# Ranked voting

Sample ballot of ranked voting using written numbers
Sample ballot of ranked voting using column marks
Sample ballot of ranked voting using written names
Sample ballot of ranked voting using touch screen

Ranked-choice voting describes certain voting systems in which voters rank outcomes in a hierarchy on the ordinal scale (ordinal voting systems). In some areas ranked-choice voting is called preferential voting, but in other places this term has various other meanings.[1] When choosing between more than two options, preferential ballots collect more information from voters than first-past-the-post voting (also called plurality voting). This does not mean that preferential voting is intrinsically the best system; see Arrow's impossibility theorem.[Mankiw 1][2] There is, accordingly, no consensus among academics or public servants as to the best electoral system.[3]

There are many types of preferential voting, with several used in governmental elections: Instant-runoff voting is employed in Australia at the state and federal levels, in Ireland[4] 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. Borda count is used in Slovenia[5] 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.

The other major branch of voting systems are cardinal voting systems, where candidates are rated, rather than ranked.

## Variety of systemsEdit

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 for a ranked system,[6] so "Condorcet efficiency" is important when evaluating different methods of preferential voting.[7] The Condorcet winner is 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,[8] 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[9] and the complexity of the mechanism necessary.[citation needed]

### Instant-runoff votingEdit

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.[10] If this does not result in any candidate receiving a majority, further rounds of redistribution occur.[10] 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."[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.[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]

### Single transferable voteEdit

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

When STV is used for single-winner elections, it becomes equivalent to IRV.[12]

### Borda countEdit

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.[citation needed]

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[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.[13]

1. ^ See table in use by polities below

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.[15][16] For example, in the Irish general election, 2002, the electronic votes were published for the Dublin North constituency.[17] 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

${\displaystyle {\frac {N!}{2(\ln 2)^{N+1}}}}$ .[18]

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

${\displaystyle \sum _{n=1}^{N-1}{\frac {N!}{n!}}=\lfloor (e-1)N!-1\rfloor =\mathrm {floor} \left((e-1)N!-1\right)}$ .[19]

## Use by politiesEdit

Countries
Nation Year of first use Type Notes
Australia 1918[20] single transferable vote, Instant-runoff voting From 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] x 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.[Sawer 1] This is no longer the case.[CEPPS 4]
Fiji[21] 1998 Instant-runoff voting Fiji stopped using instant-runoff voting and switched to an Open List Proportional system for its election on September 17, 2014.
Hong Kong 1998[22] Instant-runoff voting[23] Instant-runoff voting is only used in the 4 smallest of Hong Kong's 29 functional constituencies.[24] Officially called preferential elimination voting, the system is identical to the instant-runoff voting.[23]
Ireland[Sawer 1] 1922 Instant-runoff voting, single transferable vote Single 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] 1921 single transferable vote
Nauru 1968[Sawer 1] Borda count[CEPPS 5] Nauru uses the Dowdall system, which is an improved version of the Borda count.[CEPPS 5]
New Zealand 2004[25] single transferable vote[26] Instant-runoff voting is used in only some single-seat elections, such as district health boards as well as some city and district councils.[26]
Northern Ireland 1973[Sawer 1] single transferable vote[27]
Papua New Guinea 2007[28] 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.[29]
Slovenia 2000[30] 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] 1978 contingent 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[31] 1979-1985 Instant-runoff voting only used for white candidates
Federated states
 Province/state Country Years in use Type Notes Alberta[Sawer 1] Canada 1952-1954 Instant-runoff voting Australian Capital Territory[Sawer 1] Australia 1993–present single transferable vote British Columbia[Sawer 1] Canada 1926-1955 Instant-runoff voting Manitoba[Sawer 1] Canada 1927-1936 Instant-runoff voting New South Wales[Sawer 1] Australia 1918–present single 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] Australia 1980 only[citation needed] x Queensland[Sawer 1] Australia 1892-1942, 1962–present contingent vote (1892-1942), instant-runoff voting with compulsory preferences (1962-1992), Instant-runoff voting (1992–2016), instant-runoff voting with compulsory preferences (2016-present) South Australia[Sawer 1] Australia 1929-1935, 1982–present Instant-runoff voting in multi-member districts (1929-1935), single transferable vote (1982–present) used to decide upper house legislative elections only Tasmania[Sawer 1] Australia 1907–present single transferable vote Since 1909, instant-runoff voting has been used in Tasmania to decide upper house legislative elections. Victoria[Sawer 1] Australia 1911–present Instant-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] Australia 1907–present Instant-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 Maine[Sawer 1] United States 2016-present Instant-runoff voting
International organizations
 Organization Year of first use Type Notes European Union[CEPPS 8] x option to use single transferable vote Member countries can use either proportional representation (not a type of preferential voting)[citation needed] or single transferable vote to elect MEPs
Municipalities
 City/town Years in use Type Notes Ann Arbor, MI[32] 1975 only Instant-runoff voting Aspen, CO[33] 2009 only Instant-runoff voting Berkeley, CA[34] 2010–present Instant-runoff voting Burlington, VT[35] 2005-2010 Instant-runoff voting Cambridge, MA[36] 1941--present single transferable vote Hendersonville, NC[37] 2007–present Instant-runoff voting part of a statewide pilot program[38] London 2000[39]-present supplementary vote[40] Memphis, TN[10] 2011–present Instant-runoff voting Minneapolis, MN[41] 2009–present Instant-runoff voting Oakland, CA[34] 2010–present Instant-runoff voting Portland, ME[10] 2011–present Instant-runoff voting San Francisco, CA 2004[42]-present Instant-runoff voting[10] San Leandro, CA[34] 2010–present Instant-runoff voting Santa Fe, NM 2018–present Instant-runoff voting St. Paul, MN 2011[43]-present Instant-runoff voting[44] Takoma Park, MD[45] 2006–present Instant-runoff voting Telluride, CO[46] 2011–present Instant-runoff voting