Instant-runoff voting

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Instant-runoff voting (IRV), also known by several other names, is an electoral system used for single winner elections in which voters rank candidates in order of preference. In an IRV election, if no candidate receives an absolute majority of first preferences, then the candidates with fewest votes are eliminated one by one, and their votes transferred according to their second and third preferences (and so on), until one candidate achieves a majority. The term 'instant-runoff voting' is used because this process resembles a series of run-off elections. At a national level IRV is used to elect the Australian House of Representatives, the President of Ireland and the Fijian House of Representatives.

Contents 1 Name 2 Voting 3 Counting the votes 4 Examples 4.1 Example I 4.2 Example II 5 The ballot paper 6 History and current use 7 Similar systems 7.1 Runoff-voting 7.2 Quasi-instant-runoff systems 8 Majoritarianism and consensus 8.1 An example 9 Tactical voting and strategic nomination 10 Effect on parties and candidates 11 Practical implications 12 Evaluation by criteria 13 See also 14 External links 15 References

Name

Instant-runoff voting is known by many other names. It is known as instant-runoff voting in the United States because of its partial resemblance to run-off voting, which is also used in the U.S. It is known as the Alternative Vote in the United Kingdom and Preferential Voting in Australia, but this last term can be misleading because IRV is only one of a number of preferential voting systems. When used in Canda in the past it was known as the preferential ballot. It is also sometimes known, in the U.S, as Ranked Choice Voting.

When the Single Transferable Vote (STV) system is applied to a single winner election it becomes the same as IRV. For this reason IRV is sometimes considered to be merely a special form of STV. However, because STV was designed for multi-seat constituencies, many scholars consider it to be a separate system from IRV, and that is the convention followed in this article. IRV is sometimes referred to as the Hare system, after Thomas Hare, one of the inventors of STV. It has also been referred to as Ware's method, after its own inventor, William Robert Ware. Writers differ as to whether or not they treat instant-runoff voting as a proper noun.

Voting

Image:Preferential ballot.svg

In IRV the voter ranks the list of candidates in order of preference. Under the most common ballot layout, she places a '1' beside her most preferred candidate, a '2' beside her second most preferred, and so forth. In the ballot paper shown in the image on the right, the preferences of the voter are as follows:

1. John Citizen
2. Mary Hill
3. Jane Doe

Note that the system does not (in principle) require a voter to register a preference for every candidate. However, individual applications of the voting system may require all the candidates to recieve a preference (for instance, elections for the Australian House of Representatives does require that a preference be recorded for every candidate)<ref name="Application of IRV">"[http://www.aph.gov.au/library/handbook/elections/index.htm Election rules for the Australian House of Representatives (accessed 21/4/06).</ref>.

Counting the votes

In an IRV election ballots are initially sorted according to their expressed first-preferences. If no candidate achieves an absolute majority of first preferences (i.e. more than half of the total vote) then the candidate with the fewest first preferences is eliminated. Her votes are recounted and are distributed to the remaining candidates according to the second preferences expressed by each ballot paper. If there is still no candidate with an absolute majority of votes then the candidate with the fewest votes is again eliminated and his votes transferred in the same way, according to the second or third preferences expressed by each ballot paper. This process of counting and eliminating continues until a candidate has obtained an absolute majority.

Once a candidate is eliminated or 'excluded', no votes can be transfered to them. If, therefore, ballots being recounted express a preference for a candidate who has already been excluded, their next 'live' preference is used. While the count is intended to continue only until one candidate has a majority, this will yield the same result as continuing until there is only one candidate left. In some circumstances, where some voters have not expressed a full list of preferences on the ballot, it is possible that no candidate will receive a majority of votes until all other candidates have been excluded. In this case the count continues until only the winner remains. It is for this reason that some election rules declare incomplete ballots to be void (see above).

Examples

Example I

Imagine an election in which there are three candidates: Andrew, Brian and Catherine. There are therefore 6 possible orders in which the voter can rank the candidates: Andrew-Brian-Catherine, Andrew-Catherine-Brian, Brian-Andrew-Catherine, etc etc. Assume there are 100 voters and they vote as follows:

#	Order		Order		Order		Order		Order		Order
1st	Andrew		Andrew		Brian		Brian		Catherine		Catherine
2nd	Brian		Catherine		Andrew		Catherine		Andrew		Brian
3rd	Catherine		Brian		Catherine		Andrew		Brian		Andrew
Votes	33		3		16		2		5		41

First the first preferences are counted, so the tallies stand at:

• Andrew: 36
• Brian: 18
• Catherine: 46

No candidate has an absolute majority of votes (which in this case would be 51), so Brian, who has the fewest first-preference votes, is eliminated. All the ballot papers in which Brian was the first preference are then reviewed, with the votes being allocated to the two remaining candidates on the basis of their second preference votes. In this case, 16 of these votes are allocated to Andrew and 2 to Catherine. The totals are then recalculated:

• Andrew: 52
• Catherine: 48

Andrew now has an absolute majority so is declared the winner.

Example II

Image:Tennessee map for voting example.svg

Imagine that the population of Tennessee, a state in the United States, is voting on the location of its capital. The population of Tennessee is concentrated around its four major cities, which are spread throughout the state. For this example, suppose that the entire electorate live in one of these four cities, and that they would like the capital to be established as close to their city as possible.

The candidates for the capital are:

• Memphis, the state's largest city, with 42% of the voters, but located far from the other cities
• Nashville, with 26% of the voters
• Knoxville, with 17% of the voters
• Chattanooga, with 15% of the voters

The preferences of the voters would be divided like this:

42% of voters (close to Memphis)	26% of voters (close to Nashville)	15% of voters (close to Chattanooga)	17% of voters (close to Knoxville)
Memphis Nashville Chattanooga Knoxville	Nashville Chattanooga Knoxville Memphis	Chattanooga Knoxville Nashville Memphis	Knoxville Chattanooga Nashville Memphis

The count would proceed as follows:

• Round 1: First preferences are tallied and no candidate has a majority.
• Round 2: Chattanooga has fewest votes so is excluded. Its votes all transfer to Knoxville but there is still no candidate with a majority.
• Round 3: Nashville is excluded. Nashville's supporters have Chattanooga as their second preference but Chattanooga has already been excluded, so instead the votes are transferred to their third choice, Knoxville. Knoxville now has a majority of votes so is declared elected.
• Winner: Knoxville

The ballot paper

As seen above, voters in an IRV election rank candidates on a preferential ballot. IRV systems in use in different countries vary both as to ballot design and as to whether or not voters are obliged to provide a full list of preferences. In elections such as those for the President of Ireland and the New South Wales Legislative Assembly, voters are permitted to rank as many or as few candidates as they wish. This is known in Australia as 'optional preferential voting'.

However under optional preferential voting voters sometimes, for example, rank only the candidates of a single party, or of their most preferred parties. A minority of voters, especially if they do not fully understand the system, may even 'bullet vote', only expressing a first preference. Allowing voters to rank only as many candidates as they wish grants them greater freedom but can also lead to some voters ranking so few candidates that their vote eventually becomes 'exhausted'–that is, at a certain point during the count it can no longer be transferred and therefore loses an opportunity to influence the result.

To prevent exhausted ballots, some IRV systems instead oblige voters to give a complete ordering of all of the candidates in an election (if a voter does not rank all candidates her ballot may be considered spoilt). In Australia this is known as 'full preferential voting'. However, when there is a large set of candidates this requirement may prove burdensome and can lead to "donkey voting" in which, where a voter has no strong opinions about her lower preferences, she simply choses them arbitrarily. Partly to overcome these problems, in elections to the Australian House of Representatives many parties distribute 'how-to-vote' cards, advising their supporters on what preferences to express on the ballot paper.

The simplest way to list candidates on a ballot paper is alphabetically, though they may also be grouped by party. However any fixed ordering will give some candidates an unfair advantage, because some voters, consciously or otherwise, are influenced in their ordering of candidates by the order found on the ballot paper. To solve this problem some systems involve a random ordering of candidates, or an ordering that changes from one ballot paper to another.

History and current use

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Instant-runoff voting was invented around 1870 by American architect William Robert Ware. He evidently based IRV on the single winner outcome of the Single Transferable Vote, orginally developed by Carl Andrae and Thomas Hare. Today IRV is used in Australia for elections to the Federal House of Representatives, and for the Legislative Assemblies (lower houses) of all states and territories except Tasmania and the Australian Capital Territory, which use STV. It is also used for the Legislative Council of Tasmania. In the Pacific, IRV is used for the Fijian House of Representatives and Papua New Guinea has also decided to adopt it for future elections, starting in 2007. IRV is also used to elect the President of Ireland and for municipal elections in various places in Australia, the United States, and New Zealand.

Similar systems

Runoff-voting

The term instant-runoff voting is derived from the name of a simpler class of voting systems called runoff voting. In runoff voting voters do not rank candidates in order of preference on a single ballot. Instead a similar effect is achieved by using multiple rounds of voting, often held on different days. The simplest form of runoff voting is the two round system. Under the two round system voters vote for only one candidate but, if no candidate receives an absolute majority of votes, another round of voting is held from which all but the two candidates with most votes are excluded.

A closer system to IRV is the elimination ballot. In this system only one candidate is eliminated after each round, and many rounds of voting are used, rather than just two. Because holding many rounds of voting on separate days is generally expensive, the elimination ballot is not used for large scale, public elections. Instant-runoff voting is so named because it achieves a similar effect to runoff voting but it is necessary for voters to vote only once. The result can be found 'instantly' rather than after several separate votes.

Runoff voting differs from IRV in a number of ways. The two round system can produce different results due to the fact that it uses a different rule for eliminations, excluding all but two candidates after just one round, rather than gradually eliminating candidates over a series of rounds. However all forms of runoff voting differ from IRV in that voters can change their preferences as they go along, using the results of each round to influence their decision. This is not possible in IRV, as participants vote only once, and this prohibits certain forms of tactical voting which can be prevalent in 'standard' runoff voting.

Quasi-instant-runoff systems

There are a number of systems that are similar to IRV, but differ in that voters are only permitted to rank a certain maximum number of candidates, or more than one candidate is eliminated after the first count. The Contingent Vote, which was formerly used in Queensland in Australia, is the same as IRV except that all but the two candidates with most votes are eliminated after the first round; the count therefore only ever has two rounds. This differs from the "two round" Runoff Voting system described above in that only one ballot is conducted. The two rounds therefore take place after voting has finished.

The Supplementary Vote system, used for mayoral elections in the UK, also eliminates all but two candidates, but also differs in that voters are only permitted to rank two candidates: a first and second choice.

Under the Sri Lankan system, used to elect the President of Sri Lanka, and the Limited Preferential Vote, used to elect the National Parliament of Papua New Guinea, voters can express only three preferences.

Although superficially similar to IRV these systems can produce different results. If more than one candidate is excluded after the first count, a candidate might be eliminated who would have gone on to win the election under IRV. If voters are restricted to a maximum number of preferences then it is easier for their vote to become 'exhausted'–that is, it might occur that eventually none of a voter's ranked candidates are left in the count. This encourages voters to vote tactically, by giving at least one of their limited preferences to a candidate who is likely to win.

Majoritarianism and consensus

The intention of IRV is that the winning candidate will have the support of an absolute majority of voters. It is intended as an improvement on the 'first past the post' (plurality) voting system. Under 'First Past The Post' the candidate with most votes (a plurality) wins, even if they do not have an absolute majority (more than half) of votes. IRV tries to overcome this problem by eliminating candidates one at a time, until one has an absolute majority.

However critics argue that the absolute majority obtained by the winner of an IRV election is an artificial one. This is because there is often a candidate who voters prefer to the winner of an IRV election, but who has been eliminated because of a small number of higher preferences. Advocates of this view argue that a candidate can only claim to have majority support if they are the 'Condorcet winner' - that is, the candidate voters prefer to every other candidate when compared to them one at a time. In fact, when IRV elects a candidate other than the Condorcet winner it would be found that the majority of voters prefered the Condorcet winner over the IRV winner. See Condorcet method for more information.

IRV is less likely to elect centrist candidates than some other preferential systems, such as Condorcet's method and the Borda count. For this reason it can be considered a less consensual system than these alternatives. Some IRV supporters consider this a strength, because a more divise candidate, with the enthusiastic support of many voters, may be preferable to a mediocre compromise candidate.

IRV produces different results to Condorcet and the Borda count because it does not consider the lower prefers of all voters, only of those whose higher choices have been eliminated, and because of its system of sequential exclusions. IRV's process of excluding candidates one at a time can lead to the elimination, early in the count, of a candidate who, if they had remained in the count longer, would have received enough transfers to be elected.

An example

Consider again the preferences of the voters in the election in Example I above:

#	Order		Order		Order		Order		Order		Order
1st	Andrew		Andrew		Brian		Brian		Catherine		Catherine
2nd	Brian		Catherine		Andrew		Catherine		Andrew		Brian
3rd	Catherine		Brian		Catherine		Andrew		Brian		Andrew
Votes	33		3		16		2		5		41

In an IRV election Andrew will be elected, but under any Condorcet method Brian would win. Favouring Brian is the fact that a majority of voters prefer him to Andrew. This can be seen by the fact that 54 voters have given him a higher ranking than his opponent. Furthermore, Andrew is ranked last by 43 voters which seems to indicate that he is strongly disliked by a almost half the electorate. Brian is at least the second choice of 92% of the voters which suggests that he is a broadly acceptable compromise candidate. On the other hand Andrew is the first preference of a large number of voters while Brian is the first choice of few. This might suggest that Andrew has the enthusiastic support of a large portion of the electorate (if not a majority), while Brian is an uninspiring compromise. Under the Borda count, Catherine would win when the second preferences are added.

Tactical voting and strategic nomination

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Instant-runoff voting is intended to reduce the potential for tactical voting by eliminating 'wasted' votes. Under the 'first past the post' (plurality) system voters are encouraged to vote tactically by voting only for one of the two leading candidates, because a vote for any other candidate will not effect the result. Under IRV this tactic, known as 'compromising', is sometimes unnecessary because, even if the voter's first choice is unlikely to be elected, her vote has the opportunity of being transferred to her second or subsequent choices, who may be more successful. However the tactic of compromising can still be used in IRV elections, as can another tactic called 'push over'. IRV is immune to 'burying' which is possible under some other preferential systems.

IRV election can also be influenced by strategic nomination; this is where candidates and political factions influence the result of an election by either nominating extra candidates or withdrawing a candidate who would otherwise have stood. IRV is vulnerable to strategic nomination for the same reasons that it is open to the voting tactic of 'compromising'. This is because a candidate who knows they are unlikely to win can bring about the election of a more desirable compromise candidate by withdrawing from the race, or by never standing in the first place. By withdrawing candidates a political faction can avoid the 'spoiler effect', whereby a new candidate 'splits the vote' of its supporters. However, the spoiler effect is less of a problem in IRV than under the plurality system.

Effect on parties and candidates

Like other preferential voting systems, IRV encourages candidates to appeal to a broad cross section of voters in order to garner lower preferences. However it should be noted that lower preferences have less influence on the final result under IRV than under some other preferential systems.

IRV is an election method designed for single seat constituencies. Therefore, like other single seat methods, if used to elect a council or legislature it will not produce proportional representation (PR). This means that it is likely to lead to the representation of a small number of larger parties in an assembly, rather than a proliferation of small parties. Under a parliamentary system it is more likely to produce single party governments than are PR systems, which tend to produce coalition governments. While IRV is designed to ensure that each individual candidate elected is supported by a majority of those in her constituency, if used to elect an assembly it does not ensure this result on a national level. As in other non-PR systems the party or coalition which wins a majority of seats will often not have the support of an absolute majority of voters across the nation.

Where preferential voting is used for the election of legislative bodies, parties and candidates often advise their supporters on how to use their lower preferences. As noted above, in Australia parties even issue 'how-to-vote' cards to the electorate before polling day. These kinds of recommendations can increase the influence of party leaderships and lead to a form of pre-election bargaining, in which smaller parties bid to have key planks of their platforms included in those of the major parties by means of 'preference deals'.

Practical implications

IRV is more complex, both in terms of casting votes and counting them, than simpler systems such as 'first-past-the-post' plurality. Voters must rank candidates in order of preference rather than merely write an 'x' beside a single candidate. Changing from plurality to IRV may therefore require the replacement of voting machinery. For these reasons some electoral reformers argue that it is simpler to change from plurality to approval voting than to a preferential system.

A hand count is possible under IRV and is the method used in most jurisdictions; however it is usually more time consuming than a quick plurality count, and must occur over a number of rounds. It is nonetheless simpler than the count under some other preferential voting systems. For example the more sophisticated versions of Condorcet's method are only practical for large elections if counting is conducted by computer. IRV may be less expensive than runoff voting because it is only necessary for voters to go to the polls once. For this reason it may also be less likely to induce voter fatigue.

If counting takes place in several places for a single IRV election (as in Australia), these counting centres must be connected by a securely authenticated channel (historically, in Austrlia, the telegraph was used) to inform them which candidate has come last and should be dropped. Under IRV, unlike some other preferential systems, the record of votes cast in a particular area cannot be conveniently summarised for transfer to a central location in which they can be counted. Instead areas must report the number of votes cast for each possible order of candidates, as in the examples above. While this is initially a small number (6 possible orders for three candidates), the number of possible orders is equal to the factorial of the number of voters. The unwieldiness of this data may prolong the counting procedure, provide more opportunities for undetected tampering than in summable methods, and make recounts more costly.

Evaluation by criteria

Scholars of electoral systems often compare them using mathematically defined voting system criteria. IRV passes the majority criterion, the mutual majority criterion, the Condorcet loser criterion and, if the right tie-breaker method is used, the independence of clones criterion. IRV fails the monotonicity criterion, the consistency criterion, the Condorcet criterion, the participation criterion, reversal symmetry, and the independence of irrelevant alternatives criterion. According to Arrow's theorem, no voting system can meet all desirable criteria when there are more than two candidates standing.

See also

• List of democracy and elections-related topics
• Table of voting systems by nation
• Australian electoral system
• Electoral systems of the Australian states and territories

External links

Advocacy organisations

• Instant Runoff Voting at the Center for Voting and Democracy
• instantrunoff.com, by the Midwest Democracy Center [1]
• FIRV (Ferndale, Michigan for Instant Runoff Voting)
• California IRV Coalition
• Coalition for Instant Runoff Voting in Florida
• Green Party (United States)
• History of Use in Ann Arbor
• e-mail your U.S. Representative to Support H.R. 2690, "The Voter's Choice Act of 2005."

Advocacy positions

• "Single Transferable Vote Resists Strategic Voting" (PDF file) by John J. Bartholdi, III and James B. Orlin.
• "What is Instant Runoff Voting?" a weblog The Democratic Agenda, January 1, 2005

Con positions

• "The Problem with Instant Runoff Voting"

Analysis positions

• Nonmonotonicity in AV Article by Eivind Stensholt.
• Comparison with Condorcet Voting by Blake Cretney
• Voting methods: tutorial and essays by James Green-Armytage (for IRV, see e.g. 1 2 3 4 5)
• Advocacy of the "Avy" method, opposition to IRV

Examples

• IRV Poll For 2008 U.S. Democratic Party Nomitee at demochoice.org
• IRV poll for U.S. President, 2004 by the Independence Party of Minnesota
• pSTV -- Open source software for computing IRV and STV
• Australian Electoral Commission [2]
• Favourite Futurama Character Poll

Legislation

• Presidential Elections Act, 1993 - Republic of Ireland
• Commonwealth Electoral Act - Australia
• U.S. House Resolution 2690 the "Voter's Choice Act of 2005"

References

<references/>de:Instant-Runoff-Voting fr:Vote alternatif