Single transferable vote

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The single transferable vote (STV) is a voting system designed to achieve proportional representation through ranked voting in multi-seat constituencies (voting districts).^[1] Under STV, an elector (voter) has a single vote that is initially allocated to their most preferred candidate and, as the count proceeds and candidates are either elected or eliminated, is transferred to other candidates according to the voter's stated preferences, in proportion to any surplus or discarded votes. The exact method of reapportioning votes can vary (see Counting methods).

The system provides approximately proportional representation, enables votes to be cast for individual candidates rather than for parties, and—compared to first-past-the-post voting—reduces "wasted" votes (votes on sure losers or sure winners) by transferring them to other candidates.

Hare–Clark is the name given to STV in lower house elections in two Australian states and territories, Tasmania and the Australian Capital Territory. The name is derived from Thomas Hare, who developed the system, and the Tasmanian Attorney General, Andrew Inglis Clark, who modified the counting method on introducing it to Tasmania. Hare–Clark has been changed to use rotating ballot papers (the Robson Rotation). The upper houses of New South Wales, Victoria, Western Australia and South Australia, use a variant of STV allowing "group voting".^[2]

STV is the system of choice of groups such as the Proportional Representation Society of Australia (which calls it quota-preferential proportional representation), the Electoral Reform Society in the United Kingdom and FairVote in the USA (which calls it ranked choice voting).^[3][4][5] Its critics contend that some voters find the mechanisms behind STV difficult to understand, but this does not make it more difficult for voters to "rank the list of candidates in order of preference" on an STV ballot paper (see Voting).^[6]

Adoption

STV has had its widest adoption in the English-speaking world. As of 2010, in government elections, STV is used for:

Republic of Ireland		Parliamentary elections (since 1921) European elections Local government elections Presidential Elections
Malta		Parliamentary elections (since 1921) European elections Local government elections
United Kingdom	Northern Ireland	National assembly elections European elections Local government elections
	Scotland	Local government elections (since May 2007)
India		Upper house of Parliament elections (indirect election by state MLAs)
Pakistan		Senate elections (indirect election by members of provincial assemblies, and direct vote by the population of territories)
Australia	Federal (country-wide)	Senate elections (in the form of a group voting ticket until 2016)
	Australian Capital Territory	Legislative Assembly elections
	New South Wales	Legislative Council elections Local government elections
	South Australia	Legislative Council elections Local government elections
	Tasmania	House of Assembly elections Local government elections
	Victoria	Legislative Council elections Local government elections
	Western Australia	Legislative Council elections
New Zealand[7]		Regional council elections: Wellington Regional Council Unitary authority elections: Marlborough District Council Territorial authority elections: Palmerston North City Council, Kapiti Coast District Council, Porirua City Council, Wellington City Council, Dunedin City Council District health board elections: all 20 boards
United States		City elections in Cambridge, Massachusetts Certain city elections in Minneapolis, Minnesota (starting in 2009)

In British Columbia, Canada, STV was recommended for provincial elections by the BC Citizens' Assembly on Electoral Reform (British Columbia). In a 2005 provincial referendum, it received 57.69% support and passed in 77 of 79 electoral districts. It was not adopted, however, because it fell short of the 60% threshold requirement the Liberal government had set for the referendum to be binding. In a second referendum, on 12 May 2009, STV was defeated 60.91% to 39.09%

STV has also been used in several other jurisdictions, particularly in provincial general elections in the cities of Edmonton and Calgary in Alberta. For a more complete list, see History and use of the Single Transferable Vote.

Terminology

When STV is used for single-winner elections, it is equivalent to the instant-runoff voting (alternative vote) method.^[8] STV used for multi-winner elections is sometimes called "proportional representation through the single transferable vote", or PR-STV. "STV" usually refers to the multi-winner version, as 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, preferential voting or preference voting ("preferential voting" can also refer to a broader category, ranked voting systems).

Voting

In STV, each voter ranks the list of candidates in order of preference. In 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 completed ballot paper therefore contains an ordinal list of candidates. In the ballot paper 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

In an STV election, a candidate requires a 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 the number of valid votes cast and the number of seats to fill are nonnegative integers.

The Droop quota is an extension of requiring a 50% + 1 majority in single-winner elections. For example, at most 3 people can have 25% + 1 in 3-winner elections, 9 can have 10% + 1 in 9-winner elections, and so on.

If fractional votes can be submitted, then the Droop quota may be modified so that the fraction is not rounded down; thus the quota is a positive but not necessarily an integer value.

Finding the winners

An STV election starts with every voter's first choice, according to the following steps:

1. A candidate who has reached or exceeded the quota is declared elected.
2. If any such elected candidate has more votes than the quota, the excess votes are transferred to other candidates. Votes that would have gone to the winner go to the next preference. This can be done in several ways (see the section on Counting Methods, below).
3. If no-one new meets the quota, the candidate with the fewest votes is eliminated and those votes are transferred to each voter's next preferred candidate.
4. This process repeats until either a winner is found for every seat or there are as many seats as remaining candidates.

There are variations, such as how to transfer surplus votes from winning candidates and whether to transfer votes to already-elected candidates. When the number of votes transferred from the losing candidate with the fewest votes is too small to change the ordering of remaining candidates, more than one candidate can be eliminated simultaneously.

One simplistic formula for how to transfer surplus votes is:

however, this can produce fractional votes. See Counting Methods for a discussion of how this is handled.

If a candidate is eliminated and their votes are transferred to already victorious candidates, then the new excess votes for the victorious candidate (transferred from the eliminated candidate) will be transferred to the next preference of the victorious candidate, as happened with their initial excess. However, any votes which would transfer from the victorious candidate to one who was already eliminated must be reallocated. See the section on Counting Methods below for details.

Because votes cast for losing candidates and excess votes cast for winning candidates are transferred to voters' next choice candidates, STV is said to minimize wasted votes.

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, Pears, Chocolate, Strawberries, and Sweets. The 20 guests at the party mark their ballots according to the table below. In this example, a second choice is made by only some of the voters.

# of guests	x x x x	x x	x x x x x x x x	x x x x	x	x
1st preference
2nd preference

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						Result
Round 1	x x x x	x x	x x x x x x x x x x x x	x	x	Chocolate is declared elected, since Chocolate has more votes than the quota (with six surplus votes, to be precise).
Round 2	x x x x	x x	x x x x x x	x x x x x	x x x	Chocolate's surplus votes transfer to Strawberry and Sweets in proportion to the Chocolate voters' second choice preferences, using the formula: In this case, 8 of the 12 voters for Chocolate had the second preference of Strawberries, so (8/12)•6 = 4 of Chocolate's votes would transfer to Strawberries; meanwhile 4 of the 12 voters for Chocolate had Sweets as their second preference, so (4/12)•6 = 2 of Chocolate's votes will transfer to Sweets. Thus, Strawberries has 1 first-preference votes and 4 new votes, for an updated total of 1+4 = 5 votes; likewise, Sweets now has 1 + 2 = 3 votes; no other tallies change. Even with the transfer of this surplus no candidate has reached the quota. Therefore, Pear, which now has the fewest votes (after the update), is eliminated.
Round 3	x x x x x x		x x x x x x	x x x x x	x x x	Pear's votes are transferred in proportion to the second-preference options of voters of Pear, i.e. only Oranges in this case, which gives Oranges 2 more votes. Oranges now totals 4 (original) + 2 (new) = 6 votes, reaching the quota; so, Oranges is elected. Orange meets the quota exactly, and therefore has no surplus to transfer.
Round 4	x x x x x x		x x x x x x	x x x x x	x x x	Neither of the remaining candidates meets the quota. Strawberry has more votes, so Sweets are eliminated. Sweets' votes would be transferred proportionately, but only two preferences were selected, so Chocolate-then-Sweets votes cannot be reallocated; moreover, no-one who voted for Sweets originally gave a second preference. Therefore, all votes for Sweets disappear. Strawberries is the only remaining candidate, so it wins the final seat (despite not satisfying the quota).

Result: The winners are Chocolate, Oranges and Strawberries.

Counting methods

STV systems primarily differ in how they transfer votes and in the size of the quota. For this reason some have suggested that STV can be considered a family of voting systems rather than a single system. 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. The Hare quota, which was used in the original proposals by Thomas Hare,^[9] ensures greater proportionality, at the expense of having to count more votes and not guaranteeing majority rule.

The easiest methods of transferring surpluses involve an element of randomness; partially random systems are used in the Republic of Ireland (except Senate elections) and in Malta, among other places. The Gregory method (also known as Newland-Britain or Senatorial rules) eliminates randomness by allowing for the transfer of fractions of votes. Gregory is in use in Northern Ireland, the Republic of Ireland (Senate elections) and in Australia. Both Gregory and earlier methods have the problem that in some circumstances they do not treat all votes equally. For this reason Meek's method, Warren's method and the Wright system have been invented.^[10] While easier methods can usually be counted by hand, except in a very small election Meek and Warren require counting to be conducted by computer. The Wright system is a refinement of the Australian Senate system replacing the process of distribution and segmentation of preferences by a reiterative counting process where the count is reset and restarted on every exclusion. Meek is used in local body elections in New Zealand.

Meek in 1969^[11] was the first to realise that computers make it possible to count votes in way that is conceptually simpler and closer to the original concept of STV. One advantage of Meek's method is that the quota is adjusted at each stage of counting when the number of votes decreases because some become non-transferable. Meek also considered a variant on his system which allows for equal preferences to be expressed.^[12] This has subsequently (since 1998) been used by the John Muir Trust for electing its Trustees.^[13]

History and current use

The concept of transferable voting was first proposed by Thomas Wright Hill in 1819. The system remained unused in public elections until 1855, when Carl Andræ proposed a transferable vote system for elections in Denmark, and his system was used in 1856 to elect the Rigsraad and from 1866 it was also adapted for indirect elections to the second chamber, the Landsting, until 1915.^[14]

Although he was not the first to propose 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 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.^[9] This is unnecessary in modern elections, as a voter can discover how their vote was distributed by viewing detailed election results. This is particularly easy to do using Meek's method, where only the final weightings of each candidate need to be published.

The noted political essayist John Stuart Mill was a friend of Hare and an early proponent of STV, praising it at length in his essay Considerations on Representative Government, in which he writes: "Of all modes in which a national representation can possibly be constituted, this one affords the best security for the intellectual qualifications desirable in the representatives. At present... the only persons who can get elected are those who possess local influence, or make their way by lavish expenditure...."^[15] His contemporary, Walter Bagehot, also praised the Hare system for allowing everyone to elect an MP, even ideological minorities, but also argued 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."^[16]

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. H.G. Wells was a strong advocate, calling it "Proportional Representation."^[17]

STV was also adopted in the first half of the 20th century to elect several city councils in the United States. More than twenty cities used STV, including Cleveland, Cincinnati and New York City. As of January 2010, it is used to elect the city council and school committee in Cambridge, Massachusetts and the park board in Minneapolis, Minnesota.

Issues

Degree of proportionality

The degree of proportionality of STV election results depends directly on the district magnitude (i.e. the number of seats in each district). While Ireland originally had a median district magnitude of five (ranging from three to nine) in 1923, successive governments lowered this. Systematically lowering the number of representatives from a given district directly benefits larger parties at the expense of smaller ones.

Supposing that the Droop quota is used: in a nine-seat district, the quota or threshold is 10% (plus one vote); in a three-seat district, it would be 25% (plus one vote).

A parliamentary committee in 2010 discussed the "increasing trend towards the creation of three-seat constituencies in Ireland" and recommended not less than four-seaters, except where the geographic size of such a constituency would be disproportionately large.^[18]

STV provides proportionality by transferring votes to minimise waste, and therefore also minimises the number of unrepresented or disenfranchised voters.

Difficulty of implementation

A frequent concern about STV is its complexity compared with plurality voting methods. Before the advent of computers, this complexity would have made ballot-counting more difficult than some other voting methods.

The algorithm is complicated. In large elections with many candidates, a computer may be required. (This is because after several rounds of counting, there may be many different categories of previously transferred votes, each with a different permutation of early preferences and thus each with a different carried-forward weighting, all of which have to be kept track of.) But the equipment can be expensive to change or upgrade.

One negative to the system is that within a given voting district, all votes must be collected together centrally and the data must be combined before running the algorithm. That is, some strict subsets of the votes can yield different overall results compared to the total set of the votes.

If a computer is used, it becomes much more difficult to verify and to demonstrate that the counting has been conducted fairly and in accordance with the election law.

Role of political parties

STV differs from other proportional representation systems in that candidates of one party can be elected on transfers from voters for other parties. Hence, STV may reduce the role of political parties in the electoral process and corresponding partisanship in the resulting government. A district only needs to have four members to be proportional for the major parties, but may under-represent smaller parties, even though they may well be more likely to be elected under STV than under First Past The Post. Also, while small parties seen as reasonable second preferences by others (such as the Green Party in Ireland) more easily get elected, parties seen as more extreme by others (such as Sinn Féin in Ireland) find it harder to attract second preferences and therefore find it harder to win seats.

By-elections

As STV is a multi-member system, filling vacancies between elections can be problematic, and a variety of methods have been devised. The countback method is used in the Australian Capital Territory, Tasmania, Victoria, Malta, and Cambridge, Massachusetts. Casual vacancies could be filled by re-examining the ballot papers data from the previous election. Another option is to have a head official or remaining members of the elected body appoint a new member to fulfill the vacancy. A third way to fill 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. Yet another option would be to allow the party of the vacant member to nominate a successor, possibly subject to the approval of the voting population or the rest of the government. Another possibility 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. This method was also used in the Northern Ireland Assembly, changed in 2009 to allow political parties to nominate new MLAs in the event of a vacancy. Independent MLAs may still draw up a list of potential replacements.^[19] For its 2009 European elections, Malta set a one-off policy to elect the candidate eliminated last for filling the prospective vacancy for the extra seat to arise from the Lisbon Treaty.

Tactics

If there are not enough candidates to represent one of the priorities the electorate vote for (such as a party), all of them may be elected in the early stages, with votes being transferred to candidates with other views. On the other hand, putting up too many candidates might result in first preference votes being spread too thinly among them, and consequently several potential winners with broad second-preference appeal may be eliminated before others are elected and their second-preference votes distributed. In practice, the majority of voters express preference for candidates from the same party in order, which minimises the impact of this potential effect of STV.

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 (assuming parties and no individual independents participate in the election). 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.

A number of methods of tactical or strategic voting exist that can be used in STV elections, but much less so than with First Past the Post. (In STV elections, most constituencies will be marginal, at least with regard to the allocation of a final seat.)

Elector confusion

STV systems vary, both in ballot design and in 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 may 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.

The method can be confusing, and may cause some people to vote incorrectly with respect to their actual preferences. The ballots can also be long; having multiple pages also increases the chances of people missing the later opportunities to continue voting.

Other

Some opponents argue that larger, multi-seat districts would require more campaign funds to reach the voters. Proponents argue that STV can lower campaign costs because like-minded candidates can share some expenses. In addition, unlike in at-large plurality elections, candidates do not have to secure the support of at least 50% of voters, allowing candidates to focus campaign spending primarily on supportive voters.

Analysis of results

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 in Arrow's impossibility theorem: in particular, STV fails to achieve independence of irrelevant alternatives (like most other vote-based ordering systems) and monotonicity.

Migration of preferences

The relative performance of political parties in STV systems is analyzed in a different fashion from that used in other electoral schemes. For example, seeing which candidates are declared elected on first preference votes alone can be shown as follows:

Scottish local elections, 2012^[20]

Party		Total elected	Elected on 1st prefs
			Total	%	% (2007)
	Conservative	115	46	40.0	40.6
	Labour	394	199	50.5	37.4
	Liberal Democrat	71	20	28.2	21.7
	SNP	425	185	43.5	56.5
	Scottish Green	14	1	7.1	–
	Independent	200	79	39.5	31.6
	Other	4	2	50.0	14.3
Totals		1,223	532	43.5	39.7

The data can also be analysed to find the proportion of voters who express only a single preference,^[21] or those that express a minimum number of preferences,^[22] in order to assess party strength. Where parties nominate multiple candidates in an electoral district, analysis can also be done to assess their relative strength.^[23]

Other useful information can be found by analyzing the first terminal transfer of a major party candidate in an electoral district, where all of the other parties still had a candidate in the count:

Average first terminal transfer rates (2012)^[24]

Transferred from		% non-transferable	% transferred to
			Con	Lab	LD	SNP	Ind/Other
	Conservative	33.6	–	8.0	32.4	8.3	17.6
	Labour	47.8	5.8	–	13.2	16.5	16.7
	Liberal Democrat	23.1	21.8	20.4	–	15.5	19.3
	SNP	44.2	6.0	18.1	14.1	–	17.8
	Scottish Green	20.4	5.1	19.2	19.9	18.3	17.0

Another effect of STV is that candidates that did well on first preference votes may not be elected, and those that did poorly on first preferences can be elected, because of differences in second and later preferences. This can also be analyzed:

Candidates not in a winning position on 1st preference who secured election, by party (2012)^[25]

Political party		Elected though not in top 3 or 4	Not elected though in top 3 or 4	Net gain/loss
				2012	2007
	Conservative	1	16	−15	−24
	Labour	21	8	+13	−17
	Liberal Democrat	4	3	+1	+29
	SNP	19	29	−10	–
	Scottish Green	1	1	–	+1
	Independent	22	9	+13	+8
	Other	–	2	−2	+3

See also

Further reading

• Bartholdi III, John J.; Orlin, James B. (1991). "Single Transferable Vote Resists Strategic Voting" (PDF). Social Choice and Welfare. Springer Science+Business Media. 8 (4): 341–354. 
• Geller, Chris (2002). "Single transferable vote with Borda elimination: a new vote-counting system" (PDF). Deakin University, Faculty of Business and Law. 
• O'Neill, Jeffrey C. (2004). "Tie-Breaking with the Single Transferable Vote" (PDF). Voting matters. McDougall Trust (18): 14–17. 
• Curtice, John (2012). "2012 Scottish Local Government Elections" (PDF). Electoral Reform Society. 

References

External links

• ACE Project
• A concise STV analogy – from Accurate Democracy
• Accurate Democracy lists a dozen programs for computing the single transferable vote.