Single transferable vote

The Single Transferable Vote, or STV, is a voting system designed to accurately achieve proportional representation in multi-candidate elections. When applied in a proportional representation setting in multi-candidate elections, it is generally known as Proportional Representation through the Single Transferable Vote or PR-STV. When similar methods are applied to single-candidate elections they are sometimes called instant-runoff voting or the alternative vote and have different implications for a similar ballot. In both systems of voting the ballot choices represent an ordinal ranking of preferences, but they are tallied differently, since an "instant runoff" for only one position or measure is a trivial calculation.

Single transferable vote is used, among other places, for all elections in the Republic of Ireland [1] and Malta [2], to elect the Australian Senate [3], and for local, Assembly and European elections in Northern Ireland. In the United States, STV enjoyed some popularity in the first half of the 20th Century, but today the only official governing bodies that use STV to elect representatives are the City Council and School Committee of Cambridge, Massachusetts. The community school boards of the City of New York [4] also used STV until the boards were abolished in 2002.

The method used for electing the Legislative Assemblies of Tasmania and the Australian Capital Territory is called the "Hare system" or the "Hare-Clark system" after Thomas Hare, an English solicitor who developed the system, and Andrew Inglis Clark, a Tasmanian Attorney-General who introduced STV into State law. STV was used for provincial elections in the province of Alberta, Canada from 1926 to 1955.

Voting

Each voter ranks all candidates in order of preference. For example:

Andrea
Carter
Brad
Delilah

Setting the Quota

When all the votes have been cast, a winning quota is set. The most common formula for the quota is the Droop Quota which is most often given as:

\left({{\rm {votes}} \over {\rm {seats}}+1}\right)+1

.

Other quotas used include the Hare Quota:

{\rm {votes}} \over {\rm {seats}}

and the Imperiali Quota:

{\rm {votes}} \over {\rm {seats+2}}

.

For those keeping track, the size of the quota is then generally Hare > Droop > Imperiali.

Counting The Votes

Process A: Top-preference votes are tallied. If one or more candidates have received at least as many votes as the quota, they are declared elected. After a candidate is elected, they may not receive any more votes.

The excess votes for the winning candidate are reallocated to the next-highest ranked candidates on the ballots for the elected candidate. There are different methods for determining how to reallocate the votes. Some versions use random selection, others count each ballot fractionally.

Process A is repeated until there are no more candidates who have reached the quota.

Process B: The candidate with the least support is eliminated, and their votes are reallocated to the next-highest ranked candidates on the eliminated ballots. After a candidate is eliminated, they may not receive any more votes.

After each iteration of Process B is completed, Process A starts again, until all candidates have been elected or eliminated.

An example

2 seats to be filled, four candidates: Andrea, Brad, Carter, and Delilah.

5 voters rank the candidates:

Andrea
Brad
Carter
Delilah

17 voters rank the candidates:

Andrea
Carter
Brad
Delilah

8 voters rank the candidates:

Delilah

The threshold is: $\left({30 \over (2+1)}\right)+1=11$

In the first round, Andrea receives 22 votes and Delilah 8. Andrea is elected with 11 excess votes. Her 11 excess votes are reallocated to their second preferences (which votes are chosen may be decided by random selection). For example, 8 of the reallocated votes are for Carter, 3 for Brad. Note: this is not a realistic example - elections with a small number of votes often have special rules - for example, Irish Senate elections are conducted using thousands of votes.

As none of the candidates have reached their threshold, Brad, the candidate with the fewest votes, is eliminated. All of his votes have Carter as the next-place choice, and are reallocated to Carter. This gives Carter 11 votes and he is elected.

Is STV a proportional voting system?

STV is not a proportional system in the strict sense. STV does not guarantee that a party will get the same percentage of seats as it gets as a percentage of votes. In fact the notion of a vote "for a party" is less meaningful for STV because votes are not necessarily for a single party. A vote can list candidates from an assortment of political parties, in any order. The candidates that are elected reflect the combined preferences of all votes cast.

Another complication with proportionality under STV is the constituency system, where a set of candidates are elected in each electoral district. There is no explicit process for balancing the votes between constituencies, so the overall electoral result is merely the sum of the constituency results.

Within a constituency, however, STV can be said to be proportional for whatever characteristics the voters valued. For example, a portion of voters ranking all women first will result in this portion rounded down to next quota will of women at least represented.

STV provides this proportionality simply by wasting as few votes as possible. A vote is "wasted" if it does not elect anyone; it is partially wasted if it elects someone who gets more votes than is necessary to be elected. STV transfers votes that would otherwise be wasted, and it only transfers such votes.

The degree of national proportionality achieved is strongly related to the district magnitude, or the number of seats that are to be filled at any election. For example, under the Droop quota in a three-seat district, one vote less than a quarter of the total number of votes may not directly contribute to the election of a representative. Therefore, a desire for a high degree of proportionality is best support by large district magnitude.

The proportionality of STV can be controversial, especially in close elections such as the 1981 election in Malta. In this election the Maltese Labour Party won a majority of seats despite the Nationalist Party winning a majority of first preference votes. This caused a constitutional crisis, leading to provision for the possibility of bonus seats. These bonus seats were used in 1987 and again in 1996. Similarly, the Northern Ireland elections in 1998 led to the Ulster Unionists winning more seats than the Social Democratic and Labour Party, despite winning a smaller share of the vote.

Potential for Tactical Voting

The single transferable vote eliminates much of the reason for tactical voting. Voters are "safe" voting for a candidate they fear won't be elected, because their votes will be reallocated in Process B. They are "safe" voting for a candidate they believe will receive overwhelming support, because their votes will get reallocated in Process A.

However, in older STV systems there is a loophole: candidates who have already been elected do not receive any more votes, so there is incentive to avoid voting for your top-ranked candidate until after they have already been elected. For example, a voter might make a tactical decision to rank their top-place candidate beneath a candidate they know will lose (perhaps a fictional candidate). If the voter's true top-place candidate has not been elected by the time their fake top candidate loses, the voter's full vote will count for their true top-place candidate. Otherwise, the voter will have avoided having had their ballot in the lottery to be "wasted" on their top-ranked candidate, and will continue on to lower-ranked candidates.

Note that in more modern STV systems, this loophole has been fixed. A vote receives the same fractional weighting regardless of when it arrives at the successful candidate.

There are also tactical consideration for parties standing more than one candidate in the election. Standing too many candidates might result in first-preference votes being spread amongst them, and several being eliminated before any are elected and their second-preference votes distributed. Standing too few may result in all the candidates being elected in the early stages, and votes being transferred to candidates of other parties.

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