Instant-Runoff Voting

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Instant-runoff voting (IRV) (also known as the Alternative Vote and 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 overall majority of first preferences 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 RepresentativesAustralian Electoral Commission [link], the President of Ireland and the Fijian House of Representatives.

Terminology

Instant-runoff voting is also known by a number of other names. It is known as instant-runoff voting in the United States primarily because of its resemblance to runoff voting, which is also used in that country. It is known as the Alternative Vote (AV) 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 Canada 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 using the Droop quotais applied to a single-winner election it becomes the same as IRV, since in using the Droop quota formula i.e. votes/(# seats + 1), increased to the next whole number, the resulting quota is 50% + 1, the minimum number needed to win. 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. In New Zealand local body elections, STV is always referred to as STV, even if only one seat is to be filled (in the case of the mayor being elected.)

Voting

In IRV the voter ranks the list of candidates in order of preference. Under the most common ballot layout, the voter places a '1' beside their most preferred candidate, a '2' beside their second most preferred, and so forth. In the ballot paper shown at the top-right of this page the preferences of the voter are as follows:

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

Counting the votes

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

Once candidates are eliminated or 'excluded', no votes can be transferred to them. Therefore if ballots being recounted express a preference for a candidate who has already been excluded, their next 'live' preference is used. The count is intended to continue only until one candidate has a majority, and 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 below).

Examples

Example I

Imagine an election in which there are three candidates: Andrew, Brian and Catherine. There are 100 voters and they vote as follows (for clarity, third preferences are omitted):

#	39 voters		12 voters	7 voters		42 voters
1st	Andrew		Brian	Brian		Catherine
2nd	Brian		Andrew	Catherine		Brian

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

• Andrew: 39
• Brian: 19
• Catherine: 42

No candidate has an overall majority of votes (in this case 51), so Brian, who has the fewest votes, is eliminated. His votes must now be transferred to the two remaining candidates. To do this the ballot papers of the 19 Brian supporters are examined to see which candidates voters have given as their second preferences. Each Brian supporter then has their vote transferred to their second preference: 12 votes are transferred to Andrew and 7 to Catherine. The tallies then become:

• Andrew: 51
• Catherine: 49

Andrew now has an overall majority, so is declared the winner.

Example II

Imagine another election in which there are four candidates: Andrea, Brad, Carter and Delilah. There are 120 voters and they vote as follows (fourth preferences are omitted):

#	44 voters		3 voters		16 voters	10 voters		47 voters
1st	Andrea		Brad		Carter	Carter		Delilah
2nd	Brad		Carter		Brad	Delilah		Carter
3rd	Carter		Andrea		Andrea	Brad		Brad

The count would proceed as follows:

• Round 1: First preferences are tallied and no candidate has a majority (61).
• Round 2: Brad has fewest votes so is excluded. His supporters all give Carter as their second preference, so all his votes transfer to Carter. There is still no candidate with a majority.

• Round 3: Carter is now excluded and his votes must be transferred. Because only Andrea and Delilah remain in the contest Carter's votes will be divided between them. At this stage in the count Carter is regarded as having 29 votes. These 29 votes include 3 transferred from Brad. His votes therefore come from three groups of ballot papers. The preferences expressed on these ballot papers are:

#	3 voters	16 voters	10 voters
1st	Brad	Carter	Carter
2nd	Carter	Brad	Delilah
3rd	Andrea	Andrea	Brad

On the basis of these ballot papers Carter's 29 votes are now transferred, 19 to Andrea and 10 to Delilah. Note that the 16 ballot papers in the middle column list Brad as the second preference. However because Brad has already been eliminated these votes instead transfer to the next 'live' preference, Andrea.

• Winner: Once Carter's votes have been transferred Andrea has a majority of votes, and so is declared the winner.

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'.

Under optional preferential voting some voters may 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 'bullet vote', expressing only 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 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 at random. Partly to overcome these problems, in elections to the Australian House of Representatives many parties distribute 'how-to-vote' cards (right), 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. Any fixed ordering will give some candidates an unfair advantage, because voters, consciously or otherwise, are influenced in their ordering of candidates by the order 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

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 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.

United States

• San Francisco has used instant runoff voting to elect its Board of Supervisors since 2004.
• Burlington, VT completed its first mayoral election in 2005.
• Ferndale, MI passed instant runoff voting in 2004.
• Berkeley, CA passed instant runoff voting pending necessary implementation.

Application in Overseas Voting

Instant runoff voting and variations have been hailed as a solution the logistical problems of overseas voting in states with runoff provisions. In the event of a runoff, election administrators would have to print new ballots, mail them to far-flung places, and receive them again. In the short window between the first election and the runoff, there often is not enough time. With a ranked instant runoff ballot, the votes of overseas citizens can count even if their first choice does not make the runoff, all on a single ballot.

Arkansas, Louisiana and South Carolina all use forms of instant runoff voting on ballots for military and overseas voters.

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, where voters vote for only one candidate but, if no candidate receives an overall majority of votes, another round of voting is held from which all but the two candidates with most votes are excluded.

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 that can be prevalent in 'standard' runoff voting.

A closer system to IRV is the exhaustive 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 exhaustive 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.

Contingent vote

The contingent vote is the same as IRV except that all but the two candidates with most votes are eliminated after the first round; the count therefore has only two rounds. This differs from the 'two round' runoff voting system described above in that only one ballot is conducted. The two rounds therefore both take place after voting has finished. Two particular variants of the contingent vote differ from IRV in a further way. Under the forms of the contingent vote used in England and Sri Lanka voters are not permitted to rank all of the candidates, but only a maximum number. Under the variant used in England, called the supplementary vote, voters are permitted to express only a first and a second preference. Under the Sri Lankan form of the contingent vote voters are permitted to rank only three candidates. The supplementary vote is used for mayoral elections, while the Sri Lankan contingent vote is used to elect the President.

While superficially similar to IRV, these systems can produce different results. If, as can occur under all forms of the contingent vote, more than one candidate is excluded after the first count, a candidate might be eliminated who under IRV would have gone on to win the election. If voters are restricted to a maximum number of preferences then it is easier for their vote to become exhausted. This encourages voters to vote tactically, by giving at least one of their limited preferences to a candidate who is likely to win.

Tactical voting and strategic nomination

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 for only one of the two leading candidates, because a vote for any other candidate is unlikely to affect 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 attempt to 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 not 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 because there are opportunities for 'split votes' to be concentrated on one of the candidates as the rounds progress, whereas under the plurality system votes cast for a losing candidate are simply lost.

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 this characteristic may be diminished by the fact 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 PR systems, which tend to produce coalition governments. While IRV is designed to ensure that each 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 overall majority of voters across the nation. IRV is also one of many voting systems that is subject to vote-splitting, which almost always results in a two-party structure. In Australia, the only nation to use IRV for the election of legislative bodies, IRV produces results very similar to those produced by the plurality system. This has resulted in a two party system similar to those found in many countries that use plurality. If the first preferences of Australian voters were counted on a First Past the Post basis, their elections would produce the same victors about 94% of the timehttp://www.aceproject.org/main/english/es/esy_au.htm, accessed 11th May 2006.

Where preferential voting is used for the election of an assembly or council, 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 practical for large elections only if counting is done 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 Australia, 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 (six possible orders for three candidates), the number of possible orders is equal to the factorial of the number of candidates. The unwieldiness of IRV data may prolong the counting procedure, provide more opportunities for undetected tampering than in summable methods, and make recounts more costly.

Majoritarianism and consensus

The intention of IRV is that the winning candidate will have the support of an absolute majority of voters, or at the very least an overall majority. 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 overall majority (more than half) of votes. IRV tries to overcome this problem by eliminating candidates one at a time, until one has an overall majority.

However critics argue that the majority obtained by the winner of an IRV election is an artificial one. This is because there is often a candidate that 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 will always be that the majority of voters prefer the Condorcet winner to the IRV winner (the only system that always elects the Condorcet winner is Condorcet's method).

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 radical candidate, with the enthusiastic support of many voters, may be preferable to a consensus 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. This time the third preferences of the voters are important and so have been included:

#	39 voters		12 voters	7 voters		42 voters
1st	Andrew		Brian	Brian		Catherine
2nd	Brian		Andrew	Catherine		Brian
3rd	Catherine		Catherine	Andrew		Andrew

In an IRV election Andrew will be elected, whereas under Condorcet's method or the Borda count 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 61 voters have given him a higher ranking than his opponent. Further, Andrew is ranked last by 49 voters, which seems to indicate that he is strongly disliked by almost half the electorate. Brian is either the first or second choice of every voter, 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, while Brian is a consensus candidate.

Alternative Methods of Eliminating Candidates

In the most common method of IRV, "if no candidate achieves an overall majority of first preferences, the candidate with the fewest first preferences is eliminated" (see Counting the Votes above).

Some alternatives have been proposed that use other methods of eliminating candidates.

One alternative known as the Coombs' method eliminates the candidate that ranks lowest on the most ballots.

A second alternative that has been called "Progressive Advancement" is for the candidate with the most first preferences to advance to the next round of voting. The ballots are then recounted and the next remaining candidate with the most first preferences advances to the next round of voting. This process continues until all candidates but one have advanced to the next round, at which point the last unadvanced candidate is eliminated. The counting then resumes to determine if there is a winner based on a majority of first preferences. If not, another round of progressive advancement occurs until either a winner is found, or until all candidates except one have been eliminated.

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 non-dictatorial preferential 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

References

External links

Advocacy organisations

• [Instant Runoff Voting] at FairVote
• [instantrunoff.com], by the Midwest Democracy Center [link]
• [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"]
• [IRV page] at the [Center for Range 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
• [OpenSTV -- Open source software for computing IRV and STV]
• [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"

 

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