.[23] This is no longer the case.[26]
Fiji[27] 1998-present Instant-runoff voting
Hong Kong 1998-present[28] Instant-runoff voting[29] Instant-runoff voting is only used in the 4 smallest of Hong Kong's 29 functional constituencies.[30] Officially called preferential elimination voting, the system is identical to the instant-runoff voting.[29]
Ireland 1922-present Instant-runoff voting, single transferable vote Single transferable vote is used to decide legislative elections only. Since 1937 Ireland has used instant-runoff voting to decide presidential elections.[23]
Malta[23] 1921-present Single transferable vote
Nauru 1968-present[23] Borda count Nauru uses the Dowdall system, a variant of the Borda count that behaves more like FPTP.[31][32]
New Zealand 2004-present[33] Single transferable vote[34] Instant-runoff voting is used in only some single-seat elections, such as district health boards as well as some city and district councils.[34]
Northern Ireland 1973-present[23] Single transferable vote[35] Used for local government, European Parliament and the regional legislature, but not elections to Westminster.
Papua New Guinea 2007-present[36] Instant-runoff voting[9] Between 1964 and 1975, PNG used a system that allowed voters the option of ranking candidates.[23] Currently, voters can rank only their top three choices.[37]
Slovenia 2000-present[38] Borda count Only two seats, which are reserved for Hungarian and Italian minorities, are decided using a Borda count.[39]
Sri Lanka 1978-present Contingent vote and open list Contingent vote is used for presidential elections[23], and open list for legislative elections.[40]
Zimbabwe[41] 1979-1985 Instant-runoff voting only used for white candidates

### Federal provinces or states

Province/state Country Years in use Type Notes
Alberta[23] Canada 1952-1954 Instant-runoff voting
Australian Capital Territory[23] Australia 1993-present Single transferable vote
British Columbia[23] Canada 1926-1955 Instant-runoff voting
Maine[42] United States 2018-present Instant-runoff voting ("Ranked-choice 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[23] Canada 1927-1936 Instant-runoff voting
New South Wales[23] 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[43] 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[23] 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.[44] In the 2018 elections, the first ones conducted under the new legislation, the city of London used ranked balloting,[45] while the cities of Kingston and Cambridge held referendums on whether to adopt ranked ballots for the next municipal elections in 2022.[46]
Queensland[23] 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[23] 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[23] 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[23] 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[23] 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.

### International organizations

Organization Years in use Type Notes
European Union[64] option to use single transferable vote Member countries can use either proportional representation (not a type of preferential voting)[] or single transferable vote to elect MEPs

## References

1. ^ 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).
2. ^ 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.
3. ^ a b c d Mankiw, Gregory (2012). Principles of Microeconomics (6th ed.). South-Western Cengage Learning. pp. 475-479. ISBN 978-0538453042.
4. ^ 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.
5. ^ "Electoral Systems in Europe: An Overview". Brussels: European Centre for Parliamentary Research and Documentation. October 2000. Retrieved 2019.
6. ^ a b Toplak, Jurij (2006). "The parliamentary election in Slovenia, October 2004". Electoral Studies. 25 (4): 825-31. doi:10.1016/j.electstud.2005.12.006.
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. ^ Saari, Donald (1995). Basic Geometry of Voting. Springer. p. 46. ISBN 9783540600640.
9. ^ 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.
10. ^ a b c d Bialik, Carl (May 14, 2011). "Latest Issue on the Ballot: How to Hold a Vote". Wall Street Journal. Retrieved 2012.
11. ^ Bryden, Joan (October 19, 2016). "Is Trudeau jockeying to avoid fulfilling promise on electoral reform?". Toronto Star. The Canadian Press. Retrieved 2016.
12. ^ "Glossary". ElectionGuide. International Foundation for Electoral Systems. Archived from the original on July 17, 2012.
13. ^ "Q&A: Electoral reform and proportional representation". BBC. 2010-05-11. Retrieved 2010.
14. ^ Saari, Donald G. (1995). Basic Geometry of Voting. Springer-Verlag. pp. 101-103. ISBN 3-540-60064-7.
15. ^ 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
16. ^ Election database February 1, 2004
17. ^
18. ^ Dublin County Returning Officer complete table of votes cast Dublin North (zip file)
19. ^ Wilf, Herbert S. (January 1994) [1990]. "Chapter 5: Analytic and asymptotic methods". generatingfunctionology (Second ed.). Academic Press. pp. 175-76. ISBN 0127519564. Retrieved .
20. ^ Sloane, N. J. A. (ed.). "Sequence A007526". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
21. ^ "Our electoral system". About Australia. Australian Department of Foreign Affairs and Trade. May 2008. Retrieved 2012.
22. ^ Brent, Peter. Short History of Preferential Voting. Mumble Blog, The Australian. April 17, 2011.
23. Sawer, Marian (2001). Elections: Full, Free & Fair. Federation Press. pp. 93-95. ISBN 978-1862873957.
24. ^ "Country Profile: Australia: Learn More". ElectionGuide. International Foundation for Electoral Systems. Retrieved 2019.
25. ^ "Country Profile: Czech Republic: Learn More". ElectionGuide. International Foundation for Electoral Systems. Retrieved 2019.
26. ^ "Country Profile: Estonia: Learn More". ElectionGuide. International Foundation for Electoral Systems. Retrieved 2019.
27. ^ "Section 54: Voting and other matters". Constitution of Fiji. International Constitutional Law Project. Retrieved 2012.
28. ^ 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 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 2012.
29. ^ 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 2012.
30. ^ "Functional Constituency Elections". 2000 Legislative Council Elections. Hong Kong Electoral Affairs Commission. 2000. Retrieved 2012.
31. ^ "Country Profile: Nauru: Learn More". ElectionGuide. International Foundation for Electoral Systems. Retrieved 2019.
32. ^ 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.
33. ^ "STV legislation, background and further information". New Zealand Department of Internal Affairs. Retrieved 2015.
34. ^ a b "STV - It's Simple To Vote". New Zealand Department of Internal Affairs. 2010. Retrieved 2012.
35. ^ "Frequently Asked Questions - PR/STV Voting System". Electoral Office for Northern Ireland. 2006. Retrieved 2012.
36. ^ Blackwell, Eoin (June 20, 2012). "Observers urge peaceful PNG election". The Sydney Morning Herald. Retrieved 2012.
37. ^ "Voting". Electoral Commission of Papua New Guinea. 2011. Retrieved 2012.
38. ^ "Article 80: The National Assembly; Composition and Election" (PDF). Constitution of the Republic of Slovenia. United Nations Public Administration Network. pp. 47-48. Retrieved 2012.
39. ^ "Country Profile: Slovenia: Learn More". ElectionGuide. International Foundation for Electoral Systems. Retrieved 2019.
40. ^ "Country Profile: Sri Lanka: Learn More". ElectionGuide. International Foundation for Electoral Systems. Retrieved 2019.
41. ^ "Negotiations". Administration and Cost of Elections Project. ACE Electoral Knowledge Network. Retrieved 2012.
42. ^ Russell, Eric, "Mainers vote to keep ranked-choice voting, with supporters holding commanding lead". Portland Press Herald, June 12, 2018.
43. ^ Joyce, Robert, "Instant Runoff Voting". University of North Carolina: School of Government, November 2013.
44. ^
45. ^ "London, Ont., votes to become 1st Canadian city to use ranked ballots". CBC News Windsor, May 2, 2017.
46. ^
47. ^ "Instant Runoff Voting (IRV): History of Use in Ann Arbor". Green Party of Michigan. 1998. Archived from the original on February 8, 2012. Retrieved 2012.
48. ^ Urquhart, Janet (June 28, 2012). "Marks prevails in lawsuit over Aspen election ballots". The Aspen Times. Retrieved 2012.
49. ^ a b c "Ranked-Choice Voting". Alameda County Registrar of Voters. Retrieved 2012.
50. ^ McCrea, Lynne (March 3, 2010). "Burlington Voters Repeal Instant Runoff Voting". Vermont Public Radio. Retrieved 2019.
51. ^ "Choice Voting in Cambridge". FairVote.
52. ^ "New Voting Method for November 6, 2007: Hendersonville Pilots Instant Runoff Voting" (PDF). Henderson County Board of Elections. 2007. Retrieved 2012.
53. ^ Harbin, John (April 8, 2011). "Hendersonville votes to keep instant runoff ballots". BlueRidgeNow.com. Times-News. Retrieved 2012.
54. ^ Joyce, Robert (November 2013). "Instant Runoff Voting". Coates' Canons. Retrieved . The 2013 General Assembly repealed all legislation authorizing instant runoff elections in North Carolina.
55. ^ "London's elections: How the voting works". BBC. May 3, 2000. Retrieved 2012.
56. ^ "Voting systems in the UK". Parliament of the United Kingdom. Retrieved 2012.
57. ^ "Ranked ballots a reality for 1st time in Ontario municipal elections". CBC News. Retrieved .
58. ^ Gilbert, Curtis (November 2, 2009). "Instant runoff voting FAQ". Minnesota Public Radio. Retrieved 2012.
59. ^ Poundstone, William (2009). Gaming the Vote: Why Elections Aren't Fair (And What We Can Do About It). Macmillan. p. 170. ISBN 978-0809048922.
60. ^ Baran, Madeleine (November 7, 2011). "Election Day in St. Paul Tuesday". Minnesota Public Radio. Retrieved 2012.
61. ^ "Ranked Voting Information". Ramsey County. Retrieved 2012.
62. ^ "City of Takoma Park Election 2011". City Of Takoma Park. 2011. Retrieved 2012.
63. ^ "Instant Runoff Voting Brochure". Town of Telluride. 2011. Retrieved 2012.
64. ^ "Country Profile: European Union: Learn More". ElectionGuide. International Foundation for Electoral Systems. Retrieved 2019.

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