Instant-runoff voting

When the Single Transferable Vote 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 Single transferable vote (STV) because it is simpler and is a widely advocated electoral reform in the USA.

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

~ ~ ~ ~ ~ ~ ~ ~ ~ ~

~ ~ ~ ~ ~ ~ ~ ~ ~ ~

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. However, the result of Knoxville winning shows that in this case, a capital which is the last choice of 42% of the state's population can win; some would say that this is an undesirable result. The reason for this result is that the preferences of those who voted for Memphis are not counted beyond their first choice, because Memphis isn't eliminated until the last "round". In Schulze method, another ranked choice voting method, all preferences are counted, and Nashville, a compromise city toward the geographic center of the state, would win. To voters, both methods are the same, as the ballot is identical in most ranked choice voting methods. The method of counting (and in this case, the outome) of the votes differs.

~ ~ ~ ~ ~ ~ ~ ~ ~ ~

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. This is because 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 multicandidate 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
• FIRST ROUND: Eliminate the candidate in the tie with the lowest number of votes at the earliest stage in the count at which the candidates in question had an unequal number of votes (in effect this means the candidate with the lowest number of first-preference votes - except in the unlikely circumstance that the same candidates are tied both in the round when one has to be eliminated and in the first round).
• Traditional rule; violates purity of one person, one vote principle
• ALL: Eliminate all tied candidates at once.
• Good for weak candidates (with less than 5% of votes), but can lead to strategic nominations, which cause IRV implementations using this method to not be spoiler proof
• 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