Instant-runoff voting

Instant runoff voting (IRV) is a voting 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) and all votes retallied, 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^[1], the President of Ireland and the Fijian House of Representatives. In the United States, it has been adopted in eight local jurisdictions, including three large population cities and counties during the 2006 United States general elections.

Terminology

Instant runoff voting has been called a number of other names. In the United States it is called instant runoff voting primarily because of its resemblance to runoff voting, which is also used in that country and many presidential elections around the world. In the United Kingdom it is known as the Alternative Vote (AV). In Australia the generic term preferential voting is used (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 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 usually known simply as "STV" in New Zealand and Ireland, although the term the 'Alternative Vote' is also sometimes used in those countries. 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

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

Each voter casts only one vote but, during the process of counting votes, his vote may be 'transferred' from one candidate to another.

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) 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 overall 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 overall majority.

Once candidates are eliminated or 'excluded', no votes can be transferred to them. Therefore if a ballot paper being recounted expresses a preference for a candidate who has already been excluded, the next 'live' preference on the ballot is used instead.

While the count is intended to continue only until one candidate has an overall 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 cast. In this case the winner is strictly speaking the candidate who has a majority of 'continuing ballots' — meaning those ballots expressing preferences among candidates who have not been eliminated. To avoid this scenario some election rules declare incomplete ballots to be void.

IRV with batch elimination is a practice used in Ireland where if no candidate receives a majority of the first round votes all candidates but the top two are eliminated and their votes are redistributed.

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):

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 (which in this case would be 51), so Brian, who has the fewest votes, is eliminated. Brian's 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 instead. So 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):

The count would proceed as follows:

• Round 1: First preferences are tallied and no candidate has a majority (in this election an overall majority would be 61).
• Round 2: Brad has fewest votes so is excluded. His supporters all give Carter as their second preference. So his votes all transfer to Carter. However there is still no candidate with a majority.

• Round 3: Carter is now excluded and so 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:

On the basis of these ballot papers Carter's 29 votes are now transferred to the two remaining candidates as follows: 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 , which is Andrea.

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

Handling ties

Exact ties can happen in any election; although the odds remain low when many votes are cast, the multiple rounds of counting used in IRV create more opportunities for a tie than there are in some other voting systems. If there is a tie for last place in the elimination process, various rules can be used to break it:

1. One candidate, from among those tied, is eliminated at random (e.g. by a coin toss).
2. In Australia the candidate, from among those tied, with the fewest votes in the previous round is eliminated. If there is still a tie those counting votes then look back to the next most recent round and then, if necessary, to further progressively earlier rounds until one candidate can be eliminated.
3. In Irish presidential elections the candidate, from among those tied, with fewest first preferences is eliminated. Failing this those counting look forwards, first to find the tied candidate with fewest votes in the second round and then, if necessary, to the third, fourth and subsequent rounds.
4. In some private elections the method is to 'conditionally eliminate' candidates from the tie and recount to see if either (or any) can survive. Usually the full set will become eliminated in any order. However this option is not allowed in a political election because it would allow some voters to have two simultaneous votes.

In practice, before any of these methods are used, the first step is to see if a tie has any chance of actually affecting the result. If the total of all the combined votes of any grouping of the candidates with the fewest votes is fewer than the votes cast for the next weakest candidate, then all those bottom tier candidates can be eliminated simultaneously.

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 require or request that 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 or an informal ballot. In Australia this variant 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 his or her lower preferences, the voter simply chooses them at random. Partly to overcome these problems, in elections to the Australian House of Representatives many parties distribute 'how-to-vote' cards (right), recommending how to allocate preferences on the ballot paper.

The common way to list candidates on a ballot paper is alphabetically or by random lot, a process whereby the order of the candidates published on the ballot paper is determined by lottery. In some cases candidates may also be grouped by party.

Any fixed ordering of candidates on the ballot paper 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. The random ordering of candidates is intended to overcome this. The most effective form is Robson Rotation, a system where the order of candidates on the paper is randomly changed for each print run of the same election's ballot papers. This means that any one ballot paper is almost certainly different from the next.

History and current use

Main article: History and use of instant-runoff voting

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, originally developed by Carl Andrae and Thomas Hare. The first known use of IRV in a governmental election was in 1893 in an election for the colonial government of Queensland, in Australia. This system used for this election was a special form known as the contingent vote. IRV in its true form was first used in 1908 in a State election in Western Australia.

Today IRV is used in Australia for elections to the Federal House of Representatives, and for the 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 all elections from 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

• Minneapolis, MN [3] in November 2006 passed instant runoff voting with 65%. Implementation is scheduled for the 2009 municipal elections.
• North Carolina adopted instant runoff voting for certain judicial vacancies and will encourage municipal pilot programs starting in 2007.
• Pierce County, WA passed instant runoff voting in November 2006 [4] for implementation for most of its county offices in 2008.
• Takoma Park, MD adopted instant runoff voting for city council and mayoral elections in 2006 after an 84% win in a 2005 advisory ballot measure. It held its first IRV election to fill a city council vacancy in January 2007. [5]
• Oakland, CA voters passed a measure by 69% to 31% in November 2006 to adopt IRV for its city offices.
• Burlington, VT held its first mayoral election using IRV in 2006 after voters approved it in 2005.
• San Francisco has used instant runoff voting annually to elect its Board of Supervisors and major citywide offices since 2004.
• Ferndale, MI passed instant runoff voting with 68% in 2004 pending necessary implementation.
• Berkeley, CA passed instant runoff voting with 72% in 2004 pending necessary implementation.
• Cambridge, MA has used the single transferable vote with Droop quota method of proportional voting, which is synonymous with IRV in the case of electing a single official, for more than 60 years. [6].
• Dozens of American colleges and universities [7] use IRV, including as of November 2006 more than half of the 30 universities rated most highly by U. S. News and World Report.

Application in absentee voting

Instant runoff voting and variations have been hailed as a solution to 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. Under the two round system 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 which 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 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 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 certain maximum number. Under the variant used in England, called the supplementary vote, voters are only permitted to express a first and a second preference. Under the Sri Lankan form of the contingent vote voters are only permitted to rank three candidates. The supplementary vote is used for mayoral elections while the Sri Lankan contingent vote is used to elect the President of Sri Lanka.

While superficially similar to IRV these systems can produce different results. If, as occurs under all forms of the contingent vote, 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. This encourages voters to vote tactically, by giving at least one of their limited preferences to a candidate who is likely to win.

Practical implications

Instant runoff voting 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.

IRV has been implemented in cities using optical scan machines, as in San Francisco (CA) and Burlington (VT). A hand count also is possible under IRV and is the method used in most non-American jurisdictions; however it is usually more time-consuming than a quick plurality count, and may need to occur over a number of rounds. It is nonetheless simpler than the count under some other preferential voting systems. IRV is typically 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.

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. If areas were to report the number of votes cast for each possible order of candidates, as in the examples above, the permutations can be very large as the number of possible orders is equal to the factorial of the number of candidates. Three candidates would produce only six combinations but five candidates would produce 120 and ten candidates 3.6 million. This unwieldiness could prolong the counting procedure, provide more opportunities for undetected tampering than in more easily summable methods, and make recounts more costly. What happens in practice in Australia is a simplified count is sent through to the central location on the night with the actual ballot papers transported securely to the central location for the final count. In Ireland's presidential race, there are several dozen counting centers around the nation. Each center reports its totals for each candidate and receives instructions from the central office about which candidate or candidates to eliminate in the next round of counting.

Tactical voting and strategic nomination

Main article: Tactical manipulation of instant-runoff voting

Instant-runoff voting reduces 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 is unlikely to affect the result. Under IRV this tactic, known as 'compromising', is typically unnecessary because, even if a voter's first choice is unlikely to be elected, his or her vote has the opportunity of being transferred to 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 under unusual circumstances 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. Although hard to anticipate, 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 might be able to 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 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 that may be necessary for earning majority support. However, unlike some other preferential voting systems, IRV puts particular value on a voter's first choice; a candidate with weak first choice support is unlikely to win even if ranked relatively well on many voters' ballots.

IRV is an election method designed for single seat elections. 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 his or 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 that wins a majority of seats will often not have the support of an overall majority of voters across the nation. In Australia, the only nation with a long record of using IRV for the election of legislative bodies, IRV produces representation very similar to those produced by the plurality system, with a two party system in parliament 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 time. A negative effect of IRV, similar to Plurality voting, is that it maintains the two-party system.^[2]

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, and Australia's requirement that voters must rank all candidates contributes to some voters using them. 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'.

Majoritarianism and consensus

The intention of IRV is that the winning candidate will have the support of an overall majority of voters. It is often 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 addresses this problem by eliminating candidates one at a time, until one has an overall majority.

However, some critics argue that the majority obtained by the winner of an IRV election is not always a genuine majority, and that it is more accurate to say that IRV will elect the majority choice among the top two frontrunners. This is because there may be a candidate who is preferred by most voters to the winner of an IRV election, but whose lack of core first choice support led to elimination early in the IRV count. 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. Defenders argue that first and other higher preferences are more important than lower preferences, and point out that the Condorcet winner may be a candidate with 0% of first choices who voters would only accept as a compromise candidate.

Because of the value it puts in first choice support, IRV may be less likely to elect centrist candidates than some other preferential systems, such as Condorcet's method and the Borda count as long as candidates vote sincerely in those systems. For this reason it can be considered a less consensual system than these alternatives. Some IRV supporters consider this a strength, because an off-center candidate, with the enthusiastic support of many voters, may be preferable to a 'mediocre' compromise candidate, while still being acceptable to a majority of voters.

IRV at times produces different results to a Condorcet count because it does not consider the lower preferences of all voters, only of those whose higher choices have been eliminated, and because of its system of sequential exclusions.

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:

In an IRV election Andrew will be elected, whereas under Condorcet's method or the Borda count (with sincere voters) Brian would win. Favoring 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. Furthermore Andrew is ranked last by 49 voters which seems to indicate that he is strongly disliked by almost one half of 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 (if not a majority), while Brian is an uninspiring compromise.

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). This is called bottom up elimination.

Top-two IRV, also known as batch-style is an alternative used in some elections that simplifies the elimination process, duplicating the Two-round system of eliminating all but the top-two voted candidates in the first round. (London uses a version of this called Supplementary Vote with a further restriction that voters are only allowed to offer two rank choices.) Unlike the bottom-up elimination form of IRV, this variation does not allow for the possibility of a plurality-third or lower candidate to compete in the final round. [8]

A practical benefit of the Top-two IRV process is expediency and confidence in the result with only two rounds. Most apparent in smaller elections, like with under 100 ballots among a dozen choices, confidence can be lost in a bottom-up elimination due to cumbersome ties on the bottom (or near ties affected by counting errors). Frequent and even multiple use of tie-breaking rules in one election will leave uncomfortable doubts over whether the winner might have changed if a recount was performed.

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.

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
• Ballot Access News for occasional related news in the United States

References

Wikipedia information about Instant-runoff voting This article is licensed under the GNU Free Documentation License. It uses material from the Wikipedia article "Instant-runoff voting". It may not have been reviewed by professional editors (see full disclaimer). Help contribute to Americola and edit this article.