Single Transferable Vote

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Image:STV GVT.gif

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 local government elections in New Zealand — see History and use of the Single Transferable Vote.

Contents 1 Terminology 2 Voting 3 Counting the votes 3.1 Setting the quota 3.2 Finding the winners 4 An example 5 Differing counting methods 6 Ballot design 7 Vacancies 7.1 Countback 7.2 Appointment 7.3 By-election 7.4 Replacement list 8 History and current use 9 Issues 9.1 Proportionality 9.2 Tactical voting 9.3 Effects on factions and candidates 9.4 Voting system criteria 9.5 District size 10 See also 11 References 12 External links 12.1 Proponent groups

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

Image:Preferential ballot.svg 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:

1. John Citizen
2. Mary Hill
3. 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:

<math>\left({{\rm votes} \over {\rm seats}+1}\right)+1</math>

• 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 transferred 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 transferred 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 transferred 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 transferred 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.

An example

Imagine an election in which there are 5 candidates and 3 seats to be filled. The candidates are: Andrew, Brian, Catherine, David and Emer. There are 100 voters who vote as follows (only the first one or two preferences of voters are shown, because in this case their lower preferences will not affect the result):

	20 voters	10 voters	60 voters	5 voters	5 voters
1st	Andrew	Brian	Catherine	David	Emer
2nd	Brian	Andrew	David	Emer

First, the quota is calculated. Using the Droop quota, with 100 voters and 3 winners to be found, the number of votes required to be elected is:

<math>\left({100 \over {3+1}}\right) +1 = 26</math>

When ballots are counted the election proceeds as follows:

Candidate:	Andrew	Brian	Catherine	David	Emer
Round 1	20	10	60	5	5
Round 2	20	10	26	39	5
Round 3	20	10	26	26	18
Round 4	30	0	26	26	18

• Round 1: Catherine is declared elected, since she has more votes than the quota.
• Round 2: Catherine has a surplus of 34. Her supporters all gave David as their second preference so these 34 votes transfer to David. He has now reached the quota and is declared elected.
• Round 3: David has a surplus of 13 votes. These transfer to his supporters' second preference, Emer. However even with these transfers neither Emer nor any other candidate has enough votes to reach the quota.
• Round 4: Because no candidate has enough votes to reach the quota Brian, who has the fewest, is eliminated. His votes transfer to Andrew who has now reach the quota and is declared elected.
• Result: The winners are Andrew, Catherine and David.

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 and Malta, among other places. For this reason the Gregory method (also known as Newland-Brittan or Senatorial rules) was invented, which eliminates randomness by allowing for the transfer of fractions of votes. Gregory is in use in Northern Ireland 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 Template:Ref. 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 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's method (a single winner voting system) into STV. None of these new methods has yet been used in a government election.

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 "donkey voting" in which, where a voter has no strong opinions about her lower preferences, she simply chooses them arbitrarily.

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 influence 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.

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:

Countback

The countback method is used in the Australian Capital Territory, Tasmania, Malta, and Cambridge, Massachusetts. A new representative is selected by using the data from the previous election. The candidate who held the seat is eliminated, and a new election result is obtained by transferring votes from the now unrepresented voters. Importantly, a clone of the replaced representative would be guaranteed to win the vacated seat. An interesting consequence of the countback method's use of existing ballots for selecting replacements is that the results are often known before the vacancy actually occurs, potentially influencing the circumstances which create the vacancy in the first place.

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.

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; if there exists a true clone in the ballots, there should be no effect in this change. 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 non-independence of irrelevant alternatives discussed above. 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.

Appointment

Another option is to have a head official or remaining members of the elected body appoint a new member to fulfil 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, vacancies on local authorities are filled by co-option of a candidate nominated by the departed councillor's party colleagues.Template:Ref.

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; also for the Seanad, though there the by-election franchise is more restricted than in ordinary elections, and might equally be categorised under appointment.Template:Ref

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 member is replaced with the top eligible name from a replacement list submitted by the candidate at the time of the original election. Template:Ref

History and current use

Template:Main 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 Single Transferable Voting, 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.Template:Ref 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."Template:Ref

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.

Image:Propo-bondage.jpg

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 a majority of "no" voters gave their reason as "wasn't knowledgeable" when they were asked why, specifically, they voted against STV.Template:Ref

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.

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. 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.Template:Ref 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 guarenteeing results that are proportional to the final allocation of preferences.

STV provides proportionality by transferring votes to minimise waste, and therefore also minimises the number of unrepresented 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. Unlike other proportional representation methods employing party lists, voters in STV do not explicitly state their preferred political party; 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.

Tactical voting

The single transferable vote eliminates much of the reason for tactical voting. Voters are "safe" ranking candidates they fear may not be elected, because their votes will be transferred after they are eliminated. Similarly, voters are also "safe" voting for a candidate they believe will receive overwhelming support, because their votes will then get reallocated to their next preference, though with less than the value of a full vote. However, the Gibbard-Satterthwaite theorem states that tactical voting is possible in any deterministic voting system where any candidate can win, and that STV is no exception.

Tactical voting is chiefly accomplished in STV by making assumptions about the other voters. A preferred popular candidate can be assumed to win and thus ranked lower on a tactical voter's ballot, allowing the voter to give more weight in transfers to his second-choice candidates (and, implicitly, giving fellow supporters of the popular candidate less weight.) This is particularly effective in the older STV systems still used in many countries that prevent elected candidates from receiving additional votes, as in that case none of the tactical vote is diluted on the already winning candidate. Under such old systems, a voter may even rank a non-preferred candidate that is assumed to lose first in order to increase the chances of his vote arriving late. This method of tactical voting is much less effective in the New Zealand STV system using Meek's method, however, as votes receive the same fractional weighting regardless of when they arrive at the successful candidate.

Though still theoretically possible, figuring out how to successfully vote tactically in modern STV systems by exploiting the non-monotonicity in this way can be 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.Template:Ref 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, such as the presumed difficulty of learning the preferences of other voters. Furthermore, it is also 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. As a consequence, the difficulty of tactical voting in STV elections increases sharply as the number of voters, candidates, and winners increase. This gives an incentive for larger electoral districts other than their increased proportionality, since particularly small electoral districts may have few enough candidates to make tactical voting feasible.

Of special note is that voters have a real incentive to list their preferences honestly in STV, as it is the best strategy for securing representation if tactical voting is either impractical or impossible. This is frequently the case in large electoral districts, as successful tactical voting (when possible) requires both nearly perfect information about how others are voting and the computation of a virtually unsolvable math problem. Since tactical voting in STV works by effectively substituting one's own alternate preferences for transfers with other supporters of the same candidate, the effectiveness of tactical voting is greatly reduced when other supporters of preferred candidates have similar second-choice preferences. Although there is no way to completely prevent tactical voting by hiding support for preferred candidates, the tactical voter carries the significant danger of his assumptions about the popularity of his preferred candidate being wrong, risking his most preferred candidate losing because of his miscast tactical vote. This contrasts heavily with non-proportional, plurality-based systems, where there is both tremendous incentive and ability to vote tactically in order to avoid the spoiler effect.

Effects on factions and candidates

Image:Sweet-propo.jpgThe 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. Unlike List PR, STV can be used in elections in organizations without any political parties at all, such as in 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.

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

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. In STV and other proportional representation systems, a larger number of candidates elected results in a smaller number of wasted votes and subsequent rounding error, leading to a more proportionally representative outcome based on the preferences of the voters. For this reason, 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.Template:Ref 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. Some STV elections make use of districts with the number of seats available as small as three, however 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.

However, because STV is proportional, larger elections also reduce the support a candidate requires to become elected as a percentage of the district. With 9 candidates, for example, any with 10% electoral support may win a seat, whereas with 19 candidates only 5% popular support is required to be in the government. Because of this, proportional representation methods such as STV can implicitly allow for the election of particularly small minorities provided they secure a quota's worth of votes. The potential admission of small voting minorities into the government, perhaps including political extremists, can be quite controversial even though they would occupy only an equivalently small proportion of the government once elected. Other proportional representation methods attempt to avoid the election of small political minorities by imposing partisan threshold requirements, such as the "5% rule" in Germany's Mixed Member Proportional system. While impossible at the national level, such a threshold requirement could be approximated in STV on a per-district basis by limiting the number of seats to 19 (and therefore making the quota one more than 5% of the vote). 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.

See also

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

References

1. Template:NoteHill, I.D. (1987). "Algorithm 123 — Single Transferable Vote by Meek’s method".
2. Template:NoteLambert & Lakeman (1955). "Voting in democracies". London : Faber, pg. 245.
3. Template:NoteBagehot, Walter. "English Constitution".
4. Template:NoteMeek, Brian (1969). "A New Approach to the Single Transferable Vote". Voting Matters Issue 1. Translated to English in 1994.
5. Template:NoteVideo postmortem on BC-STV referendum (British Columbia's version of STV).
6. Template:NoteBartholdi, John J. III and Orlin, James B (2003). "Single Transferable Vote Resists Strategic Voting".
7. Template:Note Whyte, Nicholas. "A note on Gerrymandering". Accessed Aug 12, 2005.
8. Template:Note Membership of local authorities in Ireland Accessed 7 Oct, 2005
9. Template:Note Seanad Panel By-Elections Accessed 14 Oct, 2005
10. Template:Note Replacement Candidates for the European Parliament Accessed 7 Oct, 2005
11. Template:NoteCitizens' Assembly on Electoral Reform. "News release: Assembly's recommendation to B.C." British Columbia, 24th October, 2004.
12. Template:NoteBains, Camille. "STV supporters press for electoral reform despite referendum defeat". Canadian Press, May 18, 2005
13. Template:NoteMaltadata.com. "Elections in Malta: The Single-Transferable-Vote System in Action, 1921 - 2004". Accessed Aug 11, 2005.
14. Template:NoteNew Zealand Department of Internal Affairs (2004). "STV - It's simple to vote". Accessed Aug 11, 2005.
15. Template:NoteElectoral Reform Society. "A Brief History of Electoral Reform". Accessed Aug 11, 2005.
16. Template:Note CAIN "Introduction to the Electoral System in Northern Ireland" Accessed Sep 15, 2005.
17. Template:Note Scottish Parliament (2004). "Local Governance (Scotland) Bill."
18. Template:NoteProsterman, Dan. STV in New York. Accessed Aug 11, 2005.

External links

• ChoicePlus -- software for computing the single transferable vote
• pSTV -- software for computing the single transferable vote
• A concise STV analogy
• The Single Transferable Vote procedure in Ireland
• Information on BC-STV. British Columbia's Referendum on STV
• [1] Simulating 2005 BC Election if STV was used
• Single Transferable Vote Animation (BC-STV) detailed flash animation explaining the process of Single Transferable Vote.
• 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.

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

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