# Ranked voting system

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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 always the best system; Arrow's impossibility theorem proves that no method can simultaneously obtain all properties desirable in a voting system.[Mankiw 1] There is likewise no consensus among academics or public servants as to the best electoral system.[1]

There are many types of preferential voting, but currently only instant-runoff voting (alternative vote) and single transferable vote are 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, 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,[2] so "Condorcet efficiency" is important when evaluating different methods of preferential voting.[3] 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,[4] 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[5] and the complexity of the mechanism necessary.[citation needed]

### Instant-runoff or preferential voting

Used in national elections in Australia, this system simulates 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 fewest number of first choices are added to the totals of the top-ranked candidate still in the race.[6] If this does not result in any candidate receiving a majority, further rounds of redistribution occur.[6]

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, alternative voting has a lower Condorcet efficiency than similar systems when there are more than four choices.[G&F 2]

### 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.[citation needed]

However, as explained in the main article, in some circumstances the Borda count may degenerate into a first-past-the-post ballot.

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 implication here is that a Borda count can be easily manipulated simply by including additional candidates.[citation needed]

### Single transferable vote

This is currently 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 smallest amount 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

## Superiority v. FPTP

When choosing between more than two options, preferential voting achieves outcomes better than those produced by a first-past-the-post system. When endorsing a switch to a preferential voting system in 2011, British politician Nick Clegg stated, "first-past-the-post leads to a whole host of problems... it means MPs can go about their business without ever having to appeal to a majority of their own constituents...".[8] He also stated that a preferential voting method like instant runoff voting would result in politicians "work[ing] harder to appeal to more people than before".[8] Academic experts have also rejected first-past-the-post; at a 2011 LSE workshop attended by 22 voting theory specialists, none endorsed first-past-the-post as the "best voting procedure".[9]

The first-past-the-post system will indeed occasionally elect a candidate who would have lost out to every other option in a two-way contest (the so-called Condorcet loser) by splitting the opposition vote. It happens even more frequently (for a similar reason) that the winner is not the Condorcet winner.[Mankiw 2]

Many countries use a two-round system (a runoff election) to improve the fairness of the election.

Many arguments for preferential voting being superior to first-past-the-post rely to some extent on several assumptions: that voters have single peaked preferences over a single dimension (e.g. liberal v. conservative), that choices can be placed on a continuum, and that voters know accurately where each candidate lies on that continuum. However even if these assumptions are only partially true, the first-past-the-post system is still likely to be less fair.

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

$\frac{N!}{2(\ln 2)^{N+1}}$.[13]

In the case common to IRV 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

$\sum_{n=1}^{N-1} \frac{N!}{n!} = \lfloor (e-1)N! - 1 \rfloor = \mathrm{floor}\left( (e-1)N! - 1 \right)$.[14]

## Use by polities

Countries
 Nation Year of first use Type Notes Australia 1918[15] single transferable vote, alternative vote From 1949, the single transferable vote method has been used for upper house legislative elections.[Sawer 1] Alternative vote is used for lower house elections.[CEPPS 2] Austria 1949[16] open list[1] Belgium 1945[16] open list[1] Brazil x open list[17] Chile[17] 1958-1973 open list Colombia[CEPPS 3] x open list Political parties choose between open list and closed list Cyprus x open list[1] Czech Republic[CEPPS 4] x contingent vote only used to decide lower house legislative elections Denmark 1945[16] open list[1] Estonia x open list[CEPPS 5] 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 5] Estonia's current open list system may not actually be a preferential voting system as it may be that voters cast only one preference vote. Fiji[18] 1998 alternative vote Finland 1945[16] open list[1] Greece 1975-1984, 1996[16] open list[1] Hong Kong 1998[19] alternative vote[20] alternative vote is only used in the 4 smallest of Hong Kong's 29 functional constituencies.[21] Officially called preferential elimination voting, the system is identical to the alternative vote.[20] Indonesia 2004[22] open list only used to decided the elections of one legislative chamber[CEPPS 6] Iraq[23] 2009 open list Ireland[Sawer 1] 1922 alternative vote, single transferable vote Single transferable vote is used to decide legislative elections only.[Sawer 1] Since 1937 Ireland has used the alternative vote to decide presidential elections.[Sawer 1] Italy 1946-1994[16] open list[24] Latvia[CEPPS 7] x open list only used to decide legislative elections Liechtenstein x open list[1] Luxembourg 1945[16] open list[CEPPS 8] Malta[Sawer 1] 1921 single transferable vote Nauru 1968[Sawer 1] Borda count[CEPPS 9] Nauru uses the Dowdall system, which is an improved version of the Borda count.[CEPPS 9] Netherlands 1945[16] open list[CEPPS 10] only used to decide lower house legislative elections[CEPPS 10] New Zealand x single transferable vote[25] alternative vote is used in only some elections, such as district health boards as well as some city and district councils.[25] Northern Ireland 1973[Sawer 1] single transferable vote[26] Norway 1945[16] open list[CEPPS 11] Papua New Guinea 2007[27] alternative vote[G&F 3] Between 1964 and 1975 PNG used a system that allowed voters the option of ranking candidates.[Sawer 1] Currently, voters must rank only their top three choices.[28] San Marino x open list[1] Slovakia[CEPPS 12] x open list only used to decide legislative elections Slovenia 2000[29] open list[CEPPS 13] Open list is only used to decide lower house legislative elections, and two seats, which are reserved for Hungarian and Italian minorities, are decided using a Borda count.[CEPPS 13] Sri Lanka[Sawer 2] 1978 contingent vote and open list[CEPPS 14] In Sri Lanka contingent vote is used to decide presidential elections[Sawer 1] and legislative elections, open list.[CEPPS 14] Switzerland x open list[17] Zimbabwe[30] 1979-1985 alternative vote only used for white candidates
Federated states
 Province/state Country Years in use Type Notes Alberta[Sawer 1] Canada 1952-1954 open list Australian Capital Territory[Sawer 1] Australia 1993–present single transferable vote British Columbia[Sawer 1] Canada 1926-1955 open list Manitoba[Sawer 1] Canada 1927-1936 open list New South Wales[Sawer 1] Australia 1918–present single transferable vote (1918-1926), contingent vote (1926-1928), alternative vote (1929-1980), open list (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), alternative vote (1962-1992), open list (1992–present) South Australia[Sawer 1] Australia 1929-1935, 1982–present Alternative vote 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, alternative vote voting has been used in Tasmania to decide upper house legislative elections. Victoria[Sawer 1] Australia 1911–present open list (1911-1915), alternative vote (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 open list (1907-1911), alternative vote (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 15] 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[31] 1975 only alternative vote Aspen, CO[32] 2009 only alternative vote Berkeley, CA[33] 2010–present alternative vote Burlington, VT[34] 2005-2010 alternative vote Hendersonville, NC[35] 2007–present alternative vote part of a statewide pilot program[36] London 2000[37]-present supplementary vote[38] Memphis, TN[6] 2011–present alternative vote Minneapolis, MN[39] 2009–present alternative vote Oakland, CA[33] 2010–present alternative vote Portland, ME[6] 2011–present alternative vote San Francisco 2004[40]-present alternative vote[6] San Leandro, CA[33] 2010–present alternative vote St. Paul, MN 2011[41]-present alternative vote[42] Takoma Park, MD[43] 2006–present alternative vote Telluride, CO[44] 2011–present alternative vote