Ranked voting system

This article is about voting systems that use ranked ballots. For voting systems that use ballots rated on the interval scale, see cardinal voting systems.

Preferential voting or rank voting describes certain voting systems in which voters rank outcomes in a hierarchy on the ordinal scale. When choosing between more than two options, preferential voting systems provide a number of advantages over first-past-the-post voting (also called plurality voting). This does not mean that preferential voting is the best system; Arrow's impossibility theorem proves that no preferential method can simultaneously obtain all properties desirable in a voting system.[Mankiw 1][1] There is likewise no consensus among academics or public servants as to the best electoral system.[2]

There are many types of preferential voting, but only instant-runoff voting and single transferable vote are being used in governmental elections. Instant runoff voting is employed in Australia at the state and federal levels, in Ireland for its presidential elections, and by some cities in the United States, United Kingdom, and New Zealand. The single transferable vote is used for national elections in the Republic of 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.

Variety of systems

There are many 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,[3] so "Condorcet efficiency" is important when evaluating different methods of preferential voting.[4] This choice is also the one that would win every two-way contest against every other alternative.[Mankiw 2]

Another criterion used to gauge the effectiveness of a preferential voting system is its ability to withstand manipulative voting strategies,[5] 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[6] and the complexity of the mechanism necessary.

Instant-runoff voting

Main article: Instant-runoff voting

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.[7] If this does not result in any candidate receiving a majority, further rounds of redistribution occur.[7] Or, in other words, "[...] voters would rank their first, second and subsequent choices on the ballot. The candidate with the fewest votes would be dropped and his or her supporters’ second choices would be counted and so on until one candidate emerged with more than 50 per cent."[8]

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.[G&F 1] At the same time, this system fails the monotonicity criterion, where ranking a candidate higher can lessen the chances he or she will be elected. Additionally, instant-runoff voting has a lower Condorcet efficiency than similar systems when there are more than four choices.[G&F 2]

Borda count

Main article: Borda count

In the Borda count, 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.[Mankiw 1] This method is named after its inventor, French mathematician Jean-Charles de Borda.[Mankiw 1] 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. That is, the Borda count does not exhibit independence of irrelevant alternatives[Mankiw 1] or independence of clones. The Borda count can be easily manipulated by adding candidates, called clones, whose views are identical to the preferred candidate's. An example of this strategy can be seen in Kiribati's 1991 presidential nomination contest.[9]

Single transferable vote

This is one of the preferential voting systems most used by countries and states.[notes 1] It uses 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.[CEPPS 1] 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.[CEPPS 1]

  1. See table in use by polities below

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.[10][11] For example, in the Irish general election, 2002, the electronic votes were published for the Dublin North constituency.[12] 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 with ties it is equal to the corresponding ordered Bell number and is asymptotic to


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


Use by polities

Nation Year of first use Type Notes
Australia 1918[15] single transferable vote, Instant-runoff votingFrom 1949, the single transferable vote method has been used for upper house legislative elections.[Sawer 1] Instant-runoff voting is used for lower house elections.[CEPPS 2]
Czech Republic[CEPPS 3] xcontingent voteonly used to decide lower house legislative elections
Estonia1990-c. 2001single transferable vote As of 2001 single transferable vote had been in use since 1990 to decide legislative elections.[Sawer 1] This is no longer the case.[CEPPS 4]
Fiji[16] 1998Instant-runoff voting| Fiji stopped using instant-runoff voting and switched to an Open List Proportional system for its election on September 17, 2014.
Hong Kong1998[17]Instant-runoff voting[18]Instant-runoff voting is only used in the 4 smallest of Hong Kong's 29 functional constituencies.[19] Officially called preferential elimination voting, the system is identical to the instant-runoff voting.[18]
Ireland[Sawer 1]1922Instant-runoff voting, single transferable voteSingle transferable vote is used to decide legislative elections only.[Sawer 1] Since 1937 Ireland has used the Instant-runoff voting to decide presidential elections.[Sawer 1]
Malta[Sawer 1]1921single transferable vote
Nauru1968[Sawer 1]Borda count[CEPPS 5]Nauru uses the Dowdall system, which is an improved version of the Borda count.[CEPPS 5]
New Zealand2004[20]single transferable vote[21]Instant-runoff voting is used in only some single-seat elections, such as district health boards as well as some city and district councils.[21]
Northern Ireland1973[Sawer 1]single transferable vote[22]
Papua New Guinea2007[23]Instant-runoff voting[G&F 3]Between 1964 and 1975 PNG used a system that allowed voters the option of ranking candidates.[Sawer 1] Currently, voters can rank only their top three choices.[24]
Slovenia2000[25]Borda count[CEPPS 6]Only two seats, which are reserved for Hungarian and Italian minorities, are decided using a Borda count.[CEPPS 6]
Sri Lanka[Sawer 2]1978contingent vote and open list[CEPPS 7]In Sri Lanka contingent vote is used to decide presidential elections[Sawer 1] and legislative elections, open list.[CEPPS 7]
Zimbabwe[26]1979-1985Instant-runoff votingonly used for white candidates
Federated states
Province/state Country Years in use Type Notes
Alberta[Sawer 1]Canada1952-1954Instant-runoff voting
Australian Capital Territory[Sawer 1]Australia1993–presentsingle transferable vote
British Columbia[Sawer 1]Canada1926-1955Instant-runoff voting
Manitoba[Sawer 1]Canada1927-1936Instant-runoff voting
New South Wales[Sawer 1]Australia1918–presentsingle transferable vote (1918-1926), contingent vote (1926-1928), instant-runoff voting with compulsory preferences (1929-1980), Instant-runoff voting (1981–present)Since 1978, NSW has used the single transferable vote method to decide upper house legislative elections only.
Northern Territory[Sawer 1]Australia1980 onlyx
Queensland[Sawer 1]Australia1892-1942, 1962–presentcontingent vote (1892-1942), instant-runoff voting with compulsory preferences (1962-1992), Instant-runoff voting (1992–present)
South Australia[Sawer 1]Australia1929-1935, 1982–presentInstant-runoff voting in multi-member districts (1929-1935), single transferable vote (1982–present)used to decide upper house legislative elections only
Tasmania[Sawer 1]Australia1907–presentsingle transferable voteSince 1909, instant-runoff voting has been used in Tasmania to decide upper house legislative elections.
Victoria[Sawer 1]Australia1911–presentInstant-runoff voting (1911-1915), instant-runoff voting with compulsory preferences (1916–present)Prior to 1916, Victoria did not use any preferential voting method to decide upper house legislative elections.
Western Australia[Sawer 1]Australia1907–presentInstant-runoff voting (1907-1911), instant-runoff voting with compulsory preferences (1912–present)Since 1989, Western Australia has used the single transferable vote method to decide upper house legislative elections
International organizations
Organization Year of first use Type Notes
European Union[CEPPS 8]xoption to use single transferable voteMember countries can use either proportional representation (not a type of preferential voting) or single transferable vote to elect MEPs
City/town Years in use Type Notes
Ann Arbor, MI[27]1975 onlyInstant-runoff voting
Aspen, CO[28]2009 onlyInstant-runoff voting
Berkeley, CA[29]2010–presentInstant-runoff voting
Burlington, VT[30]2005-2010Instant-runoff voting
Cambridge, MA[31]1941--presentsingle transferable vote
Hendersonville, NC[32]2007–presentInstant-runoff votingpart of a statewide pilot program[33]
London2000[34]-presentsupplementary vote[35]
Memphis, TN[7]2011–presentInstant-runoff voting
Minneapolis, MN[36]2009–presentInstant-runoff voting
Oakland, CA[29]2010–presentInstant-runoff voting
Portland, ME[7]2011–presentInstant-runoff voting
San Francisco, CA2004[37]-presentInstant-runoff voting[7]
San Leandro, CA[29]2010–presentInstant-runoff voting
St. Paul, MN2011[38]-present Instant-runoff voting[39]
Takoma Park, MD[40]2006–present Instant-runoff voting
Telluride, CO[41]2011–presentInstant-runoff voting

See also

External links


  1. "Interview with Dr. Kenneth Arrow". The Center for Election Science. October 6, 2012. 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.
  2. "Electoral Systems in Europe: An Overview". European Parliament in Brussels: European Centre for Parliamentary Research and Documentation. October 2000. Retrieved July 6, 2012.
  3. Saari, Donald (1995). Basic Geometry of Voting. Springer. p. 46. ISBN 9783540600640.
  4. Gofman and Feld, 2004, pp. 649
  5. Gofman and Feld, 2004, pp. 647
  6. Gofman and Feld, 2004, pp. 652
  7. 1 2 3 4 5 Bialik, Carl (May 14, 2011). "Latest Issue on the Ballot: How to Hold a Vote". Wall Street Journal. Retrieved June 29, 2012.
  8. JOAN BRYDEN The Canadian Press (Oct 19, 2016). "Is Trudeau jockeying to avoid fulfilling promise on electoral reform?". Toronto Star. Retrieved October 27, 2016.
  9. Reilley, Benjamin. "Social Choice in the South Seas: Electoral Innovation and the Borda Count in the Pacific Island Countries". International Political Science Review (2002), Vol 23, No. 4, 355–372
  10. Election database 1st February 2004
  11. Irish Commission on Electronic Voting 2004
  12. Dublin County Returning Officer complete table of votes cast Dublin North (zip file)
  13. Wilf, Herbert S. (January 1994) [1990]. "Chapter 5: Analytic and asymptotic methods". generatingfunctionology (Second ed.). Academic Press. pp. 175–176. ISBN 0-12-751956-4. Retrieved 2006-08-06.
  14. OEIS A007526
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  16. "Section 54: Voting and other matters". Constitution of Fiji. International Constitutional Law Project. Retrieved June 29, 2012.
  17. 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.
  18. 1 2 "Ch. 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 Comisson. Retrieved June 29, 2012.
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  21. 1 2 "STV - It's Simple To Vote". New Zealand Department of Internal Affairs. 2010. Retrieved June 29, 2012.
  22. "Frequently Asked Questions - PR/STV Voting System". Electoral Office for Northern Ireland. 2006. Retrieved June 29, 2012.
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  26. "Negotiations". Administration and Cost of Elections Project. ACE Electoral Knowledge Network. Retrieved July 6, 2012.
  27. "Instant Runoff Voting (IRV): History of Use in Ann Arbor". Green Party of Michigan. 1998. Retrieved June 29, 2012.
  28. Urquhart, Janet (June 28, 2012). "Marks prevails in lawsuit over Aspen election ballots". The Aspen Times. Retrieved June 29, 2012.
  29. 1 2 3 "Ranked-Choice Voting". Alameda County Registrar of Voters. Retrieved June 29, 2012.
  30. McCrea, Lynne (March 3, 2010). vote-voting/ "Burlington Voters Repeal Instant Runoff Voting" Check |url= value (help). Vermont Public Radio. Retrieved June 29, 2012.
  31. "Choice Voting in Cambridge". FairVote.
  32. "New Voting Method for November 6, 2007: Hendersonville Pilots Instant Runoff Voting" (PDF). Henderson County Board of Elections. 2007. Retrieved June 29, 2012.
  33. Harbin, John (April 8, 2011). "Hendersonville votes to keep instant runoff ballots". BlueRidgeNow.com. Times-News. Retrieved June 29, 2012.
  34. "London's elections: How the voting works". BBC. 3 May 2000. Retrieved June 29, 2012.
  35. "Voting systems in the UK". Parliament of the United Kingdom. Retrieved June 29, 2012.
  36. Gilbert, Curtis (November 2, 2009). "Instant runoff voting FAQ". Minnesota Public Radio. Retrieved June 29, 2012.
  37. Poundstone, William (2009). Gaming the Vote: Why Elections Aren't Fair (And What We Can Do About It). Macmillan. p. 170. ISBN 9780809048922.
  38. Baran, Madeleine (November 7, 2011). "Election Day in St. Paul Tuesday". Minnesota Public Radio. Retrieved June 29, 2012.
  39. "Ranked Voting Information". Ramsey County. Retrieved June 29, 2012.
  40. "CITY OF TAKOMA PARK ELECTION 2011". City Of Takoma Park. 2011. Retrieved June 29, 2012.
  41. "Instant Runoff Voting Brochure". Town of Telluride. 2011. Retrieved June 29, 2012.
  1. 1 2 3 4 Principles of Microeconomics. p. 475.
  2. Gregory Mankiw (2012). Principles of Microeconomics (6 ed.). South-Western Cengage Learning. pp. 478–479. ISBN 978-0-538-45304-2.
  1. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 Sawer, Marian (2001). Elections: Full, Free & Fair. Federation Press. p. 93. ISBN 9781862873957.
  2. Elections: Full, Free & Fair. p. 95.
  1. 1 2 "Glossary". ElectionGuide. Consortium for Elections and Political Process Strengthening. Retrieved July 1, 2012.
  2. "Country Profile: Australia". 2010-07-26. Retrieved June 30, 2012.
  3. "Country Profile: Czech Republic". 2012-04-25. Retrieved June 30, 2012.
  4. "Country Profile: Estonia". 2011-04-15. Retrieved June 30, 2012.
  5. 1 2 "Country Profile: Nauru". 2011-11-16. Retrieved June 30, 2012.
  6. 1 2 "Country Profile: Slovenia". 2012-02-28. Retrieved June 30, 2012.
  7. 1 2 "Country Profile: Sri Lanka". 2010-02-18. Retrieved June 30, 2012.
  8. "Country Profile: European Union". February 4, 2010. Retrieved June 30, 2012.
  1. Gofman and Feld, 2004, pp. 647
  2. Gofman and Feld, 2004, pp. 652
  3. Bernard Grofman, Scott L. Feld (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: 653. doi:10.1016/j.electstud.2003.08.001.
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