single transferable vote

Single transferable vote (STV) is a type of ranked preferential electoral system which uses multiple-member constituencies where each voter casts a single ballot where they rank candidates. The preferential or ranked voting allows transfer of votes to produce proportionality, to form consensus behind the most-popular candidates and to avoid the waste of votes prevalent under other voting systems. Another name for STV is multi-winner ranked-choice voting''.''

Under STV, each elector (voter) casts a single vote in a district election that elects multiple winners. Each elector marks their ballot for the most preferred

candidate

and also marks secondary preferences. A vote goes to the voter's first preference if possible, but if the first preference is eliminated, instead of being thrown away, the vote is transferred to an alternate preference, with the vote being assigned to the voter's second, third, or lower choice if possible (or, under some systems, being apportioned fractionally to different candidates). As long as there are more candidates than seats, the least popular is eliminated and their votes transferred based on voters' marked subsequent preferences. A quota (the minimum number of votes that guarantees election) is calculated and candidates who accumulate that number of votes are declared elected.

In some systems, surplus votes not needed by successful candidates are transferred proportionally, as described below. Elections and/or eliminations, and vote transfers where applicable, continue until enough candidates are declared elected or until there are only as many remaining candidates as there are unfilled seats, at which point the remaining candidates are declared elected.

The specific method of transferring votes varies in different systems (see ).

STV enables votes to be cast for individual candidates rather than for parties or party machine-controlled party lists. Compared to first-past-the-post (FPTP) voting, STV reduces the number of "wasted" votes, which are those cast for unsuccessful candidates and for successful candidates over and above those needed to secure a seat. STV avoids this waste by transferring a vote to another preferred candidate.

STV also provides approximately proportional representation, ensuring that substantial minority factions have some representation. No one party or voting block can take all the seats in a district. The key to STV's achievement of proportionality is that each elector (voter) only casts a single vote in a district contest electing multiple winners.

Under STV, district elections grow more proportionally representative in direct relation to increase in the number of seats to be elected in a constituencythe more seats, the more the distribution of the seats in a district will be proportional.

For example, in a three-seat STV election using the Hare Quota of $() / ()$, a candidate or party with 33 percent of the votes is guaranteed to win a seat. In a seven-seat STV district, any candidate who can get the support of approximately 14 percent of the vote (either first preferences alone or a combination of first preferences and lower-ranked preferences transferred from other candidates) will win a seat.

Because of this quota-based fairness, it is extremely rare for a party to take a majority of the seats in a district without a majority of the vote. Addtionally, a majority of voters see their vote used to elect the candidates who make up a majority of the district's elected members.

Instant runoff voting (IRV) is the single-winner analogue of STV. It is also called "single-winner ranked-choice voting". Its goal is representation of a majority of the voters in a district by a single official, as opposed to STV's goals of not only the representation of a majority of voters through the election of multiple officials but also of proportional representation of all the substantial voting blocks.

Terminology

When single transferable voting is used for single-winner elections, it produces a system that is formally called instant-runoff voting.

STV uses preferential votes cast in multi-seat districts, but some use the term "preferential voting" when they are talking only about instant-runoff voting. "Preferential voting" can also refer to a broader category, ranked voting systems. In the United States, STV is sometimes also called preferential voting, choice voting or preference voting.

STV used for multi-winner elections is sometimes called "proportional representation through the single transferable vote", or PR-STV. "STV" usually refers to the multi-winner version, as it does in this article.

Hare–Clark is the name given to PR-STV elections in Tasmania and the Australian Capital Territory.

Voting

In STV, each voter casts just one vote although multiple seats are to be filled in the district. They can provide alternate preferences to be used if needed by ranking the candidates in order of preference. In practice, the candidates' names are usually organized in columns so that voters are informed of the candidates' party affiliations or whether they are standing as independents.

An alternative way to mark preferences for candidates is to use columns for the voters' preference. One column shows first preference. An X there goes beside the most-preferred candidate. The next column is for the second preference. An X there marks the second-preference candidate, etc.

Filling seats under STV

The use of quota to fill seats

In most STV elections, a quota is established to ensure that all elected candidates are elected with approximately equal numbers of votes. In some STV varieties, votes are totalled, and a quota (the minimum number of votes that guarantees election) is derived. Another system, which used four-seat districts, set quota at 25 percent of the votes in a district.

Once a quota is determined, candidates' vote tallies are consulted. If a candidate achieves the quota, they are declared elected. Then in some STV systems, any surplus vote is transferred to other candidates in proportion to the next highest preference marked on the ballots received by that candidate. If more candidates than seats remain, the candidate with the fewest votes is eliminated, with their votes being transferred to other candidates as determined by the voters' next preference. Elections and eliminations, and vote transfers where applicable, continue until enough candidates are declared elected to fill the open seats or until there are only as many remaining candidates as there are unfilled seats, at which point the remaining candidates are declared elected. These last candidates may be elected without surpassing quota, but their survival until the end is taken as proof of their general acceptability by the voters.

Finding winners using quota

An STV election count starts with a count of each voter's first choice, recording how many for each candidate, calculation of the total number of votes and the quota and then taking the following steps:

# A candidate who has reached or exceeded the quota is declared elected.
# If any such elected candidate has more votes than the quota, surplus votes are then transferred to other candidates proportionally based on their next indicated choice on all the ballots that had been received by that candidate. There are several different ways to do this. (see ).
# If there are still seats to be filled after the surplus votes of all candidates elected in the first count have been transferred, if any new candidates have been elected, their surplus votes are transferred proportionally.
# If there are still seats to be filled after all surplus votes have been transferred, the candidate with the fewest votes is eliminated and their votes are transferred to the next candidate marked on each ballot. Candidates already elected or eliminated cannot receive votes in most systems.
# This process repeats until either every seat has been filled by candidates surpassing quota or until there are only as many remaining candidates as there are remaining seats, at which point the remaining candidates are declared elected.

There are variations in conducting transfers (see ).

When the number of votes transferred from the losing candidate with the fewest votes is too small to change the ordering of remaining candidates, no transfer is made or more than one candidate is eliminated simultaneously.

Vote transfers and quota

STV systems primarily differ in how they transfer surplus votes and in the size of the quota. For this reason some have suggested that STV can be considered a family of voting systems rather than a single system.

The quota, if used, must be set at a level where no more candidates can reach quota than there are seats to be filled. The quota is the minimum number of votes that ensures a candidate is elected. Any candidate that takes the quota is declared elected. It cannot be so small that more candidates can be elected than the number of open seats, but the smaller it is, the more fair is the result.

If fair results are to be produced and the number of candidates are pre-set, a quota must be set whereby any candidate that receives it is declared elected.

There are different quotas to choose from.

The Droop quota is the most commonly used quota. It is generally considered to be the absolute lowest number that elects the correct number of candidates to fill the available seats, at least based on the original number of votes cast.

The Droop quota is given by the

floor function

formula:

:$\text = \operatorname \left(\frac \right) + 1$

The Droop quota is an extension of the majoritarian principle of requiring a 50% + 1 majority in single-winner elections under instant-runoff voting. Using Droop means 25% plus 1 is the quota in a three-seat contest because no more than three people can each have 25% of the vote + 1; using Droop means 10% of the vote + 1 is the quota in a nine-seat district because no more than nine people can each have 10% of the vote + 1, and so on.

Droop being relatively low means that the largest party, if it has majority of votes, is likely to take the majority of the seats in a district.

The Hare quota was used in the original proposals by Thomas Hare. It is larger than the Droop and sometimes ensures greater representation to less-popular parties within a district. But also, being larger than Droop, Hare presents more of an obstacle to small parties who hope to take just one seat. Being smaller than Hare, the Droop quota may give a seat to a small party that does not have the votes to take a seat under Hare.

There are variations in the conduct of transfers in different variations of STV, such as how to transfer surplus votes from winning candidates and whether to transfer votes to already-elected candidates. Under STV, votes cast for losing candidates and surplus votes cast for winning candidates are sometimes transferred to voters' next choice candidates. In these ways, STV minimizes wasted votes.

It can happen that a vote is set to be transferred but cannot be because it bears no subsequent preference for any remaining candidate. In the case of transfers of surplus votes, if the number of transferable votes is less than the number of the surplus, no math is needed to make the transfer. Transfer of the transferable votes is done simply by reference to subsequent preference on the votes.

If the variation of STV used allows transfers to candidates already elected, when a candidate is eliminated and the next preference on the ballot shows preference for a candidate already elected, votes are transferred to already victorious candidate. The new surplus votes for the victorious candidate (transferred from the eliminated candidate) are then transferred to the next preference of the victorious candidate, as happened with their initial surplus. However, any vote transfers from the victorious candidate to a candidate who was already eliminated are impossible, and reference must be made to the next marked preference, if any. See for details.

A quota set lower than Droop is sometimes workable. If fractional votes are used in an STV method, the Droop quota may be modified so that the fraction is not rounded down.

Frank Britton, of the Election Ballot Services at the Electoral Reform Society, observed that the final plus one of the Droop quota is not needed; the exact quota is then simply $(\text) / (\text+1)$. Without fractional votes, the equivalent integer quota may be written:

:$\text = \operatorname \left(\right)$

So, the quota for one seat is 50 of 100 votes, not 51.

In any case, in most STV elections the appearance of non-transferable votes means that the quota could be lowered significantly during the counting of the vote with no danger of having too many elected.

In STV, vote transfers are of two typestransfers of votes of eliminated candidates and transfers of surplus votes of elected candidates. The first type happens more often than the second type. Surplus votes are transferred only after a candidate is elected and then only if there are still open seats to be filled and if the transfers may affect the ranking of the remaining candidates.

Transfers of votes of eliminated candidates

Transfers of votes of eliminated candidates is done simply, without the use of complex math. The next usable preference on the vote gives the destination for the transfer of the vote. If there is no usable preference on the ballot, the vote goes to the "exhausted" or non-transferable pile.

Transfers of surplus votes

The transfer of surplus votes of an elected candidate may be very simply done or may be done more or less intricately, depending on the circumstances and the choice of the government or election officials.

It can happen that a vote is set to be transferred but cannot be because it bears no subsequent preference for any remaining candidate. In transfers of surplus votes, any non-transferable votes are left with the elected candidate.

If the number of transferable votes is less than the surplus, the transfer of surplus votes can be performed just as it is done in the case of transfer of eliminated candidates, the only difference being that non-transferable votes remain with the elected candidate. They do not go to the exhausted pile. Transfer of the transferable votes is done in these cases simply by reference to the next usable preference on the vote.

In cases where the number of transferable votes is more than the surplus, a more-involved method is needed in order to make the transfer proportional and to ensure that the quota left with the successful candidate is proportional as well. But election officials here have a choice of using a simpler method or more involved methods.

The basic formula for how to transfer surplus votes when there are more transferable votes than the surplus to be transferred is:

:$\begin & \text \\$

pt

= & \left( \frac \right) \times \text
\end

This can produce fractional votes, which are handled differently under different counting methods.

As well, not considering later preferences when transferring votes may influence later transfers and are thought of as being random,so instead some places use systems that break down the elected candidate's votes into many separate piles looking at all the permutation of preferences marked on the votes.

STV variants that look only to the next usable preference are used successfully in the Republic of Ireland (except Senate elections) and in Malta, and elsewhere. In these places, merely the next preference is examined. Votes are transferred as whole votes. Any randomness may arise from the later preferences, if any, that may have to be used later. But choosing the votes at random from the pile means that each transfer should be mixed and likely closely resembles the composition of the entire pile.

The Gregory method (also known as Newland–Britain or Senatorial rules) eliminates randomness by examining all the preferences marked on ballots, the later preferences dictate how later transfers, if any, will go. They transfer votes as fractions of votes. Gregory is in use in Northern Ireland, the Republic of Ireland (Senate elections) and in Australia. Both Gregory and earlier methods have the problem that in some circumstances they do not treat all votes equally. For this reason Meek's method, Warren's method and the Wright system have been invented. While easier methods can usually be counted by hand, except in a very small election Meek and Warren require counting to be conducted by computer. The Wright system is a refinement of the Australian Senate system replacing the process of distribution and segmentation of preferences by a reiterative counting process where the count is reset and restarted on every exclusion. Meek is used in local body elections in New Zealand.

Meek in 1969 was the first to realize that computers make it possible to count votes in way that is conceptually simpler and closer to the original concept of STV. One advantage of Meek's method is that the quota is adjusted at each stage of counting when the number of votes decreases because some become non-transferable. Meek also considered a variant on his system which allows for equal preferences to be expressed. This has subsequently (since 1998) been used by the John Muir Trust for electing its trustees.

Demonstration STV election

Suppose an election is conducted to determine what three foods to serve at a party. There are 5 choices - Oranges, Pears, Chocolate, Strawberries, and Hamburgers. Only three of them will be served.

The hope is that each guest will be served at least one food that they are happy with. It is decided to use STV to make the decision so each guest is given one vote and also allowed to cast one back-up preference to be used only if the first preference can not elect a food or to direct transfer of surplus votes if it does. The 23 guests at the party mark their ballots according to the table below, with first and second preferences marked by each voter.

First, the quota is calculated. Using the Droop quota, with 23 voters and 3 winners to be found, the number of votes required to be elected is:

:$Q_ = \operatorname \left(\right) +1 = 6 \mbox$.

When ballots are counted the election proceeds as follows:

Result: The winners are Chocolate, Oranges and Strawberries.

This result differs from the one that would have occurred if the three winners were decided by first preference plurality rankings, in which case Pear would have been a winner, as opposed to Strawberry, for having a greater number of first preference votes.

If the voters had been able to choose only one food to serve (as in first-past-the-post, it is likely that Chocolate, the choice of only slightly more than half of the 23 party-goers, would have won and Chocolate would be the only food served at the party.

STV in this case produced a high level of effective votesvotes used to elect the successful candidates. 18 voters saw their first preference elected, and three more saw their second preference elected. Only two, those who voted for hamburgers with pears as their second preference, did not see any of their choices elected.

History and current use

Origin

In 1896,

Andrew Inglis Clark

was successful in persuading the

Tasmanian House of Assembly

to be the first parliament in the world elected by what became known as the '' Hare-Clark electoral system'', named after himself and Thomas Hare.

H. G. Wells

: in particular, STV fails to achieve independence of irrelevant alternatives (like most other vote-based ordering systems) and monotonicity.

Migration of preferences

The relative performance of political parties in STV systems is analysed in a different fashion from that used in other electoral schemes. For example, seeing which candidates are declared elected on first preference votes alone can be shown as follows:

The data can also be analysed to find the proportion of voters who express only a single preference, or those who express a minimum number of preferences, to assess party strength. Where parties nominate multiple candidates in an electoral district, analysis can also be done to assess their relative strength.

Other useful information can be found by analysing terminal transfersi.e., when the votes of a candidate are transferred and no other candidate from that party remains in the countespecially with respect to the first instance in which that occurs:

Another effect of STV is that candidates who did well on first preference votes may not be elected, and those who did poorly on first preferences can be elected, because of differences in second and later preferences. This can also be analysed:

See also

* Tally (voting)
* None of the above
* Approval voting
* Single non-transferable vote
* Table of voting systems by country
* ''Voting matters'', a journal concerned with the technical aspects of STV

Notes

References

Bibliography

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Further reading

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External links

ACE Project


– fro
Accurate Democracy


lists a dozen programs for computing the single transferable vote.

Australia's Upper Houses – ABC Rear Vision
A podcast about the development of Australia's upper houses into STV elected chambers.

{{DEFAULTSORT:Single Transferable Vote
Single transferable vote,
Non-monotonic electoral systems
Preferential electoral systems
Proportional representation electoral systems
Electoral systems

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