Single Transferable Vote

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Single transferable vote (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. It 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 the Republic of Ireland (since 1919), Northern Ireland (except elections to the British House of Commons) and Malta. It is also used for federal Senate and certain regional and local elections in Australia, and some local government elections in British Columbia[1] and New Zealand — see History and use of the Single Transferable Vote. It will be used to elect for all council elections in Scotland in 2007. In the United States, it is used for city elections in Cambridge, Massachusetts, and will be used for certain city elections in Minneapolis, Minnesota, starting in 2009.

Contents 1 Terminology 2 Voting 3 Counting the votes 3.1 Setting the quota 3.2 Finding the winners 4 An example 5 Another example and a curious result 6 Differing counting methods 7 Ballot design 8 Vacancies 8.1 Countback 8.2 Appointment 8.3 By-election 8.4 Replacement list 9 History and current use 10 Issues 10.1 Effects on parties, factions and candidates 10.2 Proportionality 10.3 District size 10.4 Tactical voting 10.5 Vote management systems 10.6 Voting system criteria 11 See also 12 References 13 External links 13.1 Information and summaries 13.2 Simulations and software 13.3 Articles and publications 13.4 Proponent groups

[edit] Terminology

When STV is used in a single-winner election, it is the same as instant-runoff voting. When used in multi-seat constituencies, it is also called proportional representation through the single transferable vote (PR-STV). Because instant-runoff is not a form of proportional representation, some scholars consider it a separate system from PR-STV. STV usually refers to PR-STV, and it does in this article. In Australia STV is known as the Hare-Clark Proportional method, while in the United States it is sometimes called choice voting and preference voting.

[edit] Voting

In STV, each voter ranks the list of candidates in order of preference. In other words (under the most common ballot design), they place a '1' beside their most preferred candidate, a '2' beside their 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:

1. John Citizen
2. Mary Hill
3. Jane Doe

[edit] Counting the votes

[edit] Setting the quota

In an STV election, a candidate requires a certain minimum number of votes – the quota (or threshold) – to be elected. A number of different quotas can be used; the most common is the Droop quota, given by the formula:

where:

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

[edit] Finding the winners

Any candidate with either more than enough, or too few, votes to be elected has votes transferred to other candidates, and the process continues until all positions are filled. The candidates to whom votes are transferred are determined by the preferences given by voters on the ballot paper.

To count the votes in an STV election, ballot papers are tallied and distributed to candidates according to the voters' first preferences. Any candidate who has reached or exceeded the required quota is declared elected. If an insufficient number of candidates have been elected, the count continues. If a candidate has more votes than the quota, then their surplus value is transferred to other candidates according to the voters' allocated preferences. If enough candidates have not reached the quota, then the candidates with the fewest votes are eliminated one by one and their votes are transferred accordingly. Candidates who obtain the required quota are declared elected and any surplus is distributed to the remaining candidates. This process continues until the required number of candidates have been declared elected. Candidates who are eliminated are removed from the remainder of the count and no further votes may be transferred to them. Whether votes are transferred to elected candidates depends on the particular counting system chosen; systems that allow this subsequently redistribute the surplus, again.

An STV election proceeds according to the following steps which are repeated:

1. Any candidate who has reached or exceeded the required quota is declared elected.
2. If enough candidates have not been elected, the count continues.
3. If a candidate has more votes than the quota, then their surplus value is transferred to other candidates according to each voters allocated preferences.
4. The candidate with the fewest votes is eliminated and his or her votes are transferred to remaining candidates according to voters' preferences.

This process continues until the required number of candidates have been elected. Candidates who do not receive any more transferred votes. Whether votes are transferred to elected candidates depends on the particular counting system chosen; systems that allow this subsequently redistribute the surplus, again.

Most STV elections today are assisted by the use of computer technology where voters' preferences are transcribed and entered into a database which is used to count and determine the results of the election.

A manual count is often halted when the number of seats to be filled equals the number of remaining candidates, instead of counting votes until all candidates have reached a quota. Also, if the number of votes transferred is insufficient to either elect a candidate or change the order of candidates in the ranking, then multiple candidates may be excluded at once or a surplus may be held instead of being transferred. These procedures are common if ballots which do not list a full ranking of candidates become exhausted, because it is then possible for an insufficient number of candidates to reach the quota.

Because in STV, candidates who receive excess votes and candidates who are excluded 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 schoolyard election among children. In the election children line up behind the candidates of their choice but candidates cannot be elected unless have a minimum number of children have lined up behind them. Since the children would all know that each candidate needs a minimum number of classmates' votes to be elected, those arriving last in line for a candidate who already has enough votes would choose not to waste their vote and would instead move to another line to help someone else 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, except that the elimination of the candidate with the least votes sometimes disadvantages candidates who may have gone on to win had they not been eliminated. Also, those who preferred the loser on the final count remain unrepresented. 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.

There are two basic forms of counting an STV election: one is based on the number of ballot papers allocated to a candidate; the other, more accurate system, is based on the value of the vote as it progresses throughout the count. This variance is important in the calculation of a candidate's surplus. The paper-based formula (the surplus divided by the number of ballot papers) undermines proportionality and the "one vote, same value" principle due to some votes increasing in value at the expense of other votes. The value-based formula (the value of the vote divided by the surplus) avoids these shortcomings, ensuring proportionality and maintaining the "one vote, same value" principle.

[edit] An example

Suppose a food election is conducted to determine what to serve at a party. There are 5 candidates, 3 of which will be chosen. The candidates are: Oranges, Tangerines, Chocolate, Strawberries, and Candy. The 20 guests at the party have the preferences marked on their ballots in the two tables below (the first is a numerical representation, the second is pictorial). In this election only the first one or two preferences of voters are shown, because in this case their lower preferences will not affect the result.

	4 voters	2 voters	8 voters	4 voters	1 voter	1 voter
1st	Orange	Tangerine	Chocolate	Chocolate	Strawberry	Candy
2nd	Tangerine	Orange	Strawberry	Candy

#	x x x x	x x	x x x x x x x x	x x x x	x	x
1st
2nd

First, the quota is calculated. Using the Droop quota, with 20 voters and 3 winners to be found, the number of votes required to be elected is:

When ballots are counted the election proceeds as follows:

Candidate:	Orange	Tangerine	Chocolate	Strawberry	Candy
Round 1	4	2	12	1	1
Round 2	4	2	6	5	3
Round 3	6		6	5	3
Round 4	6		6	5	3

Candidate:
Round 1	x x x x	x x	x x x x x x x x x x x x	x	x
Round 2	x x x x	x x	x x x x x x	x x x x x	x x x
Round 3	x x x x x x		x x x x x x	x x x x x	x x x
Round 4	x x x x x x		x x x x x x	x x x x x	x x x

• Round 1: Chocolate is declared elected, since Chocolate has more votes than the quota.
• Round 2: Chocolate's surplus votes transfer proportionately to Strawberry and candy according to the Chocolate voters' second choice preferences. However, even with the transfer of this surplus no candidate has reached the quota. Therefore Tangerine, who has the fewest votes, is eliminated.
• Round 3: Tangerine's votes transfer to their second preference, Oranges, causing Orange to reach the quota and be elected. Orange barely meets the quota, and therefore has no surplus to transfer.
• Round 4: Neither of the remaining candidates meets the quota, so Candy is eliminated. Strawberry is the only remaining candidate and so wins the final seat.
• Result: The winners are Chocolate, Oranges and Strawberries.

[edit] Another example and a curious result

Imagine that the population of Tennessee, a state in the United States, is voting on the location of its capital. The population of Tennessee is concentrated around its four major cities, which are spread throughout the state. For this example, suppose that the entire electorate lives in one of these four cities, and that they would like the capital to be established as close to their city as possible.

The candidates for the capital are:

• Memphis, the state's largest city, with 42% of the voters, but located far from the other cities
• Nashville, with 26% of the voters
• Knoxville, with 17% of the voters
• Chattanooga, with 15% of the voters

The preferences of the voters would be divided like this:

42% of voters (close to Memphis)	26% of voters (close to Nashville)	15% of voters (close to Chattanooga)	17% of voters (close to Knoxville)
Memphis Nashville Chattanooga Knoxville	Nashville Chattanooga Knoxville Memphis	Chattanooga Knoxville Nashville Memphis	Knoxville Chattanooga Nashville Memphis

With just one winner, Knoxville wins. The quota is about 51%:

• Round 1: No city meets the quota so Chattanooga is eliminated.
• Round 2: Chattanooga votes transfer to Knoxville raising Knoxville's support to 32%. No city meets the quota so Nashville is eliminated.
• Round 3: Nashville's votes transfer to Knoxville raising Knoxville's support to 58%. Knoxville now exceeds the quota and wins.

If two winners were to be selected, Memphis and Nashville would win. The quota would be about 34%:

• Round 1: Memphis exceeds the quota and wins.
• Round 2: Memphis's surplus of 8% transfers to Nashville raising Nashville's support to 34%. Nashville now meets the quota and takes the second winning place.

If three winners were to be selected, Memphis, Nashville and Chattanooga would win. The quota would be about 26%:

• Round 1: Memphis exceeds the quota and wins. Nashville meets the quota and wins.
• Round 2: Memphis's surplus of 16% transfers to Chattanooga raising Chattanooga's support to 31%. Chattanooga now exceeds the quota and takes the third winning place.

So Knoxville wins if there is one winner but loses if there are two or three winners.

[edit] Differing counting methods

Main article: Counting Single Transferable Votes

STV systems differ in a number of ways, primarily in how they transfer votes as well as in the exact size of the quota used for determining winners. In fact, for this reason some have suggested that STV can be considered a family of voting systems rather than a single system. Today the Droop quota is the most commonly used quota. This ensures majority rule (except in rare cases) while maintaining the condition that no more candidates can reach a quota than there are seats to be filled. As originally conceived STV used the Hare quota, but this is now generally considered to be technically inferior. New Zealand uses a quota similar to the Droop quota–see: Electoral system of New Zealand.

The simplest methods of transferring surpluses under STV involve an element of randomness; partially random systems are used in the Republic of Ireland (except Senate elections) and Malta, among other places. For this reason the Gregory method (also known as Newland-Britain or Senatorial rules) was invented, which eliminates randomness by allowing for the transfer of fractions of votes. Gregory is in use in Northern Ireland, Republic of Ireland (Senate elections) and Australia. Both Gregory and these earlier methods have the problem, however, that in some circumstances they do not treat all votes equally. For this reason Meek's method and Warren's method have been invented.^[1] However, while simpler methods can usually be counted by hand, except in a very small election Meek and Warren require counting to be conducted by computer. Meek is currently used in STV local body elections in New Zealand.

The most recent refinements of STV involve attempting to remove the problem of sequential exclusions. Sequential exclusions mean that sometimes STV eliminates, at an early stage in the count, a candidate who might have gone on to be elected later had they been allowed to remain in the contest. Systems such as CPO-STV and Sequential STV have been invented to overcome this problem by incorporating elements of Condorcet methods into STV. A method known as BTR-STV deals with the problem differently and more simply than these systems by simply making sure no such candidate could possibly be eliminated. None of these new methods has yet been used in a government election.

Most of the systems that are currently in use were designed to facilitate a manual counting process. With the ever increasing use of computer technology, many of the processes are in need of review. For example, in calculating a candidate's surplus, some systems use the number of ballot papers (surplus/number of papers) as opposed to the allocated value of the ballot papers to determine the value of any candidates surplus (value of the vote/surplus). Computers make it feasible to use the more accurate allocated value method, which maintains the one vote one value principle. A paper-based formula distorts the vote, increasing the value some votes at the expense of others.

Manual counting issues, like segmentation transfers, need to be further considered in a computerised count. Segmentation transfers are where votes are distributed according to either the order in which they where received, last bundle or the grouping of common value of ballot papers to be transferred from highest to lowest. To simplify the counting process in a computerised count there should be single transaction per candidate without segmentation.

[edit] Ballot design

As seen above, voters in an STV election rank candidates on a preferential ballot. STV systems in use in different countries vary both as to ballot design and to whether or not voters are obliged to provide a full list of preferences. In jurisdictions such as the Republic of Ireland and Northern Ireland voters are permitted to rank as many or as few candidates as they wish. Consequently voters sometimes, for example, rank only the candidates of a single party, or of their most preferred parties. A minority of voters, especially if they do not fully understand the system, may even 'bullet vote', only expressing a first preference. Allowing voters to rank only as many candidates as they wish grants them greater freedom but can also lead to some voters ranking so few candidates that their vote eventually becomes 'exhausted'–that is, at a certain point during the count it can no longer be transferred and therefore loses an opportunity to influence the result.

To prevent exhausted ballots, some STV systems instead oblige voters to give a complete ordering of all of the candidates in an election (if a voter does not rank all candidates her ballot may be considered spoilt). However, when there is a large set of candidates this requirement may prove burdensome and can lead to random voting, or "donkey voting" in which a voter who has no strong opinions about her lower preferences simply chooses them in the given order. Some jurisdictions compromise by setting a minimum number of preferences that must be filled for a ballot paper to be valid (for example Tasmania and Australian Capital Territory, which both require five preferences).

To facilitate a complete ballot, some STV systems provide the voter with the option of using group voting tickets rather than having to manually identify a complete list of individual preferences. For example, in elections to the Australian Senate a voter can either rank the candidates herself or place the number one in a box "above the line" to vote for a predetermined ordering of candidates drawn up by one of the political parties. This system diminishes the emphasis on individual candidates and increases the power of party leaders who submit the predetermined rankings; in practice it may even lead to a system resembling party-list proportional representation.

The simplest way to list candidates on a ballot paper is alphabetically, though they may also be grouped by party. However, any fixed ordering will give some candidates an unfair advantage, because some voters, consciously or otherwise, are influenced in their ordering of candidates by the order found on the ballot paper. For example, studies conducted in the Republic of Ireland, where candidates are listed alphabetically, have shown that candidates whose surnames begin with an early letter in the alphabet enjoy a small electoral advantage over candidates with later letters. To solve this problem some systems involve a random ordering of candidates, or an ordering that changes from one ballot paper to another (the latter is often called the Robson rotation, after Neil Robson, a Tasmanian MHA who championed such a system).

[edit] Vacancies

When compared with other voting methods, the question of how to fill vacancies which occur under STV can be difficult given the way that results depend upon transfers from multiple candidates. There are several possible ways of selecting a replacement:

[edit] Countback

The countback method is used in the Australian Capital Territory, Tasmania, Victoria, Malta, and Cambridge, Massachusetts. Casual vacancies are filled re-examining the ballot papers data from the previous election. The candidate who held the seat is eliminated, and a new election result is obtained by transferring votes that were originally allocated to the elected candidate at the time of his or her election to unsuccessful candidates. This process maintains the proportionality of the representation according to the voters choice without the need and associated costs of holding fresh elections.

Although the countback method is designed to select a replacement representing the same group of voters who elected the original candidate, it remains possible that no similar candidates remain on the ballot. In 1985 the Tasmanian parliament amended the electoral act to allow true by-elections if no candidates of the same party as the outgoing representative remained on the ballot; in this circumstance the party may request that a by-election be held, however this has not yet happened as most political parties and community groups now nominate a surplus number of candidates in order to fill any casual vacancies.

Countback methods vary by whether or not wasted and exhausted ballots are additionally used during the countback. The effect this has on the result of the countback depends on the differences in the next preferences of voters. Moreover, in STV systems that use exhausted ballots during countbacks, it becomes theoretically possible that the order of multiple resignations will affect who the ultimate replacements are - this is a consequence of the order of election as votes allocated to elected candidates are locked that value of which are no longer used in the determination of the election of further vacancies. Additionally, if ballots are allowed to be exhausted in the election, then by either method it remains possible that the chosen replacement will only meet a fraction of a quota of voters; when this fraction is particularly small, and therefore no similar candidates remain on the ballot, election rules may call for a different method of filling the vacancy to be used. The method is the calculation of a candidates surplus also contributes with a paper based formula (see above) complicating the countback process. A value based system being more accurate and less complicated. With the aid of computer based technology the results of a count-back can be determined immediately.

[edit] Appointment

Another option is to have a head official or remaining members of the elected body appoint a new member to fulfill the vacancy. In Australia, for example, the state legislatures appoint replacements members to the Australian Senate, now done at the suggestion of the party of the outgoing senator. Before this rule, disputes over Senate vacancies contributed to the Australian constitutional crisis of 1975, ultimately resulting in a 1977 amendment to the Constitution of Australia to provide that the legislature must elect a member of the same party as the outgoing senator. Vacancies in the New South Wales Legislative Council are filled in a similar way by a joint sitting of both the legislative council and assembly.

In the Republic of Ireland and Northern Ireland, vacancies on local authorities are filled by co-option of a candidate nominated by the departed councillor's party colleagues, although in Northern Ireland this requires unanimous approval from the Council.^[2] In the Republic of Ireland, vacancies from amongst the Taoiseach's nominees to the Seanad are filled by appointment.

[edit] By-election

A third alternative to fulfill a vacancy is to hold a single-winner by-election (effectively instant-runoff); this allows each party to choose a new candidate and all voters to participate. This often leads to a different party winning the seat (usually one of the largest parties, since the quota is large). In the Republic of Ireland, by-elections are used for the Dáil and for the Seanad where voters in the Dáil constituency or Seanad panel vote to fill to vacancy or vacancies.^[3] This removes the balance of proportionality of the original election. The costs of holding a by-election in a multi-member constituency is considerable. In a recent review of the City of Melbourne, Australia, electoral requirements the cost of holding a City wide ballot to fill a casual vacancy was estimated to cost over 1 million Australian Dollars.

[edit] Replacement list

Another alternative is to have the candidates themselves create an ordered list of successors before leaving their seat. In the European Parliament, a departing Republic of Ireland or Northern Ireland member is replaced with the top eligible name from a replacement list submitted by the candidate at the time of the original election.^[4]

This system is also used for the Northern Ireland Assembly.

[edit] History and current use

Main article: History and use of the Single Transferable Vote

The concept of transferable voting was first proposed by Thomas Wright Hill in 1821. The system remained unused in real elections until 1855, when Carl Andrae proposed a transferable vote system for elections in Denmark. Andrae's system was used in 1856 to elect the Danish Rigsdag, and by 1866 it was also adapted for indirect elections to the second chamber, the Landsting, until 1915.

Although he was not the first to propose a system of transferable votes, the English barrister Thomas Hare is generally credited with the conception of STV, and he may have independently developed the idea in 1857. Hare's view was that STV should be a means of "making the exercise of the suffrage a step in the elevation of the individual character, whether it be found in the majority or the minority." In Hare's original STV system, he further proposed that electors should have the opportunity of discovering which candidate their vote had ultimately counted for, to improve their personal connection with voting.^[5] This is unnecessary in modern STV elections, however, as an individual voter can discover how their vote was ultimately distributed by viewing detailed election results.

The noted political essayist, John Stuart Mill, was a friend of Hare and an early proponent of STV, praising it in his essay "On Representation." His contemporary, Walter Bagehot, also praised the Hare system for allowing everyone to elect an MP, even ideological minorities, but also added that the Hare system 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."^[6]

Advocacy of STV spread through the British Empire, leading it to be sometimes known as British Proportional Representation. In 1896, Andrew Inglis Clark was successful in persuading the Tasmanian House of Assembly to be the first parliament in the world elected by what became known as the Hare-Clark system, named after himself and Thomas Hare.

Meek also considered a variant on his system which would have allowed for equal preferences to be expressed.

[edit] Issues

A frequent concern with STV among electorates considering its adoption is its relative complexity compared with plurality voting methods. For example, when the Canadian province of British Columbia held a referendum on adopting the BC-STV single transferable vote in 2005, according to polls most of the "no" voters gave their reason as "wasn't knowledgeable" when they were asked why, specifically, they voted against STV.^[7]

However, as with all voting systems, once STV is understood there remain a number of areas of controversy surrounding its use. In particular, arguments for and against proportional representation in general are frequently referenced in debates among electorates considering STV, however the specific implications of a particular STV system can be examined as well. Most of the arguments for and against STV and proportional representation in general are based around the expected outcomes of the alternative proposed system and not on the system itself.

[edit] Effects on parties, factions and candidates

STV differs from all other Proportional Representation systems in actual use in that candidates of one party can be elected on transfers from voters for other parties. Hence, the use of STV may reduce the role of political parties in the electoral process and corresponding partisanship in the resulting government. Unlike proportional representation systems employing party lists, voters in STV are not explicitly constrained by parties even when they do exist; voters may ignore candidate party labels and mix their preferred candidate rankings between parties. Similarly, candidates may achieve electoral success by obtaining a quota of voters not generally within their own party, perhaps by winning transfers from moderates or by championing a specific issue contrary to party doctrine. STV advocates boast that, by requiring a candidate to appeal to the supporters of other candidates for their second and further preferences, it reduces adversarial confrontation, and indeed, gives a substantial advantage to candidates who broaden their appeal by being not only collegial but as open-minded and flexible in their principles as they can manage. STV detractors see this alleged virtue as a flaw. Political parties should be able to structure public debate, mobilize and engage the electorate, and develop policy alternatives. Effective parties attract members who share basic beliefs about how the jurisdiction should be governed. They develop policies that reflect their goals and priorities, and they promote public debate on important issues. STV, on this view, works against maintaining effective parties.

Unlike List PR, STV can be used in elections in organizations without any political parties at all, such as in municipal non-partisan elections, trade unions, clubs, and schools.

Some STV variations, however, may encourage the role of political parties and actually strengthen them. In Australian Senate elections, where a combination of large districts, mandatory complete ballots, and compulsory voting results in the near 95% usage of partisan group voting tickets, political parties gain significant power in determining election results by adjusting the relative ordering of their tickets, both in terms of their own candidates and of transfers to other parties.

Successful campaign strategy in STV elections may differ significantly from other voting systems. In particular, individual candidates in STV have little incentive for negative campaign advertising, as reducing a particular opponent's ranking among voters does not necessarily elevate one's own; if negative campaigning is seen as distasteful by the voters, the practice may even prove harmful to the attacking candidate. Conversely, in order to avoid elimination in early counting rounds by having too few first place votes, candidates have a significant incentive to convince voters to rank them explicitly first as their top preference, rather than merely higher. This incentive to attain top preferences, in turn, may lead to a strategy of candidates placing greater importance on a core group of supporters. Avoiding early elimination, however, is usually not enough to win election, as a candidate must still subsequently win enough votes on transfers to meet the quota; consequently, strategies which sacrifice wide secondary support in favor of primary support amidst a core group may ultimately fail unless the group is particularly large.

There are also tactical considerations for political parties in the number of candidates they stand in an election where full ballots are not required. Standing too few candidates may result in all of them 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 too thinly amongst them, and consequently several potential winners with broad second-preference appeal may be eliminated before others are elected and their second-preference votes distributed. This effect is amplified when 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. Similarly, in Australian Senate elections, voters also tend to vote along party lines due to the relative ease of selecting a party's declared preferences rather than individually casting their own complete list. In the Republic of Ireland, the main political parties usually give careful consideration as to how many candidates to put forward in various Dáil (parliamentary) constituencies. Transfers are often not along party lines, but rather go towards more prominent local personalities. Election posters for the most prominent candidate of a political party usually list preferred 2nd (and possibly 3rd) preferences for that party.

There is evidence that the STV system has given a small advantage to candidates whose surnames are near the top of the alphabet. In the Irish Dáil (lower house of parliament) elected in 2002, about 4.5% of members had surnames beginning with A, 8% beginning with B, and 12% beginning with C.^[8] From listings in the Eircom telephone directories for the 01, 06 and 07/09 areas combined, the expected percentages would be about 1.5%, 7% and 9.5% respectively. Similar deviations from the norm have been noted after previous elections. The effect seems to be minimal, as the Dáil median surname currently falls within the letter K, which accurately reflects the distribution of Irish names. An analysis of likely voting patterns seems to predict a small bias of this kind. A voter votes 1 for the candidate he/she most favours. If he/she wishes to support other candidates of the same party, but has no strong preference between them, the voter is likely to number them downwards from the top of the ballot sheet, in normal reading fashion. Later preferences to candidates of another party are likely to be numbered in the same way. If candidates' names are listed alphabetically, this pattern will mean that earlier preferences will go to candidates earlier in the alphabet. Over a series of elections, such a minor bias would have a cumulative effect, as elected members stand for election again. In Ireland, it has been suggested that names on ballot papers should be printed in random order to prevent this.

[edit] Proportionality

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 and vote along strict party lines. 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. Differential turnout across districts, for example, may alter the impact of individual votes in different constituencies, and when combined with rounding error associated with a finite number of winners in each constituency the election as a whole may throw up anomalous results. For example, the 1981 election in Malta resulted in the Labour Party winning a majority of seats despite the Nationalist Party winning 51% of the first-preference vote.^[9] Controversy over the election ultimately resulted in a constitutional crisis, leading to an amendment adjusting the voting system to allow for the possibility of bonus seats and making the Maltese voting system more similar to an open-list PR system. This kind of difference due to rounding error can occur with any PR system used at a district level, although greater rounding error occurs with smaller districts and there is a tendency for STV elections to use smaller districts when compared with PR elections employing party lists.

Similarly to differences in voter turnout, instances of malapportionment across districts can also cause disproportionate results for the legislature as a whole. 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. By contrast, the New South Wales Legislative Council avoids the use of districts entirely, electing all 21 members using a single, statewide constituency and guaranteeing results that are proportional to the final allocation of preferences. In Victoria, Australia, legislation is in place to ensure that each electorate contains the same number of constituents. Problems occur when the number of candidates to be elected is different in each electorate, as the percentage of voters required to elect a candidate varies, whilst the number of voters remain the same. The percentage breakdown varies considerably, adding to the argument that the number of voters and the percentage required for election should be the same across all electorates. Under Victorian legislation an electoral review is required should the number of electors in each electorate fall outside the nominated tolerance level. Municipal Electoral reviews are undertaken every second term of office.

STV differs from other PR systems in that it allows the voter to decide the issues that should matter for the proportionality. In most PR systems the voter can only influence a single aspect - party representation. STV allows the voter to choose other criteria that can be used to create the proportionality: gender, ethnicity, age, place of residence or character as examples. A perceived problem arises from the fact that voters and the political elite are often not in accord with what sort of proportionality should be achieved. Increased voter choice and control reduces the power and influence of the political elite to determine the political debate.

STV provides proportionality by transferring votes to minimise waste, and therefore also minimises the number of unrepresented/ disenfranchised voters. In this way STV provides Droop proportionality - an example STV election using the Droop quota method for 9 seats and with no exhausted preferences would guarantee representation to every distinct group of 10% of the voters, with at most only 10% of the vote being wasted as unneeded excess (in most cases it would be much less). Unlike other proportional representation methods employing party lists, voters in STV do not explicitly state their preferred political party (with the exception where above-the-line voting systems are in place); this in turn can create some difficulty when attempting to analyze how an STV election's results compare with the nationwide partisan makeup. One common method of estimating the party identification of voters is to assume their top-preference on their ballot represents a candidate from their preferred party, however this method of estimation is made more complicated by the possibility of independent candidates and of cross-party voting. However valid comparisons have and can still be made if sufficient data and information is available. In Victoria, Australia it is possible to make a direct comparison between the Australian Senate election and the Victorian Upper House elections although individual circumstance will always exist voting patterns have shown that most voters stick to their chosen party within a limited percentage range based on local issues and circumstances. The main advantage in Victoria's case is that both systems are similar in design with one being a subset of the other. Victoria will hold its first Multi-member proportional representation elections in November 2006.

[edit] District size

Another issue commonly considered with STV elections is the size of the voting districts in terms of the number of candidates elected and, to a lesser extent, the total size of the body being elected.

Because STV is proportional, larger districts reduce the support a candidate requires to become elected as a percentage of the district. With 9 to be elected, for example, any who reach (with transfers) 10% electoral support may win a seat, whereas with 5 to be elected 16.7% is required. Some STV elections make use of districts with the number of seats available as small as three. A larger number of candidates elected also results in a smaller number of wasted votes on the final count. However, larger districts and the implicit larger number of candidates also increase the difficulty of giving meaningful rankings to all candidates from the perspective of the individual voter, and may result in increased numbers of exhausted ballots and reliance on party labels or group voting tickets.

Larger electoral districts can also significantly reduce the effects of gerrymandering; because gerrymandering relies on wasted votes to award the "last seat" in each district, proportional representation systems such as STV with larger multimember districts are intrinsically more difficult to gerrymander.^[10] Larger districts can also make for significantly harder tactical voting: since the problem of making correct assumptions about other voter's behavior and rearranging one's tactical ballot is NP-hard, the difficulty of tactical voting increases sharply as the number of candidates grows.

There is no theoretical upper limit to the size of districts in STV, and they may not even be needed at all: Thomas Hare's original proposal was for a single, nationwide district. In theory, STV could allow for the election of particularly small minorities provided they secure a quota's worth of votes, if very large districts were used. However, no jurisdiction actually uses districts larger than nine for election to its main legislature.

[edit] Tactical voting

According to the Gibbard-Satterthwaite theorem tactical voting is possible in all non-dictatorial deterministic voting systems. A number of methods of tactical or strategic voting exist that can be used in elections conducted using STV. In general these methods are only effective in marginal districts and only affect the allocation of a single seat per district.

One potential strategy in STV involves casting a first preference vote for a candidate that has no chance of winning. This vote will then be transferred at full value and carry more weight in determining the winners at the later stages of the count. This strategy can be effective due to two features of some STV counting systems.

1. Simple Gregorian transfer (SGT) systems such as ERS97 and Newland-Britton Northern Ireland consider for transfer only the last parcel of votes received by an elected candidate.
2. Both simple Gregorian transfer systems and weighted inclusive Gregorian transfer (WIGT) systems such as BC-STV do not transfer votes to already elected candidates.

For example in an election in which 5 candidates are contesting 3 seats the following 400 votes are cast:

105: A>D>B

90: B

80: C>B

75: D>B

50: E>A>C>D

The quota is 100 and A is elected at stage 1. E is the first candidate to be eliminated. Under SGT the 50 E>A>C>D votes ‘skip’ candidate A and transfer to candidate C; who is then elected. These votes then transfer again to candidate D who wins the final seat. The SGT winners are A, C and D.

Under WIGT the 50 E>A>C>D votes again 'skip' candidate A and transfer to C who wins the second seat. All C's votes (both the E>A>C>D votes and the C>B votes) then transfer at reduced value. As a result of this transfer candidate B wins the third seat. The WIGT winners are A, C and B.

The Meek system, which is immune to this strategy, elects A, B and D.

Under SGT the E>A>C>D voters effectively determine the winners of the two final seats. Under WIGT as a result of the E>A>C>D votes failing to contribute to the election of candidate A and transferring at an increased value, C wins a seat as opposed to D. SGT systems are more vulnerable to this form of tactical voting than WIGT systems.

While this appears an effective strategy in theory there are a number of problems with it in practice. Firstly accurate information is needed about how other voters are going to vote, in practice this information is difficult to obtain. Secondly if all voters vote for candidates they believe will lose, these candidates will win. In general, this strategy will not work if everyone uses it. Little evidence exists of the use of this strategy in the real world.^[11]

[edit] Vote management systems

Two vote management systems exist in STV. Vote equalisation works for all systems except those that allow group voting (above the line voting). The other method, party designated transfer, only works for systems that allow group voting. A party employing a vote equalisation strategy would attempt to ensure that all its candidates obtain an equal number of first preference votes, in the hope that transfers from candidates of other parties eliminated early in the count will lead to the election of an increased number of its candidates.

For example in an election for 3 seats, 2 parties (A and C) present two candidates and a third party B presents a single candidate. All party A voters prefer party B to party C. All party C voters prefer party B to party A. All party B voters prefer party C to party A. The following 1000 votes are cast:

220: A1>A2>B

200: A2>A1>B

190: B>C1>C2

250: C1>C2>B

140: C2>C1>B

The quota is 250. C2 is eliminated first and candidates A1, B and C1 are elected.

If party C distributes its vote equally between its two candidates for example:

220: A1>A2>B

200: A2>A1>B

190: B>C1>C2

195: C1>C2>B

195: C2>C1>B

B is eliminated first and candidates A1, C1 and C2 are elected. By equalizing the distribution of its vote party C wins an additional seat.

Evidence from Ireland^[12] indicates that this form of vote management has been attempted on a number of occasions. To work, vote equalization requires accurate information about voting intentions and party strengths and also the active cooperation of the voters themselves. If a party misjudges the situation a vote equalization strategy can go badly wrong. For example in the 2003 elections to the Northern Ireland Assembly, a vote management strategy by Sinn Fein in West Belfast intended to replace an Social Democratic and Labour Party member with a Sinn Fein member led instead to the election of a member of the Democratic Unionist Party, a party extremely hostile to Sinn Féin.^[13]

The party designated transfer system of vote management is applicable only to systems that allow group voting. Under group voting a voter places a '1' next to his or her first choice of party list. His or her vote then transfers down the party list in an order designated by the party and then to the lists of other parties in an order predetermined by the voter's first choice party. The published lists that show the designated transfers can be long and complicated and can effectively disguise who an ‘above the line’ vote is likely to end electing. An example of the use of this strategy is provided by the 2004 Australian Senate election in Tasmania. The Liberal and Labor parties and an independent Labor candidate designated that their above the line vote should transfer to the Family First party in preference to the Green party. Had all voters in Tasmania cast ‘above the line' votes the Green party candidate, who obtained almost a quota of first preference votes, would have lost to a candidate of the little supported Family First party.^[14]

[edit] Voting system criteria

Academic analysis of voting systems such as STV generally centers on the voting system criteria that they pass. No preference voting system satisfies all the criteria described in Arrow's impossibility theorem: in particular, STV fails to achieve independence of irrelevant alternatives (like most other vote-based ordering systems) as well as monotonicity. Failure to satisfy independence of irrelevant alternatives makes STV slightly prone to strategic nomination, albeit less so than with plurality methods where the spoiler effect is more pronounced and predictable. Non-monotonicity, in turn, makes it possible under some circumstances to elect a preferred candidate by reducing his position on some of the ballots; by helping elect a candidate who displaces the preferred candidate's main rival, a voter may cause the preferred candidate to profit from transfers resulting from the rival's defeat. STV fails the participation criterion which can result in a more favorable outcome to an STV voter by not voting at all. However, a voter who truncates a candidate off the ballot does not harm a ranked candidate, nor is another truncated candidate helped on the ballot.

STV is also susceptible to the Alabama paradox: a candidate elected in an n seat constituency may or may not be elected in the same constituency with n + 1 seats even when voters express exactly the same preferences. This is due to the use of quotas; list PR by a largest remainder method is similarly affected, though a highest averages method is not. Intuitively, a candidate who was elected largely because of transfers from two similar groups (neither obtaining a quota) may not be elected when the number of winning candidates increases, as both groups would instead get their preferred candidates elected (with the new, smaller quota) rather than automatically compromising on their mutual second choice as their votes transfer.

Some modifications to STV have been proposed in order to pass monotonicity and other criteria. The most common method of proposed modification to STV is to alter the order in which candidates are eliminated: theoretically, a candidate who ranked second on every ballot could be the first candidate eliminated even if he is a Condorcet winner. Meek noted this problem in proposing his variation of transferring votes to nearly eliminate tactical voting in STV, however Meek himself did not propose a method for satisfying the Condorcet criterion. Other theorists have proposed further refinements of STV, such as using a Condorcet method to rank candidates for elimination order. Some of these modifications alter STV in a way such that it no longer reduces to instant-runoff voting when applied to a single seat but instead reduces to some other single winner system, such as a Condorcet method.

See also: CPO-STV, Quota Borda system

[edit] See also

• Table of voting systems by nation
• Single Non-Transferable Vote
• Instant-runoff voting
• Voting system
• Proportional representation

[edit] References

[edit] External links

[edit] Information and summaries

• Advantages and Disadvantages of STV - from the ACE Project
• Malta: STV with some twists - from the ACE Project
• Ireland: The archetypal STV system - from the ACE Project
• Electoral Systems and Conflict Management: Comparing STV and AV Systems - from the ACE Project
• A concise STV analogy - from Accurate Democracy

[edit] Simulations and software

• Guth an Phobail - a Java animation of all recent STV elections in Ireland as Gaelige
• ChoicePlus — software for computing the single transferable vote
• OpenSTV — software for computing the single transferable vote
• BC DemoChoice Simulating 2005 BC Election if STV was used
• Single Transferable Vote Animation (BC-STV) detailed flash animation explaining the process of Single Transferable Vote.
• Joey's STV free Excel spreadsheet for computing simple STVs without additional software.
• Accurate Democracy lists a dozen programs for computing the single transferable vote.

[edit] Articles and publications

• Voting Matters - Technical Journal on STV and similar Electoral Systems
• P.R. in Ireland - by Proinsias Mac Aonghusa. A series of articles explaining the history and workings of the P.R. system in Ireland - published in 1959.
• The Single Transferable Vote procedure in Ireland
• Information on BC-STV. British Columbia's Referendum on STV
• A Technical Description of the Single Transferable Vote Article by Brian Wichmann.
• Tie-Breaking with the Single Transferable Vote Article by Jeffrey C. O'Neill
• Single Transferable Vote with Borda Elimination: A New Vote Counting System Article by Chris Geller.
• List of Organisations which use STV for their Elections
• "Single Transferable Vote Resists Strategic Voting" by John J. Bartholdi, III and James B. Orlin.

[edit] Proponent groups

• FairVote (USA, formerly the Center for Voting and Democracy)
• Proportional Representation Society of Australia
• Electoral Reform Society (United Kingdom) See also the Wikipedia article