Single transferable vote

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The Single Transferable Vote, or STV, is a preference voting system designed to minimise wasted votes in multi-candidate elections while ensuring that votes are explicitly for candidates rather than party lists.

When promoted as a proportional representation method in multi-party multi-seat elections, it is generally known as Proportional Representation through the Single Transferable Vote or PR-STV. When a similar method is applied to single-seat elections it is sometimes called instant-runoff voting or the alternative vote or, simply, preferential voting, and has different proportionality implications for a similar ballot. In both systems of voting the ballot choices represent an ordinal ranking of preferences, but an "instant runoff" for only one position or measure is a simple calculation.

Voting

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

  1. Andrea
  2. Carter
  3. Brad
  4. 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:

.

Other quotas used include the Hare Quota:

and the Imperiali Quota:

.

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, she may not receive any more votes (though see below for a modernisation).

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 excess 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 his votes are reallocated to the next-highest ranked candidates on the eliminated ballots. After a candidate is eliminated, he 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.

16 voters rank the candidates:

  1. Andrea
  2. Brad
  3. Carter
  4. Delilah

24 voters rank the candidates:

  1. Andrea
  2. Carter
  3. Brad
  4. Delilah

17 voters rank the candidates:

  1. Delilah
  2. Andrea
  3. Brad
  4. Carter

The threshold is:

In the first round, Andrea receives 40 votes and Delilah 17. Andrea is elected with 20 excess votes. Her 20 excess votes are reallocated to their second preferences (NB in practice all 40 second preference votes are transfered with a value of 0.5 (half) a vote each, which the value of the excess (20) divided by the total (40)[[1]]). For example, 12 of the reallocated votes go to Carter, 8 to Brad.

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 20 votes and he is elected.

Is STV a proportional voting system?

The outcome of voting under STV is proportional within a single election to the collective preference of voters, assuming voters have ranked their real preferences. However, due to other voting mechanisms usually used in conjunction with STV, such as a district or constituency system, an election using STV may not guarantee proportionality (across all districts put together). For example, in STV elections to the Australian Senate, states with vastly different populations have the same number of seats, and so while the results for individual states are proportional, the nationwide result is not, giving greater voting power to individual voters in less populated states. The lack of proportionality is derived from unequal representation rather than any deficiency in STV.

Because STV is a preference voting system, whereby voting is done by ranking a list of candidates, the type of proportionality contrasts with many other proportional voting systems for which proportionality is apportioned as a percentage of first-preference-only votes for each candidate. STV provides proportionality by transferring votes to minimise their waste. Votes are wasted when they have no affect on the outcome of a vote. Under STV each voter has a single (transferable) vote, regardless of whether there is one vacancy or several.

The more winners there are in a single constituency, the fewer votes that may be wasted (assuming voters are willing to vote for enough candidates) and therefore the more proportionate the outcome will be in that constituency. In some countries, such as Australia, voters have to rank every candidate when casting a vote.

Failures to produce exact proportionality in elections can be controversial, and this situation has arisen in elections using STV. The outcome may be particularly controversial 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 needed to be 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 first-preference votes. In the Republic of Ireland in 2002, Sinn Fein won 6% of the votes and 3% of the seats, being the fourth most popular party in terms of first preferences, but coming sixth in terms of the number of seats won.

STV also suffers from the theoretical curiosity that, unlike proportional party list systems, if a candidate is elected in an n seat constituency, she may not be elected in the same constituency with n + 1 seats even when voters express exactly the same preferences. This would occur if much of her support is from transfers rather than first preference votes.

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 will not 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.

Though still theoretically possible, figuring out how to vote tactically in STV systems by exploiting the non-monotonicity of STV is extremely computationally difficult. It is NP-hard to determine whether there exists an insincere ballot preference that will elect a preferred candidate, even in an election for a single seat. This makes tactical voting in STV elections vastly more difficult than with other commonly-used election methods. Importantly, this resistance to manipulation is inherent to STV and does not depend on hopeful extraneous assumptions like the presumed difficulty of learning the preferences of other voters. Furthermore, it is NP-hard to determine when an STV election has violated the monotonicity criterion, greatly reducing the likelihood that the electorate will know if even accidental tactical voting has occurred.

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 he has already been elected. For example, a voter might make a tactical decision to rank her top-place candidate beneath a candidate she knows will lose (perhaps a fictional candidate). If the voter's true top-place candidate has not been elected by the time her fake top candidate loses, the voter's full vote will count for her true top-place candidate. Otherwise, the voter will have avoided either having had her ballot in the lottery to be "wasted" on their top-ranked candidate or with only a fraction transfered, and will continue on to lower-ranked candidates.

Note that in some 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. This modernisation has not been adopted in all STV systems.

There are also tactical considerations for parties standing more than one candidate in the election. Standing too few may result in all the candidates being elected in the early stages, and votes being transferred to candidates of other parties. Standing too many candidates might result in first-preference votes being spread among them, and several being eliminated before any are elected and their second-preference votes distributed, if voters do not stick tightly to their preferred party's candidates; however, if voters vote for all candidates from a particular party before any other candidates and before stopping expressing preferences, then too many candidates is not an issue - in Malta, where voters tend to stick tightly to party preferences, parties frequently stand more candidates than there are seats to be elected.

In practice

Places that use STV for governmental elections include:

All local governments in Scotland will be using STV to elect their councillors. The Local Governance (Scotland) Bill [6] passed on June 23, 2004.

STV enjoyed some popularity in the United States in the first half of the 20th Century. The community school boards of the City of New York [7] used STV until they were abolished in 2002.

This method used for electing the Legislative Assemblies of Tasmania and the Australian Capital Territory and the elections in the province of Alberta, Canada from 1926 to 1955.

British Columbia will decide by referendum on May 17, 2005 whether to adopt STV to replace its current First Past the Post electoral system, after a recommendation of STV [8] by the Citizens' Assembly on Electoral Reform.

Some non-governmental organisations also use STV. For instance, all National Union of Students of the United Kingdom elections and those of their constituent members are under the system.

Historical assessments

An early proponent of STV was John Stuart Mill, who praised it in "On Representation." In the "English Constitution" Walter Bagehot praised the Hare system for allowing everyone, even ideological minorities, to elect an MP, but said that the Hare would create more problems than it solved. "[the Hare system] is inconsistent with the extrinsic independence as well as the inherent moderation of a Parliament - two of the conditions we have seen, are essential to the bare possibility of parliamentary government."

See also

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