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# Single Transferable Vote

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 called instant-runoff voting, 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 to elect the Australian senate [1] and the City Council in Cambridge, Massachusetts. The government of Tasmania calls the single transferable vote 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 in British Columbia in the 1949 and 1952 provincial elections.

 Table of contents 1 Voting 2 Setting the Quota 3 Counting The Votes 4 An example 5 How It Gives Proportional Representation 6 Potential for Tactical Voting 7 External links

## Voting

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

## 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:

.

Other quotas used include the Hare Quota:

Process A: Top-preference votes are tallied. If one or more candidates have received more votes than 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:

17 voters rank the candidates:

1. Andrea
2. Carter
4. Delilah

8 voters rank the candidates:

1. Delilah

The threshold is:

In the first round, Andrea receives 22 votes and Delilah 8. Andrea is elected with 11 excess votes. Her votes are reallocated in proportion to her second preferences (which votes are chosen may be decided by random selection), and 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 thousandths 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.

## How It Gives Proportional Representation

STV is proportional for every characteristic the voters value. e.g. a portion of voters ranking all women first will result in this portion rounded down to next quota will of women at least represented.

It ensures proportional representation simply by wasting few votes.

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.

## Potential for Tactical Voting

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

However, there are loopholes: 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.

A vote is wasted if it ends up on the last candidate to be eliminated.