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The term proportional representation (PR) characterises electoral systems by which divisions in an electorate  – political, religious, regional, ethnic, linguistic, of gender  – are reflected proportionately in the elected body. The essence of such systems is that all votes count, and they all count equally. If 30% of the electorate support a particular political party then roughly 30% of seats will be won by that party.

Proportional representation is achieved by the use of multiple-member voting districts (also called super-districts), although multiple-member districts are not in themselves a guarantee of proportionality. Proportional representation is not possible using single-member districts alone.

There are three distinct types of PR voting systems:

• Party-list PR systems where political parties define candidate lists and voters vote for a list, that is they vote for a party rather than for specific candidates (a "closed list"). The relative vote for each list determines how many from each list are actually elected. An "open list" variant allows voters to indicate individual candidate preferences. Voting districts can be as large as a province or an entire nation, in which case a high degree of political proportionality is achieved.
• Single transferable vote (STV), where voters rank candidates in order of preference. During the count unused votes for winning and eliminated candidates (that would otherwise be wasted) are transferred to other candidates according to the preferences. STV achieves good proportionality while enabling voters to elect independent candidates.
• Mixed (by which is meant hybrid) systems, principally Mixed-member PR (MMP), that combine single-member voting districts with some other mechanism  – MMP uses a nationwide party-list PR vote  – to provide compensatory proportionality. Under MMP voters have two votes, one for the district and one for a national list. The Additional member system (AMS) is very similar except that overhang seats are not compensated for so it is not always proportional. Parallel voting (also called Mixed Member Majoritarian, MMM) is also like MMP except that there is no compensatory link so that it is not usually considered proportional.

A further method approaches perfect proportionality by dispensing with voting altogether: the random selection of representatives from the populace, known as sortition. It was used in ancient Athens and the Venetian Republic and is still used today in the summons to jury duty. In the 21st century sortition has been used to select members for special citizens' assemblies in Ontario, British Columbia, Iceland, Belgium and elsewhere, and the concept has received academic attention.

A majority of countries use some form of PR in national lower house elections, party-list PR being the most widely used system (35%) followed by mixed systems (15%). STV, despite long being admired by political scientists, is used in only two national lower houses, Ireland (since 1921) and Malta (since 1921)  – political interests generally oppose its use because it so effectively transfers power from politicians to the electorate.

Nonetheless, a majority of voters still vote in non-proportional elections because the largest democracies, India and the USA, and others, many with historical links to the UK, use plurality voting systems.

Advantages and disadvantages of proportional representation

The case for proportional representation was made by John Stuart Mill in his 1861 essay Considerations on Representative Government:

In a representative body actually deliberating, the minority must of course be overruled; and in an equal democracy, the majority of the people, through their representatives, will outvote and prevail over the minority and their representatives. But does it follow that the minority should have no representatives at all? ... Is it necessary that the minority should not even be heard? Nothing but habit and old association can reconcile any reasonable being to the needless injustice. In a really equal democracy, every or any section would be represented, not disproportionately, but proportionately. A majority of the electors would always have a majority of the representatives, but a minority of the electors would always have a minority of the representatives. Man for man, they would be as fully represented as the majority. Unless they are, there is not equal government ... there is a part whose fair and equal share of influence in the representation is withheld from them, contrary to all just government, but, above all, contrary to the principle of democracy, which professes equality as its very root and foundation.

Most academic political theorists agree with Mill, that in a representative democracy the representatives should be representative.

Fairness

PR attempts to resolve the unfairness of majoritarian and plurality voting systems, where the largest parties receive an "unfair" "seat bonus" and smaller parties are disadvantaged and have difficulty winning any representation at all (Duverger's law). The established parties in US and UK elections can win formal control of the parliament with support from as little as 20-25% of eligible voters, due in part to low voter turnout. In Canada, governments are regularly formed by parties with support of under 40% of actual voters and hold majority power for full five-year terms. Coupled with turnout levels in the electorate of less than 60%, this can lead to a party obtaining a majority government by convincing as few as one quarter of the electorate to vote for it.

Election of minor parties

The use of multiple-member districts enables a greater variety of candidates to be elected. The more representatives per district and the lower the minimum threshold of votes required for election the more minor parties can gain representation. In emerging democracies inclusion of minorities in the legislature can be essential for social stability and to consolidate the democratic process.

Critics, on the other hand, claim this can give extreme parties a foothold in parliament, sometimes cited as a cause for the collapse of the Weimar government. With very low thresholds very small parties can act as "king-makers", holding larger parties to ransom during coalition discussions. The example of Israel is often quoted.

Another criticism is that the dominant parties from plurality systems, often looked on as "coalitions" or as "broad churches", can fragment under PR as the election of candidates from smaller groups becomes possible. Israel, again, and Brazil and Italy are examples. However, in other countries using PR such as Germany, Ireland and Malta dominant parties have shown little or no tendency to fragment.

STV, the only PR system which does not require political parties, enables independent candidates to be elected. In Ireland over the years about 10% of representatives have been independent.

Coalitions

The election of smaller parties gives rise to the principle objection to PR systems, that they invariably result in coalition governments.

Supporters of PR see coalitions as an advantage, forcing compromise between parties to form a coalition at the centre of the political spectrum, and so leading to continuity and stability. Opponents counter that with many policies compromise is not possible (for example funding a new stealth bomber, or leaving the EU), neither can many be easily positioned on the left-right spectrum (for example, the environment), so policies are horse-traded during coalition formation with the consequence that voters have no way of knowing which policies will be pursued by the government they elect; voters have less influence on governments. Also, coalitions do not necessarily form at the centre, and small parties can have excessive influence, supplying a coalition with a majority only on condition that a policy or policies favoured by few voters is adopted. Most importantly, the ability of voters to vote a party in disfavour out of power is curtailed.

All these disadvantages are avoided by two-party plurality systems. Coalitions are rare, the two dominant parties necessarily compete at the centre for votes so that governments are more reliably moderate, the strong opposition necessary for proper scrutiny of government is assured, and governments remain sensitive to public sentiment because they can be, and are, regularly voted out of power.

Voter apathy

Plurality systems usually result in single-party government because relatively few votes in the most finely balanced districts, the "swing seats", can transfer sufficient seats to the opposition to swing the election. More partisan districts remain invulnerable to swings of political mood. In the UK, for example, about half the constituencies have always elected the same party since 1945; in the 2012 US House elections 45 districts (10% of all districts) were uncontested by one of the two dominant parties.

With PR there are no "swing seats", most votes contribute to the election of a candidate so parties need to campaign in all districts, not just those where their support is strongest or where they perceive most advantage. This fact in turn encourages parties to be more responsive to voters, producing a more "balanced" ticket by nominating more women and minority candidates.

Since most votes count there are fewer "wasted votes", so voters, aware that their vote can make a difference, are more likely to make the effort to vote, and less likely to vote tactically. As compared to countries with plurality voting systems voter turnout improves and the population is more involved in the political process.

Gerrymandering

To ensure approximately equal representation plurality systems are dependent on the drawing of arbitrary boundaries of their single-member districts, a process vulnerable to political interference, that is to gerrymandering. To compound the problem, boundaries have to be periodically re-drawn to accommodate population changes. Even apolitically drawn boundaries can unintentionally gerrymander, reflecting naturally occurring diversity. PR systems with their multiple-member districts are less prone to this  – research suggests five-seat districts are immune to gerrymandering. The district boundaries are less critical and so can be aligned with historical boundaries such as cities, counties, states, or provinces; population changes can be accommodated by simply adjusting the number of representatives elected. For example, Professor Mollison in his 2010 plan for STV for the UK set an upper limit of 100,000 electors per MP so that a constituency of 500,000 electors would have five seats (1:100,000) but one of 500,001 six seats (1:83,000). His district boundaries follow historical county and local authority boundaries, yet he achieves more uniform representation than does the Boundary Commission, the body responsible for balancing the UK's first-past-the-post constituency sizes.

The single-seat districts used by Mixed-member PR are susceptible to gerrymandering and this can impair proportionality if the rules for awarding compensatory list seats are rigged. This has happened in Hungary where in 2014 Fidesz combined gerrymandering and a number of other tricks to contrive a two-thirds parliamentary majority from a 45% vote.

Link between constituent and representative

An accusation against PR is that because districts are larger the link between voters and their parliamentary representative is lost, or at best weakened. The argument does not apply to mixed-member systems because they incorporate single-member districts, but has to be conceded in the case of party-list systems with larger districts, especially those with a nationwide district (the Netherlands and Israel). With smaller districts, in particular with STV, there are counter-arguments: about 90% of constituents can consult a representative of a party to which they gave their first preference, someone whom they might see as more sympathetic to their problem. In any case they have a variety of representatives to choose from. With plurality systems only 48% of voters, on average, vote for the single representative, others may hesitate to ask for help from a political opponent, or someone who, indeed, may be the subject of the complaint.

How important the link between constituent and representative is, is another matter. In Britain some MPs may overstate their importance to their constituents, most people, after all, do not know the name of their MP. But under the Irish STV system the amount of constituency work has been criticised as excessive, suggesting an effective, perhaps too effective, link.

Attributes of PR systems

District magnitude

Academics agree that the most important influence on proportionality is an electoral district's magnitude, that is the number of representatives elected from the district. Proportionality improves as the magnitude increases. Scholars recommend voting districts of between three and seven members.

At one extreme, the Chilean Binomial system, a nominally proportional open-list system, uses two-member districts resulting in the election of one candidate from each of the two dominant political blocks, and so cannot be considered proportional.

At the other, where the district encompasses the entire country, and with a low minimum threshold, highly proportionate representation of political parties can result, and parties gain by broadening their appeal by nominating more minority and women candidates.

After the introduction of STV in Ireland in 1921 magnitude slowly diminished as more and more three-member constituencies were defined, benefiting the dominant Fianna Fáil, until 1979 when an independent boundary commission was established reversing the trend. In 2010 a parliamentary constitutional committee recommended a minimum magnitude of four. Nonetheless, despite relatively low magnitudes Ireland has generally experienced highly proportional results.

In the FairVote plan for STV (which FairVote calls choice voting) for the US House of Representatives three- to five-member super-districts are proposed. In Professor Mollison's plan for STV in the UK four- and five-member districts are used, with three and six as necessary to fit existing boundaries.

Minimum threshold

The minimum threshold is the minimum vote required to win a seat. The lower the threshold the higher the proportion of votes contributing to the election of a candidate.

All electoral systems have thresholds, either formally defined or as a mathematical consequence of the parameters of the election.

A formal threshold usually requires parties to win a certain percentage of the vote in order to be awarded seats from the party lists. In Germany and New Zealand (both MMP) the threshold is 5% of the national vote but both define an alternate threshold of constituency seats won, three in Germany, one in New Zealand. Turkey defines a threshold of 10%, the Netherlands 0.67%. Israel has raised its threshold from 1% (before 1992) to 1.5% (up to 2004), 2% (in 2006) and 3.25% in 2014.

In STV elections winning the quota (ballots/seats+1) of first preference votes assures election. However, well regarded candidates who attract good second (and third, etc.) preference support can hope to win election with only half the quota of first preference votes. Thus in a six-seat district the effective threshold would be 7.14% of first preference votes (100/(6+1)/2). The need to attract second preferences tends to promote consensus and disadvantage extremes.

Party magnitude

Party magnitude is the number of candidates elected from one party in one district. As party magnitude increases a more balanced ticket will be more successful encouraging parties to nominate women and minority candidates for election.

But under STV too many candidates can be counter-productive, splitting the vote and so losing seats. An example of this was identified in a ward in the 2007 Scottish local elections where Labour, putting up three candidates, won only one seat but where they would have won two had a candidate particularly favoured by Labour voters not stood. The same effect may have contributed to the collapse of Fianna Fáil in the 2011 Irish general election.

Others

Other aspects of PR can influence proportionality such as the size of the elected body, the choice of open or closed lists, ballot design, and vote counting methods.

Measuring proportionality

A number of ways of measuring proportionality have been proposed, including the Loosemore-Hanby Index, the Sainte-Laguë Index and the Gallagher Index. None of these fully support ranked voting.

PR voting systems

Party list PR

The parties each list their candidates according to that party's determination of priorities. In closed list systems, voters vote for a list of candidates, with the party choosing the order of candidates on the list and thus, in effect, their probability of being elected. Each party is allocated seats in proportion to the number of votes it receives, using the party-determined ranking order. In a local list system, parties divide their candidates in single member-like constituencies, which are ranked inside each general party-list depending by their percentages. This method allows electors to judge every single candidate as in an FPTP system. In an open list, voters may vote, depending on the model, for one person, or for two, or indicate their order of preference within the list – nevertheless the number of candidates elected from the list is determined by the number of votes the list receives.

There is an intermediate system in countries like Uruguay, where each party presents several closed lists, each representing a faction. Seats are distributed between parties according to the number of votes, and then between the factions within each party.

This system is used in many countries, including Finland (open list), Latvia (open list), Sweden (open list), Israel (national closed list), Brazil (open list), the Netherlands (open list), Russia (closed list), South Africa (closed list), Democratic Republic of the Congo (open list). For elections to the European Parliament, most member states use open lists; but most large EU countries use closed lists, so that the majority of EP seats are distributed by those. Local lists were used to elect the Italian Senate during the second half of the 20th century.

Mixed or hybrid

Mixed systems are hybrid systems combining a non-proportional and a proportional vote. The principle example is the mixed member system, which combine single seat constituencies elected by a single winner system with a compensating national or regional proportional vote, attempting to achieve some of the positive features of each.

Mixed systems are often helpful in countries with large populations, since they balance local and national concerns. They are used in nations with diverse geographic, social, cultural and economic issues. Such systems, or variations of them, are used in Germany, Lesotho, Mexico, Bolivia and New Zealand.

Single transferable vote

This system uses single transferable vote, a ranked voting system. Each constituency elects two or more representatives in constituencies equivalent in size to the sum of single-member constituencies that would produce the same number of representatives. Parties tend to offer as many candidates as they optimistically could expect to win. Major parties usually nominate more than minor parties. Voters rank some or all candidates in order of their preferences.

To be elected, a candidate must achieve a certain quota of votes. There are different ways of setting the quota, but the most commonly used is the Droop quota, calculated by "dividing the Total Valid Poll by one more than the number of seats to be filled, ignoring any remainder and then adding 1 vote." Also used is the Hare quota (also known as the simple quota), established by dividing the number of votes by the number of seats.

Only by rare coincidence would all candidates reach the quota and be elected in the first count. This is where voters' second choices come in. If one candidate is elected on the first count, that candidate's votes in excess of the quota (called surplus votes) are transferred to the candidates of each voter's second choice. In the event that no candidate is elected in the first count, the least popular candidate is eliminated and that candidate's votes are redistributed according to voters' second choices.

It is possible for more than one candidate to be eliminated after the first count if it is clear that these candidates would be eliminated in the next round anyway. This could happen when eliminating only one candidate with a small number of votes would not generate enough second choice votes to ensure that any candidate would meet the quota in the second count. This means that one or more additional candidates would need to be eliminated regardless, and it would be more efficient to eliminate simultaneously the required number of candidates to potentially fill a seat.

The process repeats itself until all seats are filled, either when the required number of candidates achieve the quota or when the number of remaining candidates matches the number of remaining seats. Although the counting process is complicated, voting is clear and most voters get at least one of their preferences elected.

All deputies are answerable directly to their local constituents. Some political scientists argue that STV is more properly classified as 'semi-proportional' as there is no assurance of a proportional result at a national level. Indeed, many advocates of STV argue that preventing nationwide proportionality is one of the primary goals of the system, to avoid the perceived risks of a fragmented legislature.

This system is used in the Upper House in India, Australia (Senate, Tasmanian and Australian Capital Territory Houses of Assembly and the Legislative Councils in New South Wales, South Australia, Western Australia and Victoria), Ireland, Northern Ireland (assembly, local government and European elections, but not national), Malta, local government elections in Scotland and selected (optional) local governments in New Zealand. The system was also used in several cities in the United States in the early 20th century.

History

One of the earliest proposals of proportionality in an assembly was by John Adams in his influential pamphlet Thoughts on Government, written in 1776 during the American Revolution:

It should be in miniature, an exact portrait of the people at large. It should think, feel, reason, and act like them. That it may be the interest of this Assembly to do strict justice at all times, it should be an equal representation, or in other words equal interest among the people should have equal interest in it.

Mirabeau, speaking to the Assembly of Provence on January 30th 1789, was also an early proponent of a proportionally representative assembly:

A representative body is to the nation what a chart is for the physical configuration of its soil: in all its parts, and as a whole, the representative body should at all times present a reduced picture of the people, their opinions, aspirations, and wishes, and that presentation should bear the relative proportion to the original precisely.

In February 1793 the Marquis de Condorcet led the drafting of the Girondist constitution which proposed a limited voting scheme with proportional aspects. Before that could be voted on the Montagnards took over the National Convention and produced their own constitution. On June 24th, Saint-Just proposed the single non-transferable vote, which can be proportional, for national elections but the constitution was passed on the same day specifying first-past-the-post voting.

STV, that is an election method where voters have one transferable vote, was first invented in 1819 by an English schoolmaster, Thomas Wright Hill, who devised a "plan of election" for the committee of the Society for Literary and Scientific Improvement in Birmingham that used not only transfers of surplus votes from winners but also from losers, a refinement that later both Andræ and Hare initially omitted. But the procedure was unsuitable for a public election and wasn't publicised. In 1839 Hill's son, Rowland Hill, recommended the concept for public elections in Adelaide, but a simpler process was used in which voters formed as many groups as there were representatives to be elected, each group electing one representative.

The first practical PR election method, a list method, was conceived by Thomas Gilpin in a paper he read to the American Philosophical Society in Philadelphia in 1844: "On the representation of minorities of electors to act with the majority in elected assemblies". But the paper appears not to have excited any interest.

A practical election using a single transferable vote was devised in Denmark by Carl Andræ, a mathematician, and first used there in 1855, making it the oldest PR system, but the system never really spread. It was re-invented (apparently independently) in the UK in 1857 by Thomas Hare, a London barrister, in his pamphlet The Machinery of Representation. This was enthusiastically taken up by John Stuart Mill, ensuring the scheme international publicity. In 1865, in the fifth edition of the pamphlet, Hare added the transfer of preferences from dropped candidates and the STV method was essentially complete. Mill proposed it to the House of Commons in 1867, but the British parliament rejected it. The name evolved from "Mr.Hare's scheme" to "proportional representation", then "proportional representation with the single transferable vote", and finally, by the end of the 19th century, to "the single transferable vote",

A party-list proportional representation system was devised and described in 1878 by Victor D'Hondt in Belgium. D'Hondt's method of seat allocation, the D'Hondt method, is still widely used. Victor Considerant, a utopian socialist, devised a similar system in an 1892 book. Some Swiss cantons (beginning with Ticino in 1890) used the system before Belgium, which was first to adopt list-PR in 1900 for its national parliament. Many European countries adopted similar systems during or after World War I. List-PR was favoured on the Continent because the use of lists in elections, the scrutin de liste, was already widespread. STV was preferred in the English-speaking world because its tradition was the election of individuals.

STV was used in Tasmania in 1907. In the last Irish elections to the UK Parliament in 1919, STV was used in the University of Dublin constituency; two Independent Unionists were elected. STV has been in use since Irish independence. A mainly centrist party, Fianna Fáil, typically receives 30%-50% of the vote while opposition parties, traditionally the centre-right Fine Gael and the centre-left Labour Party, are comparatively weak. This has led to a series of coalition governments; there has not been a single-party government since 1989.

PR is used by more nations than the single winner system, and it dominates Europe, including Germany, most of northern and eastern Europe, and is used for European Parliament elections (as enforced by EU law). France adopted PR at the end of World War II, but discarded it in 1958. In 1986 it was used for parliament elections.

Proportional representation is less common in the English-speaking world; New Zealand adopted it (MMP) in 1993. STV has some history in the United States. Many cities, including New York City, once used it to break up the Democratic Party monopolies on elective office. Cincinnati, Ohio, adopted STV in 1925 to get rid of a Republican Party monopoly, but the Republicans returned the city to FPTP in 1957. From 1870 to 1980, Illinois used a semi-proportional cumulative voting system to elect its House of Representatives. Each district across the state elected both Republicans and Democrats year-after-year. Cambridge, Massachusetts (STV) and Peoria, Illinois (cumulative voting) continue to use PR. San Francisco had city-wide elections in which people would cast votes for five or six candidates simultaneously, delivering some of the benefits of proportional representation.

Switzerland has the largest use of proportional representation, which is the system used to elect not only national legislatures and local councils, but also all local executives.

List of countries using proportional representation

This is a list of countries using proportional representation for central government.

Further reading

Books

• Amy, Douglas J. (1993). Real Choices/New Voices: The Case for Proportional Representation Elections in the United States. Columbia University Press.
• Denis Pilon (2007). The Politics of Voting. Edmond Montgomery Publications.
• Colomer, Josep M. (2003). Political Institutions. Oxford University Press.
• Colomer, Josep M., ed. (2004). Handbook of Electoral System Choice. Palgrave Macmillan.
• Pukelsheim, Friedrich (2014). Proportional Representation. Springer.
• Jess; Mary Southcott (1998). Making Votes Count: The Case for Electoral Reform. London: Profile Books.
• Forder, James (2011). The case against voting reform. Oxford: Oneworld Publications. ISBN 978-1-85168-825-8.

Journals

• John Hickman and Chris Little. "Seat/Vote Proportionality in Romanian and Spanish Parliamentary Elections" Journal of Southern Europe and the Balkans Vol. 2, No. 2, November 2000

News

• Roland Nicholson, Jr., "Proportional Representation Elections in Hong Kong", New York Times, September, 1992
• Roland Nicholson, Jr., "Proportional Representation Suits School Elections", New York Times, May 29, 1993

See also

• Apportionment (politics)
• D'Hondt method
• List of politics-related topics
• Sainte-Laguë method
• Hare quota

External links

• Proportional Representation Library
• "Proportional representation" Center for Voting and Democracy
• Handbook of Electoral System Choice
• "Electoral Systems", World Policy Institute
• Quantifying Representativity Article by Philip Kestelman
• The De Borda Institute A Northern Ireland-based organisation promoting inclusive voting procedures
• Electoral Reform Society founded in England in 1884, the longest running PR organization. Contains good information about Single Transferable Vote -the Society's preferred form of PR
• Electoral Reform Australia
• Proportional Representation Society of Australia
• Fair Vote Canada
• FairVote, USA
• Why Not Proportional Representation?
• Vote Dilution means Voters have Less Voice Law is Cool site
• Proportional Representation and British Democracy Debate on British electoral system reform
• Felsenthal, Dan S. (2010). "Review of paradoxes afflicting various voting procedures where one out of m candidates (m ≥ 2) must be elected" (PDF). Assessing Alternative Voting Procedures. London, UK: London School of Economics and Political Science. Retrieved October 9, 2011.

Notes

1. ^ Mill, John Stuart (1861). "Chapter VII, Of True and False Democracy; Representation of All, and Representation of the Majority only". Considerations on Representative Government. London: Parker, Son, & Bourn. {{cite book}}: External link in |chapterurl= (help); Unknown parameter |chapterurl= ignored (|chapter-url= suggested) (help)
2. ^ "Electoral System Design: the New International IDEA Handbook". International Institute for Democracy and Electoral Assistance. 2005. Retrieved 9 April 2014.
3. ^ Norris, Pippa (1997). "Choosing Electoral Systems: Proportional, Majoritarian and Mixed Systems" (PDF). Harvard University. Retrieved 9 April 2014.
4. Bird, Karen (11 November, 2003). "The Political Representation of Women and Ethnic Minorities in Established Democracies: A Framework for Comparative Research" (PDF). McMaster University. Retrieved 9 April 2014. {{cite web}}: Check date values in: |date= (help)
5. "Fair Voting/Proportional Representation". FairVote. Retrieved 9 April 2014.
6. "Voting Counts: Electoral Reform for Canada" (PDF). Law Commission of Canada. 2004. p. 22.
7. ^ Forder, James (2011). The case against voting reform. Oxford: Oneworld Publications. ISBN 978-1-85168-825-8.
8. Hall, Matt (18 May 2012). "Sorting out sortition". openDemocracy.
9. "The Citizen Legislature: Sortition". Sydney: newDemocracy Foundation. Retrieved 1 June 2014.
10. Abrahams, Marc (16 April 2012). "Improbable research: why random selection of MPs may be best". The Guardian.
11. Delannoi, Gil; Dowlen, Oliver, eds. (2010). Sortition: Theory and Practice. Exeter: Imprint Academic. ISBN 9-781845-401993.
12. Hirczy de Miño, Wolfgang, University of Houston; Lane, John, State University of New York at Buffalo (1999). "Malta: STV in a two-party system" (PDF). Retrieved 24 July 2014. {{cite web}}: Cite has empty unknown parameter: |1= (help)CS1 maint: multiple names: authors list (link)
13. ^ Amy, Douglas J. "A Brief History of Proportional Representation in the United States". Mount Holyoke College. Retrieved 9 April 2014.
14. Roberts, Iain (29th June 2010). "People in broad church parties should think twice before attacking coalitions". Liberal Democrat Voice. Retrieved 29 July 2014. {{cite web}}: Check date values in: |date= (help)
15. Amy, Douglas J. "Single Transferable Vote Or Choice Voting". Mount Holyoke College. Retrieved 9 April 2014.
16. ^ Mollison, Denis. "Fair votes in practice STV for Westminster" (PDF). Heriot Watt University. Retrieved 3 June 2014.
17. "Democrats' Edge in House Popular Vote Would Have Increased if All Seats Had Been Contested". FairVote. Retrieved 7 July 2014.
18. ^ Amy, Douglas J. "How Proportional Representation Would Finally Solve Our Redistricting and Gerrymandering Problems". Mount Holyoke College. Retrieved 13 July 2014.
19. Mollison, Denis (2010). "Fair votes in practice: STV for Westminster". Heriot-Watt University. Retrieved 3 June 2014.
20. Scheppele, Kim Lane (April 13 2014). "Legal But Not Fair (Hungary)". The Conscience of a Liberal, Paul Krugman Blog. The New York Times Co. Retrieved 12 July 2014. {{cite web}}: Check date values in: |date= (help)
21. Office for Democratic Institutions and Human Rights (11 July 2014). "Hungary, Parliamentary Elections, 6 April 2014: Final Report". http://www.osce.org. OSCE. {{cite web}}: External link in |website= (help)
22. "Single Transferable Vote". London: Electoral Reform Society. Retrieved 28 July 2014.
23. Amy, Douglas J. "PR Weakens the Constituency-Representative Link". Mount Holyoke College. Retrieved 28 July 2014.
24. "Localism in Irish politics and local government reform" (PDF). Dublin: Houses of the Oireachtas. February 2013. Retrieved 28 July 2014.
25. "Electoral Systems". ACE Electoral Knowledge Network. Retrieved 9 April 2014.
26. Laver, Michael (1998). "A new electoral system for Ireland?" (PDF). The Policy Institute, Trinity College, Dublin.
27. "Joint Committee on the Constitution" (PDF). Dublin: Houses of the Oireachtas. July 2010.
28. "National projections" (PDF). Monopoly Politics 2014 and the Fair Voting Solution. FairVote. Retrieved 9 July 2014.
29. Lubell, Maayan (Mar 11, 2014). "Israel ups threshold for Knesset seats despite opposition boycott". Thomson Reuters. Retrieved 10 July 2014.
30. "Party Magnitude and Candidate Selection". ACE Electoral Knowledge Network.
31. O'Kelly, Michael. "The fall of Fianna Fáil in the 2011 Irish general election". Significance. Royal Statistical Society, American Statistical Association.
32. Kestelman, Philip (March 1999). "Quantifying Representativity". Voting matters (10). London: The McDougall Trust. Retrieved 10 August 2013. {{cite journal}}: Invalid |ref=harv (help)
33. Hill, I D (May 1997). "Measuring proportionality". Voting matters (8). London: The McDougall Trust.
34. As counted from the table in http://www.wahlrecht.de/ausland/europa.htm ; "Vorzugsstimme(n)" means "open list".
35. Proportional Representation Irish citizens information
36. Adams, John (1776). "Thoughts on Government". The Adams Papers Digital Edition. Massachusetts Historical Society. Retrieved 26 July 2014.
37. ^ Hoag, Clarence; Hallett, George (1926). Proportional Representation. New York: The Macmillan Company.
38. Humphreys, John H (1911). Proportional Representation, A Study in Methods of Election. London: Methuen & Co.Ltd.

• Proportional representation electoral systems
• Voting systems