Games - Single Transferable Vote

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The Single Transferable Vote, or STV, is a preferential voting system designed to minimise wasted votes and provide proportional representation while ensuring that votes are explicitly for candidates rather than party lists. STV achieves this by using multi-seat constituencies (districts) and by transferring votes that would otherwise be wasted. STV initially allocates an individual's vote to their most preferred candidate, and then subsequently transfers unneeded or unused votes after candidates are either elected or eliminated, according to the voter's stated preferences.

As of 2006, STV is used for elections in Australia, the Republic of Ireland, Northern Ireland and Malta. It is also used for some minor elections in New Zealand– see History and usage of the Single Transferable Vote.

Terminology

When the rules of STV are used in a single winner election it is the same as instant-runoff voting, which is not a form of proportional representation. When used in multi-seat constituencies it is also sometimes known as Proportional Representation through the Single Transferable Vote or PR-STV. Because instant-runoff is not a form of proportional representation it is considered by some scholars to be a separate system from PR-STV. In any case, when the term STV is used it is usually PR-STV that is being referred to and that is the convention followed in this article. STV is also known by other names. In Australia it is sometimes known as the Hare-Clark Proportional method, while in the United States it is sometimes called choice voting.

Voting

In STV the voter ranks the list of candidates in order of preference. In other words (under the most common ballot design), she places a '1' beside her most preferred candidate, a '2' beside her second most preferred, and so on. The ballot paper submitted by the voter therefore contains an ordinal list of candidates. In the ballot paper shown in the image on the right, the preferences of the voter are as follows:

#Henry Ford #Mary Hill #Jane Doe

Counting the votes

Setting the quota

A number of different quotas can be used in STV elections, but the most common is the Droop quota. This is given by the formula:

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

Votes = the total number of valid (unspoilt) votes cast
Seats = the number of seats to be filled

Finding the winners

Put simply, in an STV election a candidate requires a certain minimum number of votes–the quota (or threshold)–to be elected. However any candidate with either too many, or too few, votes to be elected has votes transferred to other candidates, and the process continues until all seats have been filled. The candidates to whom votes are transferred are determined by the preferences given by voters on the ballot paper.

To begin an election only first preferences are tallied and any candidate who has more than the quota is declared elected immediately. If a candidate has more than the quota their surplus is transfered to other candidates. If enough candidates have still not reached the quota, then the candidates with the fewest votes are eliminated one by one, and their votes are transferred, until enough candidates have reached the quota so that every seat has been filled. When, at any stage, a candidate is either elected or eliminated they are removed from the remainder of the count and no further votes may be transfered to them. In full, an STV election proceeds according to the following steps:

Step I: Any candidate with at least a quota of votes is declared elected.

Step II: If any candidate has received more than a quota of votes then the excess or 'surplus' of votes is transfered to other candidates remaining in the count. If any candidate has now reached a quota they are declared elected and the count returns to Step I. Otherwise it proceeds to Step III.

Step III: The candidate with the fewest votes is eliminated or 'excluded' and their votes are transfered to other candidates remaining in the count. The process is then repeated from Step I until all seats have been filled.

Usually, to avoid unnecessary counting, instead of the count proceeding until every candidate has reached the quota, the count stops when there are no more remaining candidates than there are seats to be filled. This approach is unavoidable if ballots which do not list a full ranking of candidates are allowed to be exhausted, as it then becomes possible for an insufficient number of candidates to reach the quota.

Because in STV candidates with either too many, or too few, votes to be elected can have their votes transferred to other candidates, it is said to minimise wasted votes. For illustrative purposes, an STV election is sometimes compared to a school yard election among children. In the election children line up behind the candidates of their choice but no candidate can be elected unless have a minimum number of children lined up behind them. Since the children would all know that each candidate only needs a certain number of classmates' votes to be elected, those arriving last in line for a candidate who already has enough votes would choose to not waste their vote and would instead move to another line to help someone else to win. Likewise, those children whose candidate obviously could not win would move to another line, and so on, until all of the representatives had been chosen. STV can be considered an automated version of this process. Each winner requires a quota of votes rather than a certain number of children lined up behind them, and instead of children moving from one line to another votes are transferred according to preferences listed on the ballot papers.

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