# Instant-runoff voting

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When the single transferable vote (STV) voting system is applied to a single-winner election it is sometimes called instant-runoff voting (IRV), as it is much like holding a series of runoff elections in which the lowest polling candidate is eliminated in each round until someone receives majority vote. IRV is often considered independently of multi-winner STV because it is simpler and because it is the most widely advocated electoral reform in the United States.

Outside the US, IRV is known as the Alternative Vote, preferential voting, single-winner STV, or the Hare System, though there is room for confusion with some of these terms, since they can also refer to STV in general. In the US, IRV is also known as Ranked Choice Voting (RCV), a term preferred by election officials in San Francisco in 2004 because election results were not instant, and voters are responsible for ranking candidates.[1]

Instant-Runoff Voting was invented around 1870 by American architect William Robert Ware, who simply applied Hare's method to single-winner elections.[2][3] Ware was not a mathematician, thus never subjected his election method to any rigorous analysis. He evidently based IRV on the single winner outcome of the Single Transferable Vote or STV developed in 1855 originally by Carl Andrae in Denmark. It was introduced into England in 1857 by the barrister Thomas Hare, where it earned public praise from John Stuart Mill, an English philosopher, member of parliament, and employee of the East India Company.

IRV is used to elect the Australian House of Representatives, the lower houses of most of Australia's state parliaments, the President of Ireland, the Papua New Guinea National Parliament, and the Fijian House of Representatives. See below for a more detailed list.

## How IRV works

### Voting

Each voter ranks at least one candidate in order of preference. In most Australian elections, voters are required to rank all candidates. In other elections, votes may be "truncated", for example if the voter only ranks his first five choices.

### Counting the votes

First choices are tallied. If no candidate has the support of a majority of voters, the candidate with the least support is eliminated. A second round of counting takes place, with the votes of supporters of the eliminated candidate now counting for their second choice candidate. After a candidate is eliminated, he or she may not receive any more votes.

This process of counting and eliminating is repeated until one candidate has over half the votes. This is equivalent to continuing until there is only one candidate left. However it is possible, with voter truncation, for the process to continue until there is only one candidate left, who does not end up with more than half the votes.

### An example

Imagine that Tennessee is having an election 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 lives in these four cities, and that everyone wants to live as near the capital 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, near the center of Tennessee
• 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)
1. Memphis
2. Nashville
3. Chattanooga
4. Knoxville
1. Nashville
2. Chattanooga
3. Knoxville
4. Memphis
1. Chattanooga
2. Knoxville
3. Nashville
4. Memphis
1. Knoxville
2. Chattanooga
3. Nashville
4. Memphis
City Round 1 Round 2 Round 3
Memphis 42 42 42
Nashville 26 26 26 0
Chattanooga 15 15 0 0
Knoxville 17 17 32 32 58

Chattanooga, having the smallest vote, is eliminated in the first round. All of the votes for Chattanooga have Knoxville as a second choice, so they are transferred to Knoxville. Nashville now has the smallest vote, so it is eliminated. The votes for Nashville have Chattanooga as a second choice, but as Chattanooga has been eliminated, they instead transfer to their third choice, Knoxville. Knoxville now has 58% of the vote, and it is the winner.

In a real election, of course, voters would show greater variation in the rankings they cast, which could influence the result.

### Special cases of IRV eliminations

Instant Runoff Voting as an ideal does not explicitly define how to handle special cases such as ties and different rules can be considered. A good IRV election must define rules to handle these cases before the votes are cast. The reason why is that there are cases where one set of rules will select a winner different from another set of rules and the set of rules used may affect how the voters cast their ballots.

Especially when performing IRV counts on smaller elections, there can be frequent last-place ties that prevent clear bottom elimination.

Here are some approaches to consider, individually and combined. The first class of rules allows many candidates to be eliminated at the first count regardless of actual ties. These are practical rules before the first round that reward stronger candidates among the full set of competition. Such rules won't likely affect the winner but they will reduce the number of elimination rounds and thus the number of opportunities for ties to develop. A second class of rules consider actual ties that can't be avoided.

• Consider multi-candidate elimination of weak candidates as the first step:
• CANDIDATE COUNT: Define a maximum number of candidates that can survive the first round.
• Example top-two
• VOTE MINIMUM: Define a minimum vote threshold (5 vote for example) and eliminate all weaker candidates together.
• Requires limitations for rule to apply
• PERCENT MINIMUM: Define a minimum percent vote threshold (5% for example) and eliminate all weaker candidates together.
• Again, requires limitations for application
• PERCENT RETENTION: Define a minimum percent of votes by top candidates to be retained.
• Example - retain the top set of candidates who combined control 50% of the vote
• Tie-breaking rules:
• LOGIC: If the tied candidates combined have fewer votes than the next highest candidate, the entire tied set can be eliminated at once.
• Logically deterministic, but may not apply
• LAST ROUND: Eliminate the candidate in the tie with the least votes from a previous round.
• Traditional rule; violates purity of one-person, one vote ideal
• ALL: Eliminate all tied candidates at once.
• RANDOM: Eliminate one randomly to break the tie.
• ORDER: If the order of the candidates on the ballot paper has been determined by lot, then ties can be eliminated by choosing say the top candidate.
• Random Voter Hierarchy (RVH): Randomly determine a strict ordering of the candidates and when selecting a candidate to eliminate, pick one based on this strict ordering.
• Similar to random elimination, but with many nice properties not found with random elimination

### Variants

IRV can be done with equal ranking allowed. The two main ways of doing this are either fractional (split the voter's ballot equally between all of their highest-ranked candidates that are ranked equally (3 candidates ranked 1st each get 1/3rd of a vote)), or whole votes (give each highest-equally-ranked candidate one vote (3 candidates get 1 vote each and 3 votes total)).

With whole votes equal-ranking, there are two ways to find a winner (which give the same result in standard IRV but differ for whole votes): either eliminate candidates until only two remain, and declare the one with more votes the winner, or eliminate candidates until one or more candidates are supported by a majority of active ballots, and then elect the candidate with the largest majority. Some have argued[4] that in order to limit opportunities for pushover strategy with whole votes, a ballot that equally ranks candidates should be allowed to help those candidates win, but not prevent those candidates from getting eliminated.

## Where IRV is used

The single-winner variant of STV is used in Australia for elections to the Federal House of Representatives, for the Legislative Assemblies ("lower houses") of all states and territories except Tasmania and the Australian Capital Territory, which use regional multi-member constituencies. It is also used for the Legislative Councils ("upper houses") of Tasmania and Victoria, although the latter will switch to the multi-member variant from 2006. The multi-member variant of STV is used to elect the Australian Senate and the Legislative Councils of New South Wales and South Australia in statewide constituencies, and of Western Australia in regional constituencies.

Ireland uses STV to elect its own parliament and its delegation to the European Parliament (by the multi-member variant), and its President (by the single-member variant). Northern Ireland also uses the multi-member variant for elections to its Assembly and for its European Parliamentary MPs. Malta uses the multi-member variant for its parliamentary elections.

In the Pacific, the single-member variant is used for the Fijian House of Representatives. Papua New Guinea has also decided to adopt it for future elections, starting in 2007. The Fijian system has been modified to allow for both "default preferences", specified by the political party or candidate, and "custom preferences", specified by the voter. Each political party or candidate ranks all other candidates according to its own preference; voters who are happy with that need only to vote for their own preferred candidate, whose preferences will automatically be transferred according to the ranking specified by the candidate. Voters who disagree with the ranking, however, may opt to rank the candidates according to their own preferences. In the 2001 election, about a third of all voters did so. The ballot paper is divided by a thick black line, with boxes above (for the default options) and below (for customized preferences).

The countries mentioned above all use STV for some or all of their municipal elections. Starting in 2004, some municipal areas in New Zealand also adopted STV to elect mayors (by the single-member variant) and councilors (by the multi-member variant). Political parties, cooperatives and other private groups also use STV and/or IRV.

The single winner version of IRV is also used to select the winning bid of both the Summer and Winter Olympics in the International Olympic Committee.

### Adoption in the United States

Suggested by a recent version of Robert's Rules of Order, instant-runoff voting is increasingly used in the United States for non-governmental elections, including student elections at many major universities.

Notable supporters include Republican U.S. Senator John McCain and 2004 Democratic presidential primary election candidates Howard Dean and Dennis Kucinich. The system is favored by many third parties, most notably the Green Party and the United States Libertarian Party|Libertarian Party, as a solution to the "spoiler" effect third-party sympathizers suffer from under plurality voting (i.e., voters are forced to vote tactically to defeat the candidate they most dislike, rather than for their own preferred candidate). In order to increase awareness of the voting method and to demonstrate it in a real-world situation, the Independence Party of Minnesota tested IRV by using it in a straw poll during the 2004 Minnesota caucuses (results favored John Edwards).

This dilemma rose to attention in the United States in the U.S. 2000 presidential election. Supporters of Ralph Nader who nevertheless preferred Democrat Al Gore to Republican George W. Bush found themselves caught in a dilemma. They could vote for Nader, and risk Gore losing to Bush, or, they could vote for Gore, just to make sure that Bush is defeated. It has been argued that Bush won largely due to the "spoiler effect" of Nader supporters in Florida.

In March 2002, an initiative backed by the Center for Voting and Democracy passed by referendum making instant runoff voting the means of electing local candidates in San Francisco. It was first used in that city in Fall of 2004. (Note: The San Francisco Department of Elections prefers the term "Ranked Choice Voting" because "the word 'instant' might create an expectation that final results will be available immediately after the polls close on election night.") Although polls showed voters generally understood and liked the new voting system, certain software and logistical difficulties delayed the election results for several days (the 'first-round' results were available the next day).

In September 2003, an amendment to the California State Constitution was proposed (SCA 14) with wide-ranging goals of election reform, including ranked-choice voting for statewide offices.

The voters in the city of Ferndale, Michigan, a Detroit suburb, amended their city charter in 2004 to allow for election of the mayor and city council by instant runoff voting.

Washington State has an initiative seeking ballot access in 2005 (I-318) that would change the state primary system to IRV.

## Assessing IRV

### Comparison of IRV to normal runoff voting

Advantages of instant runoff ballot (IRV) vs. normal runoff voting

• FEWER GAMES: Voters and parties have less opportunity for playing games in early round(s) to influence the elimination order in favor of easier competition. (Runoffs allow more flexibility in tactical votes, influencing elimination, and still having a chance to move back to a favorite in the final round)
• MORE POSITIVE: Candidates are discouraged from negative campaigning. (A winning candidate will usually need first, second and lower ranked preferences to win, and can't safely afford to make enemies with no second chance vote)

Advantages to normal runoff voting vs. IRV

• EASIER TO VOTE: A runoff allows voters and factions to refocus their attention on remaining candidates in each round. (In IRV, voters must make careful choices among a large set of candidates in one ballot and may not have enough information to make informed rankings among the competitive candidates.)
• CHANCE FOR APPEAL: Candidates that were eliminated are given another chance to endorse and remaining candidates have another chance to court voters supporting the eliminated candidates.

### Effect on parties and candidates

Unlike runoff voting, however, there are no chances to deal in between rounds, change voters' minds, or gain support of the other candidates.

Giving them only one chance to do so, instant runoff preference voting encourages candidates to balance earning core support through winning first choice support and earning broad support through winning the second and third preferences of other candidates' core supporters. As with any winner-take-all voting system, however, any bloc of more than half the voters can elect a candidate regardless of the opinion of the rest of the voters.

This is considered a weakness by the advocates of a more deliberative democracy, who point to the French system of presidential election where such between-round dealings are heavily exploited and useful (they say) to draw together a very factionalized electorate. However, critics of the French runoff system point to the dreaded "votez escroc, pas facho" (vote for the crook, not the fascist) phenomenon, which awarded Chirac an undeserved landslide victory in 2002.

The Australian system also allows minority parties to have key planks of their platforms included in those of the major parties by means of so-called "preference deals". This is seen as legitimate political activity. If enough people care about (for instance) green party issues that that party's second preference can swing the vote, then it is fair enough that it have some limited say in policy.

Another advantage of runoff voting is that it allows a "protest vote" to be made without penalty. A person voting for a minority party doers not "throw their vote away", as with first-past-the-post systems, so allowing the electorate to send clear signals to the major parties.

### Flaws of IRV

IRV meets few of the formal voting system criteria defined by political scientists for assessment of voting systems. Although the Gibbard-Satterthwaite theorem shows that all reasonable voting systems allow for some form of tactical voting, the scope and impact of tactical voting varies a great deal for different systems.

IRV is unusual in that it does not satisfy the monotonicity criterion —in some situations, if a voter or group of voters decides to rank a preferred candidate lower, it can result in that candidate winning the election, whereas if they had ranked the candidate higher, according to their sincere preference, that candidate would not have won.

These theoretical objections correspond with several serious practical 'failure modes' for IRV, discussed below. The first two, compromise and push-over, are common forms of tactical voting, where voters must change their preferred ranking of candidates to increase the likelihood of a favored outcome. Traditional plurality elections are also vulnerable to 'compromise' tactical voting. The other failure modes are more specific to IRV.

It should be noted that Condorcet methods can avoid the Return of the '3rd-party spoiler effect' and Failure to pick a good compromise problems.

#### Compromise

Assume the earlier Tennessee example. If the voters from Memphis suspect that they do not comprise half of the voters and that Memphis is the last choice of all other voters, they can "compromise" by ranking Nashville over Memphis, and thus ensure that Nashville, their second choice, will win, rather than Knoxville, their last choice.

Alternatively, if the voters from Memphis are unlikely to vote tactically (because they think they have a chance of winning outright or for any other reasons), voters from Nashville can improve their result by "compromising" and ranking Chattanooga over Nashville. This would allow Chattanooga to defeat Knoxville in the first round and go on to become eventual winner, a better result for Nashville voters than a Knoxville win.

#### Push-over

Tactical voters can intentionally promote "push-overs", candidates unlikely to win, past their real preference. This can sometimes benefit voters by bringing their preferred candidate to a more winnable final runoff round, basically using the push-overs as a shield for protection of their primary vote.

#### Return of the '3rd-party spoiler effect'

main article: Favorite betrayal criterion

IRV only stops the '3rd-party spoiler effect' as long as the 3rd party clearly does not have a chance to win. Just when the 3rd party grows to a competitive size, voters may start to find again that they benefit from tactically ranking a major party candidate over their favorite candidate.

This failure mode occurs if the voter fears that their 1st-choice candidate (the 3rd party) might first win from his best-liked major party, then not get enough of the redistributed votes, and finally almost certainly lose to the other major party. The voter would wind up with his least-favored outcome. The voter may seek to prevent this by ranking the best-liked major party over their actual first choice.

This problem is known as "favorite betrayal". A video which explains this problem more is "How our voting system (and IRV) betrays your favourite candidate" by Dr. Andy Jennings at Center for Election Science, and an overall summary of Favorite betrayal criterion can be found on this wiki.

#### Failure to pick a good compromise

IRV can ignore a good compromise in favor of a polarized choice that enjoys smaller actual support.

This failure mode occurs in a 3-choice election where parties A and B are bitterly opposed, and party C is first choice for a minority but tolerable for a large majority. For a real-life example, consider the 17th-century Europe struggle over "government-enforced Catholicism" versus "government-enforced Protestantism", with "freedom of private worship" as the compromise C.

Voting turnout would resemble the following:

38% of voters 38% of voters 11% of voters 13% of voters
1. A 1. B 1. C 1. C
2. C 2. C 2. A 2. B
3. B 3. A 3. B 3. A

In IRV, the compromise (choice C) is eliminated immediately. Choice B is elected, giving severely lower total satisfaction among voters than choice C.

Failure to count the ballots in a way most favorable to the voters

26% of voters 25% of voters 49% of voters
1. A 1. C 1. D
2. B 2. B

Here, a majority is split between two candidates as their 1st choice, but can unanimously agree on a third candidate as their 2nd choice. IRV instantly eliminates the majority's 2nd choice for having no 1st choice votes, then eliminates C, and then elects D. Yet a majority of voters preferred a different outcome.

### Logistical issues

Ballots in IRV cannot be easily summarized. (Political scientists call this the Summability criterion.) In most forms of voting, each district can examine the ballots locally and publish the total votes for each candidate. Anyone can add up the published totals to determine the winner, and if there are allegations of irregularities in one district only that district needs to be recounted.

With IRV, each time a candidate is dropped, the ballots assigned to them must be re-examined to determine which remaining candidate to assign them to. Repeated several times, this can be time-consuming. If there is a candidate X who got more votes than all of the candidates who got less than X put together, then all of these candidates who lost to X can be dropped simultaneously without affecting the final outcome, which can speed up counting.

If counting takes place in several places for a single IRV election (as in Australia), these counting centers must be connected by a securely authenticated channel (historically the telegraph was used) to inform them which candidate has come last and should be dropped. Centralizing the counting to avoid this problem can add opportunity for tampering.

### Logistical issues in Australia

#### House of Representatives

Initially, in Australia, ballots are counted at the booth level, with first preference results reported to the Divisional Returning officer and then to the National Tally Room. If it is clear who the two leading candidates will be, a notional distribution of the preferences of the minor candidates may be made. Postal and absentee ballots are of course yet to be processed - that takes another week or two.

Over the next few weeks, ballots and matching documentation are concentrated in the offices of the Divisional Returning Officer, where an actual distribution of preferences is made. This may be done by physically moving the ballots around, or by entering ballot data into a suitable computer.

If a candidate wins 51% of first preferences, a distribution of minor party preferences is strictly speaking not necessary, however the law now allows that such preferences be distributed to see what the "two-party preferred vote" actually is.

Federal elections are conducted by the Australian Electoral Commission, who employ all the workers at all the booths, to a common standard of neutrality and efficiency. Candidates may appoint scrutineers to watch (but not touch) what is going on.

## Notes

IRV always elects a Condorcet winner who receives at over 1/3rd of 1st choice votes. More generally, a candidate who at any point when they are uneliminated receives over 1/3rd of all active votes and pairwise beats (is preferred by more voters than) all other uneliminated candidates is guaranteed to win. This is because when all but two candidates are eliminated, the one preferred by more voters will win, and a candidate with over 1/3rd of active votes is guaranteed to be one of the final two remaining candidates, because at most any other two candidates can each get just under 1/3rd of the active votes, and therefore one of them will be eliminated before the over-1/3rd candidate.

Several variations of IRV have been proposed to meet the Condorcet and Smith criteria. The simplest of these are to eliminate everyone except the Condorcet winner (if they exist)/the candidates in the Smith Set, and then run IRV.