Transferable individual voting

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The system of transferable Einzelstimmgebung ( english single transferable vote , STV) is a proportional people voting procedures that the problem of invalid votes in the pure majoritarian fix and better representation should cause all votes cast. In this process, several winners are determined per constituency. It is used explicitly for the choice of people, not the choice of party lists. The procedure is one of the preferential voting systems .

In the case of transferable individual votes, each voter creates a ranking of all (or even just a few) candidates. According to different calculation methods (mostly called the droop quota method), a number of votes is calculated from the seats to be allocated and the votes cast, which is necessary for the election. Now the ballot papers are processed according to the specified preferences. If a candidate has already been elected (number of votes greater than the result of the droop quota), this vote will benefit the next candidate on the voter's personal ranking list.

In the same way, in the following step, the votes for non-elected candidates are now transferred up the ranking list. The candidate with the least total number of votes is removed from all lists, the vote is given to the candidate who is above him on the list. In this way, both excess votes and votes for non-elected candidates are carried over to the other candidates until all seats are occupied.


In 2007, single transferable voting was used in elections in Australia , Malta , the Republic of Ireland , Northern Ireland (except in the House of Commons elections ) and Iceland . The system is also used in some local elections in New Zealand and in local elections in Scotland . Since 2002, single transferable voting has only been used in the United States in elections to governing bodies in Cambridge, Massachusetts .


If the rules of the STV are used in an election where only a single person (e.g. single constituencies or president) is to be elected, it is the same as instant runoff voting , which is not itself a proportional representation procedure. If several seats are to be allocated in constituencies, the procedure is sometimes referred to as proportional representation through the single transferable vote or PR-STV . Since instant runoff is not a proportional representation system, it is considered by some skilled in the art to be a different system from PR-STV. When the term STV is used, it is usually referred to as PR-STV, as is the case in this article. STV is also known by other names: in Australia sometimes as the Hare-Clark proportional method, in the USA it is sometimes called choice voting .


In the case of transferable individual votes (STV), the voter arranges the list of candidates according to his preferences. In other words: He places a “1” next to his most preferred candidate, a “2” next to his second most preferred candidate, and so on. The completed ballot thus contains a ranking of the candidates. An example:

  1. Horst Sengelmann
  2. Maria tree base
  3. Eveline Schaudich

Counting the votes

Determination of the quota

A few different odds can be used in STV elections, but the most common is the droop odds .

  • valid votes = total number of valid votes cast
  • Seats = number of seats to be filled

Determine the winner

Simply put, every candidate in an STV election needs a certain minimum number of votes - the quota - in order to be elected. Any candidate with either more votes than necessary or too few to be elected will have votes transferred to other candidates. This process continues until all seats have been taken. The candidates to whom votes are transferred will be determined by the preferences that voters have indicated on their ballot papers.

Initially, only the first preferences are counted. Any candidate whose number of votes is greater than the quota is immediately declared elected. His excess votes are then transferred to other candidates. If not enough candidates have reached the quota, the candidates with the fewest votes will be eliminated one by one and their votes transferred until enough candidates have reached the quota so that all seats are taken. Once a candidate is either elected or eliminated, they will be excluded from the remainder of the count; no further votes can then be transferred to him (except for the Meek method). The counting of an STV election is completed in the following steps:

Step I.
Every candidate whose number of votes corresponds at least to the quota is declared elected.
Step II
If a candidate has received more votes than the quota is, the excess or “remaining” votes are carried over to other candidates who continue to participate in the counting. If a candidate has now reached the quota, he is declared elected and the counting returns to step I. Otherwise, continue with step III.
Step III
The candidate with the fewest votes is eliminated or “excluded”; his votes will be transferred to other candidates who will continue to take part in the counting. The process is repeated from step I until all seats have been taken.

In order to avoid unnecessary counting, the counting is usually not continued until every candidate has reached the quota, but ends when there are no more candidates than there are still seats to be allocated. If the number of votes to be transferred is insufficient to elect someone or to change the order of the candidates in the order of preference, then several candidates can be excluded at once, or an excess can be kept instead of being transferred. This is unavoidable when ballot papers that do not contain a complete ranking of candidates are allowed to be exhausted (i.e. not all preferences have been assigned), as there is then the possibility that not enough candidates will reach the quota.

Since the single transferable vote transfers the votes for candidates who either have more votes than necessary or too few to be elected to other candidates, it is said that this procedure minimizes the number of wasted votes.

Illustration of the principle

By way of illustration, an STV election is sometimes compared to an election among children in the schoolyard. When voting, the children stand behind the candidate of their choice, but no candidate can be elected unless he has a minimum number of children behind him. Since the children know that each candidate only needs the votes of a certain number of classmates to be elected, those who are the last to gather behind a candidate who already has enough votes decide not to waste their vote, but rather to stand behind someone else to help him win. In the same way, all those children whose candidate apparently can no longer win change. This goes on until all representatives have been selected.

STV can be thought of as an automated version of this process, except that eliminating the candidates with the fewest votes sometimes penalizes candidates who might have won if they hadn't been eliminated right away. Each winner needs a quota of votes instead of a certain number of children standing behind them, and instead of the children, votes are cast according to the preferences on the ballot papers.

Another example

Suppose there is a vote going on to determine what foods to offer at a party. There are five candidates, three of which are to be elected. The candidates are: "oranges", "pears"; "Chocolate", "Strawberries" and "Bonbons". The 20 guests at the party indicated their preferences on their ballot papers in the following two tables (the first gives numbers, the second shows pictures). With this choice, only the first one or two preferences are displayed, as the lower preferences have no influence on the result in this case.

4 voters 2 voters 8 voters 4 voters 1 voter 1 voter
1. orange pear chocolate chocolate strawberry sweets
2. pear orange strawberry sweets

# xxxx xx xxxx
xxxx x x
1 orange pear Chocolate Chocolate Strawberry sweets
2 pear orange Strawberry sweets

First the quota is calculated. When using the droop rate, 20 voters and 3 winners to be determined, the number of votes required to be elected is:

The vote count is as follows:

Candidate: orange pear chocolate strawberry sweets
Round 1 4th 2 12 1 1
round 2 4th 2 6th 5 3
Round 3 6th 6th 5 3
Round 4 6th 6th 5
Candidate: orange pear Chocolate Strawberry sweets
Round 1 xxxx xx xxxx

x x
round 2 xxxx xx xxxx
x x x
Round 3 xxxx
x x x
Round 4 xxxx
x x x
Round 1
Chocolate is declared elected because chocolate has more votes than the quota.
round 2
The surplus of the chocolate votes is carried over proportionally to the strawberries and sweets according to the secondary preferences of the chocolate voters. However, even with the transfer of the surplus, no candidate reaches the quota. Therefore, the pears that have the fewest votes are eliminated.
Round 3
The voices of the pears are transferred to their second preference, the oranges. As a result, the oranges reach the quota and are selected. Since the oranges barely reach the quota, there is no excess to transfer.
Round 4
None of the remaining candidates reach the quota, so the candies are eliminated. The strawberries are the only remaining candidate, so they win the final seat.
The winners are chocolate, oranges and strawberries.

Different counting methods

STV systems differ in a number of characteristics, mainly in how votes are broadcast and in the exact size of the odds used to determine the winners. For this reason there have been proposals to view STV as a family of electoral processes rather than as a single electoral process. Nowadays the droop rate is the most widely used rate. This ensures (except in rare cases) the majority rule, while at the same time adhering to the condition that no more candidates can reach the quota than seats are available. In the original concept, STV used the hare quota (votes / seats), but this is now generally viewed as a technically poorer solution. New Zealand uses odds that are similar to droop odds.

The simplest method of transferring excess in STV involves an element of chance. Systems that are partly based on chance are used in the Republic of Ireland (except for Senate elections) and Malta, but also in other places. This is why the Gregory Method (also known as Newland-Britton or Senate Rules) was designed, which eliminates chance by allowing fractional votes to be transmitted. Gregory is used in Northern Ireland, the Republic of Ireland (in Senate elections) and Australia. The problem with both Gregory and these earlier methods, however, is that in some circumstances they do not treat all voices equally. This is why Meek's method and Warren's method were invented. While counting by hand is possible with simpler methods, with Meek and Warren, except for very small elections, counting by computer is necessary. Meek is currently used in STV elections in New Zealand.

The latest refinements to STV include an attempt to address the issue of sequential exclusions. Successive exclusions mean that STV sometimes eliminates candidates early in the count who could have won a seat later if they had been allowed to stay in the race longer. Techniques such as CPO-STV (Comparison of Pairs of Outcomes by the Single Transferable Vote) and Sequential STV were invented to overcome this problem by incorporating elements of the Condorcet methods into STV. One method known as BTR-STV approaches the problem differently and more simply than these methods by simply ensuring that no such candidate can be eliminated. None of these new methods have been used in a state election.


Compared to other electoral processes, the question of how vacant seats should be filled is more difficult, as the results depend on transfers of several candidates. There are various ways of determining a successor: countback method, appointment, by-election, replacement list.

Implications and problems

Impact on political groups and candidates

The use of STV can lead to a decline in the role of political parties in voting and a decline in party affiliations in electoral governments. In contrast to those proportional representation systems that use party lists, voters in STV are not explicitly committed to parties, even if they exist; voters can ignore party affiliation and freely rank their preferred candidates from candidates from different parties. Candidates can achieve electoral success by getting enough votes from voters who usually do not support their party, possibly by getting cast votes from politically close supporters of other parties, or by taking a stand against the party line on a particular issue. In contrast to proportional representation with lists, STV can be used in elections in organizations in which there are not necessarily clear camps and currents, e.g. B. in trade unions , clubs and schools.

However, there are also some STV variants that strengthen the role of parties. In Australian Senate elections, the combination of large constituencies, compulsory voting and ballot papers that have to be filled in completely to the last preference means that 95% of voters follow prepared party nominations. This gives the parties considerable power in determining the election result by determining the order of recommended candidates, both their own candidates and the transfers to other parties.

Since it is not only important for a candidate to receive first preferences, but also second and third preferences, the incentive for negative campaigning decreases as this reduces the chances of receiving second and third preferences from supporters of other candidates.

Tactical considerations for the number of candidates

For political parties there are tactical considerations as to how many candidates they should send into the race in an election if the election does not require completely filled out ballot papers. Starting with too few candidates can mean that all candidates are already elected at an early stage of the counting and then votes are transferred to candidates from other parties. Coming up with too many candidates could mean that the candidates each receive too few first preferences and thus candidates who could have been successful with large second preference support are eliminated before others are elected and their second preferences have been transferred. This effect is exacerbated if voters do not stick closely to the candidates of their preferred party; however, if voters vote all candidates from a particular party before voting for other candidates and before not specifying any further preferences, then too many candidates are not a problem.

In Malta, where voters closely follow party preferences, parties often put forward more candidates than there are seats to be elected. In Australian Senate elections, voters similarly vote along party lines, as it is much easier to choose a party's stated preferences than to compile a full list yourself. In the Republic of Ireland, the main political parties think carefully about how many candidates they will put up in different constituencies. Broadcasts often do not take place along party lines, but often benefit more prominent local personalities. Election posters for the most prominent candidate of a party usually also mention the party's preferred second preference (and sometimes also the third preference).

Electoral system criteria

In the case of scientific analyzes of electoral systems such as B. STV are mostly the electoral system criteria that they meet, the focus. No preference voting procedure fulfills all the criteria that are described in Arrow's theorem of impossibility : STV does not fulfill the independence of irrelevant alternatives (like most other vote-based ranking systems) and neither does the monotony criterion . Failure to be independent of irrelevant alternatives makes STV somewhat susceptible to strategic nominations, but to a lesser extent than procedures with a simple majority, in which the spoiler effect is more pronounced and predictable.

The non-monotony makes it possible in some circumstances to choose a preferred candidate by reducing his position on some ballot papers; by helping to elect a candidate who ousts the preferred candidate's main opponent, a voter can sometimes cause his preferred candidate to benefit from votes cast from the defeated opponent.

STV does not meet the participation criterion , which can mean that an STV voter can achieve a result that is more convenient for him by not voting at all. If, however, a voter does not consider a candidate in his preference ranking on his ballot paper, he does not harm any candidate he has considered and does not help any of the candidates who are not included in the ranking on the ballot paper.

STV is also susceptible to the Alabama Paradox : A candidate elected in a particular multi-mandate constituency may be in the same constituency and with an equal distribution of votes. May not be elected if the constituency had one more seat. The reason for this is the use of quotas; Proportional voting with list voting according to the Hare-Niemeyer process is similarly affected, but maximum number processes such as the D'Hondt process and Sainte-Laguë / Schepers process are not affected.

Some modifications to the STV have been proposed to meet the monotony and other criteria. The most common method among the proposed amendments is to change the order, are eliminated in the candidate: A candidate who is in second place on all ballots, it can happen in theory, that it is already eliminated as the first, even if he Condorcet winner is . Meek noticed this problem and suggested a change in the broadcasting of votes to largely eliminate tactical voting on STV. However, Meek himself did not propose a method that met the Condorcet criterion . Other theorists have suggested further refinements to the STV, e.g. B. to use a Condorcet method to determine the elimination sequence .

Some of these changes change STV in such a way that if only one seat to be allocated is applied, it no longer amounts to instant runoff voting . B. on a Condorcet method.

Constituency size

Another question that is often considered in elections with transferable individual votes is the size of the constituency , i.e. the number of candidates to be elected in the constituency. To a lesser extent, the overall size of the organ to be chosen also plays a role. In transferable individual voting and other proportional representation systems, the number of wasted votes and the subsequent rounding errors, the lower the number of candidates to be elected. As a result, the distribution of seats in larger constituencies better corresponds to the preferences of the voters. Therefore, in large constituencies, the effects of gerrymandering are greatly reduced; since gerrymandering relies on wasted votes for the “last seat” of each constituency, it is more difficult to manipulate multi-person constituencies. In some elections with transferable individual votes, the constituency size is just three seats; there is no theoretical upper limit for the constituency size with this procedure. Thomas Hare's original proposal was for a single nationwide constituency.

However, since the transferable individual voting is a proportional representation procedure, a candidate in large constituencies only needs a small percentage of votes to be elected. With nine candidates, each candidate who receives more than 10% of the vote wins a seat; with 19 candidates 5% is sufficient.

Larger constituencies and - indirectly linked to this - a larger number of candidates make it more difficult for the individual voter to rank all candidates in a meaningful order. This can lead to an increased number of incompletely filled in ballot papers and to mere orientation towards party affiliations.

See also

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