In closed list systems, each party lists its candidates according to the party's "candidate selection process. This sets the order of candidates on the list and thus, in effect, their probability of being elected. The first candidate on a list, for example, will get the first seat that party wins. Each voter casts a vote for a list of candidates. Voters, therefore, do not have the option to express their preferences at the ballot as to which of a party's candidates are elected into office. A party is allocated seats in proportion to the number of votes it 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.["citation needed]
Open list PR
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. These votes sometimes rearrange the order of names on the party's list and thus which of its candidates are elected. Nevertheless, the number of candidates elected from the list is determined by the number of votes the list receives.["citation needed]
Local list PR
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.
Two-tier party list systems
Some party list proportional systems with open lists use a two-tier compensatory system, as in Denmark, Norway, and Sweden. In "Denmark, for example, the country is divided into ten multiple-member voting districts arranged in three regions, electing 135 representatives. In addition, 40 compensatory seats are elected. Voters have one vote which can be cast for an individual candidate or for a party list on the district ballot. To determine district winners, candidates are apportioned their share of their party's district list vote plus their individual votes. The compensatory seats are apportioned to the regions according to the party votes aggregated nationally, and then to the districts where the compensatory representatives are determined. In the 2007 general election, the district magnitudes, including compensatory representatives, varied between 14 and 28. The basic design of the system has remained unchanged since its introduction in 1920.
Single transferable vote
The single transferable vote (STV), also called choice voting, is a "preferential voting system: voters rank candidates in order of preference. Voting districts usually elect three to seven representatives. The count is cyclic, electing or eliminating candidates and transferring votes until all seats are filled. A candidate is elected whose tally reaches a "quota, the minimum vote that guarantees election. The candidate's surplus votes (those in excess of the quota) are transferred to other candidates at a fraction of their value proportionate to the surplus, according to the votes' preferences. If no candidates reach the quota, the candidate with the fewest votes is eliminated, those votes being transferred to their next preference at full value, and the count continues. There are many methods for transferring votes. Some early, manual, methods transferred surplus votes according to a randomly selected sample, or transferred only a "batch" of the surplus, other more recent methods transfer all votes at a fraction of their value (the surplus divided by the candidate's tally) but may need the use of a computer. Some methods may not produce exactly the same result when the count is repeated. There are also different ways of treating transfers to already elected or eliminated candidates, and these, too, can require a computer.
In effect, the method produces groups of voters of equal size that reflect the diversity of the electorate, each group having a representative the group voted for. Some 90% of voters have a representative to whom they gave their first preference. Voters can choose candidates using any criteria they wish, the proportionality is implicit. Political parties are not necessary; all other PR voting systems presume that parties reflect voters wishes, and so give power to parties. STV satisfies the "voting system criterion "proportionality for solid coalitions – a solid coalition for a set of candidates is the group of voters that rank all those candidates above all others – and is therefore considered a system of proportional representation. However, the small district magnitude used in STV elections has been criticized as impairing proportionality, especially when more parties compete than there are seats available,:50 and STV has, for this reason, sometimes been labelled "quasi proportional".:83 While this may be true when considering districts in isolation, results overall are proportional. In Ireland, with particularly small magnitudes, results are "highly proportional".:73 In "1997, the average magnitude was 4.0 but eight parties gained representation, four of them with less than 3% of first preference votes nationally. Six independent candidates also won election. STV has also been described as the most proportional system.:83 The system tends to handicap extreme candidates because, to gain preferences and so improve their chance of election, candidates need to canvass voters beyond their own circle of supporters, and so need to moderate their views. Conversely, widely respected candidates can win election with relatively few first preferences by benefitting from strong subordinate preference support.
Australian Senate STV
The term STV in Australia refers to the Senate voting system, a variant of Hare-Clark characterized by the "above the line" "group voting ticket, a party list option. It is used in the Australian upper house, the "Senate, and some state upper houses. Due to the number of preferences that are compulsory if a vote for candidates (below-the-line) is to be valid – for the Senate a minimum of 90% of candidates must be scored, in 2013 in "New South Wales that meant writing 99 preferences on the ballot – 95% and more of voters use the above-the-line option, making the system, in all but name, a party list system. Parties determine the order in which candidates are elected and also control transfers to other lists and this has led to anomalies: preference deals between parties, and "micro parties" which rely entirely on these deals. Additionally, independent candidates are unelectable unless they form, or join, a group above-the-line. Concerning the development of STV in Australia researchers have observed: "... we see real evidence of the extent to which Australian politicians, particularly at national levels, are prone to fiddle with the electoral system".:86
As a result of a parliamentary commission investigating the 2013 election, from 2016 the system has been considerably reformed (see "Australian federal election, 2016), with group voting tickets (GVTs) abolished and voters no longer required to fill all boxes.
Other proportional systems
In asset voting, the voters vote for candidates and then the candidates negotiate amongst each other and reallocate votes amongst themselves. Asset voting was independently rediscovered by each of Lewis Carroll, Warren D. Smith, and Forest Simmons.
Reweighted Range Voting
The Reweighted Range Voting (RRV) procedure is (quoted from ):
- Each voter casts a ballot rating the candidates from 0 to M
- Each ballot is given a weight equal to: C/(C + sum of the scores given to all elected candidates on that ballot)
- Sum up all the ballots using those weightings
- The candidate with the highest score wins and is declared elected
- goto (2) unless all seats are filled
The two parameters M and C are:
- M = maximum rating (say 10)
- C = determines how proportionality occurs: C = M ⇒ Greatest divisors (d'Hondt, Jefferson) proportionality; C = M/2 ⇒ Major fractions (Webster, Sainte-Lague) method. The C parameter mainly affects small parties.
Reweighted Range voting was used for the nominations in the Visual Effects category for recent Academy Award Oscars from 2013 thru 2017.
Mixed electoral systems
Mixed systems combine different methods of vote apportionment, typically one majoritarian method and a second method based on proportionality. Of the mixed systems that are designed to produce proportional results, the most prominent example is "mixed member proportional representation (MMP). This system, which has been used in "Germany since 1949, combines single-winner districts with a compensating party list PR vote at the national level. "Biproportional apportionment and "dual member proportional representation mix the principles of local popularity and overall proportionality, but elect only district-level representatives.
Mixed member proportional representation
Mixed member proportional representation (MMP), known regionally as Additional Member System in the "United Kingdom, is a hybrid two-tier "mixed-member system which varies in proportionality. MMP combines a single-district vote, usually "first-past-the-post, with a compensatory regional or nationwide party list proportional vote. The system aims to combine the local district representation of "FPTP and the proportionality of a national party list system. MMP has the potential to be proportional or "semi-proportional depending on a number of factors such as the ratio of FPTP seats to PR seats, the existence or nonexistence of compensatory seats to make up for "overhang seats, and "election thresholds. It was invented for the German "Bundestag after the Second World War and has spread to "Lesotho, "Mexico, "Bolivia and "New Zealand. The system is also used for the "Welsh and "Scottish assemblies where it is called the "additional member system. Voters have two votes, one for their district representative and one for the party list, the list vote determining the relative strength of parties in parliament. After the district winners have been determined, sufficient candidates from each party list are elected to "top-up" each party to the overall number of parliamentary seats due to it according to its overall list vote. Before apportioning list seats, all list votes for parties which failed to reach the minimum threshold are discarded, the proportions for remaining parties improve. Also, any direct seats won by independent candidates are subtracted from the parliamentary total used to apportion list seats.
The system has the potential to produce proportional results, but proportionality can be compromised if the ratio of list to district seats is too low, it may then not be possible to completely compensate district seat disproportionality. Another factor can be how "overhang seats are handled, district seats that a party wins in excess of the number due to it under the list vote. To achieve proportionality, other parties require "balance seats", increasing the size of parliament by twice the number of overhang seats, but this is not always done. Until recently, Germany increased the size of parliament by the number of overhang seats but did not use the increased size for apportioning list seats. This was changed for the 2013 national election after the constitutional court rejected the previous law, not compensating for overhang seats had resulted in a "negative vote weight effect. Lesotho, Scotland and Wales don't increase the size of parliament at all, and, in 2012, a New Zealand parliamentary commission also proposed abandoning compensation for overhang seats, and so fixing the size of parliament. At the same time, it would abolish the single-seat threshold – any such seats would then be overhang seats and would otherwise have increased the size of parliament further – and reduce the vote threshold from 5% to 4%. Proportionality would not suffer.
Biproportional apportionment applies a mathematical method ("iterative proportional fitting) for the modification of an election result to achieve proportionality. It was proposed for elections by the mathematician "Michel Balinski in 1989, and first used by the city of "Zurich for its council elections in February 2006, in a modified form called "new Zurich apportionment" (Neue Zürcher Zuteilungsverfahren). Zurich had had to modify its party list PR system after the "Swiss Federal Court ruled that its smallest "wards, as a result of population changes over many years, unconstitutionally disadvantaged smaller political parties. With biproportional apportionment, the method of election, the use of open party lists, hasn't changed, but the way winning candidates are determined has. The proportion of seats due to each party is calculated according to their overall, citywide, vote, and then the district winners are adjusted to conform to these proportions. This means that some candidates, who would otherwise have been successful, can be denied seats in favor of initially unsuccessful candidates, in order to improve the relative proportions of their respective parties overall. This peculiarity is accepted by the Zurich electorate because the resulting city council is proportional and all votes, regardless of district magnitude, now have equal weight. The system has since been adopted by other Swiss cities and "cantons.
Balinski has proposed another variant, "fair majority voting (FMV), for Plurality/Majoritarian voting systems, specifically for the "US House of Representatives, introducing proportionality while changing neither the plurality method of election nor the, possibly gerrymandered, district boundaries. The upper apportionment tier would be at the "state level. In another proposal, for the "UK parliament, whose elections are contested by many more parties, the authors note that parameters can be tuned to adopt any degree of proportionality deemed acceptable to the electorate. In order to elect smaller parties, a number of constituencies would be awarded to candidates placed fourth or even fifth in the constituency – unlikely to be acceptable to the electorate, the authors concede – but this effect could be substantially reduced by incorporating a third, regional, apportionment tier, or by specifying minimum thresholds.
Dual member proportional representation
Dual member proportional representation (DMP) is a single-vote system that elects two representatives in every district. The first seat in each district is awarded to the candidate who wins a plurality of the votes, similar to "first-past-the-post voting. The remaining seats are awarded in a compensatory manner to achieve proportionality across a larger region. DMP employs a formula similar to the "best near-winner" variant of "MMP used in the German state of "Baden-Württemberg. In Baden-Württemberg, compensatory seats are awarded to candidates who receive high levels of support at the district level compared with other candidates of the same party. DMP differs in that at most one candidate per district is permitted to obtain a compensatory seat. If multiple candidates contesting the same district are slated to receive one of their parties' compensatory seats, the candidate with the highest vote share is elected and the others are eliminated. DMP is similar to "STV in that all elected representatives, including those who receive compensatory seats, serve their local districts. Invented in 2013 in the "Canadian province of "Alberta, DMP received attention on "Prince Edward Island where it appeared on a November 2016 plebsite as a potential replacement for "FPTP but was eliminated on the third count.
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 30, 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 24, "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.
Already in 1787, "James Wilson, like Adams a "US Founding Father, understood the importance of multiple-member districts: "Bad elections proceed from the smallness of the districts which give an opportunity to bad men to intrigue themselves into office", and again, in 1791, in his Lectures on Law: "It may, I believe, be assumed as a general maxim, of no small importance in democratical governments, that the more extensive the district of election is, the choice will be the more wise and enlightened". The 1790 "Constitution of Pennsylvania specified multiple-member districts for the state Senate and required their boundaries to follow "county lines.
STV, or, more precisely, 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, and a simple 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, a retired paper-mill owner, 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 and expanded on in his 1859 Treatise on the Election of Representatives. The scheme was enthusiastically taken up by "John Stuart Mill, ensuring international interest. The 1865 edition of the book included 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.
In the UK, the 1917 "Speaker's Conference recommended STV for all multi-seat Westminster constituencies, but it was only applied to "university constituencies, lasting from 1918 until 1950 when those constituencies were abolished. In Ireland, STV was used in 1918 in the "University of Dublin constituency, and was introduced for devolved elections in 1921.
STV is currently used for two national lower houses of parliament, Ireland, since independence (as the "Irish Free State) in 1922, and Malta, since 1921, long before independence in 1966. In Ireland, two attempts have been made by "Fianna Fáil governments to abolish STV and replace it with the '"First Past the Post' plurality system. Both attempts were rejected by voters in referendums held "in 1959 and "again in 1968..
STV is also used for all other elections in Ireland except for that of the presidency, for the Northern Irish assembly and European and local authorities, Scottish local authorities, some New Zealand and Australian local authorities, the "Tasmanian (since 1907) and "Australian Capital Territory assemblies, where the method is known as Hare-Clark, and the city council in "Cambridge, Massachusetts, (since 1941).
PR is used by more nations than Plurality/Majoritarian systems. Among the world's 35 most robust democracies with populations of at least two million people, only six use winner-take-all systems for elections to the legislative assembly (plurality, runoff or instant runoff); four use parallel systems; and 25 use PR.
PR dominates Europe, including Germany and most of northern and eastern Europe; it is also used for "European Parliament elections. France adopted PR at the end of World War II, but discarded it in 1958; it was used for parliament elections in 1986. "Switzerland has the most widespread use of proportional representation, which is the system used to elect not only national legislatures and local councils, but also all local executives. PR is less common in the English-speaking world; "New Zealand adopted MMP in 1993, but the UK, Canada, India and Australia all use winner-take-all systems for legislative elections.
In "Canada, STV was used by the cities of "Edmonton and "Calgary in "Alberta from 1926 to 1955, and by "Winnipeg in "Manitoba from 1920 to 1953. In both provinces the "alternative vote (AV) was used in rural areas. "First-past-the-post was re-adopted in Alberta by the dominant party for reasons of political advantage, in Manitoba a principal reason was the underrepresentation of Winnipeg in the provincial legislature.:223–234
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 citywide elections in which people would cast votes for five or six candidates simultaneously, delivering some of the benefits of proportional representation.
List of countries using proportional representation
Detailed information on voting systems applying to the first chamber of the legislature is maintained by the ACE Electoral Knowledge Network. This includes both a map and a detailed table by country. What follows is a more summary presentation on countries using proportional representation.
|"Albania||Party list, 4% national threshold or 2.5% in a district|
|"Armenia||For elections to National Assembly : two-tier party list. Nationwide "Closed list and an "Open list in each of 13 election districts. Two best placed parties run-off "FPTP to get additional seats ensuring stable majority of 54% if it is not achieved either immediately or through building a coalition. Threshold of 5% for parties and 7% for election blocs.|
|"Australia||For "Senate only, "Single transferable vote|
|"Austria||Party list, 4% threshold|
|"Belgium||Party list, 5% threshold|
|"Bolivia||"Mixed-member proportional representation, 3% threshold|
|"Bosnia and Herzegovina||Party list|
|"Bulgaria||Party list, 4% threshold|
|"Burkina Faso||Party list|
|"Burundi||Party list, 2% threshold|
|"Cape Verde||Party list|
|"Chile||"Binomial voting system|
|"Costa Rica||Party list|
|"Croatia||Party list, 5% threshold|
|"Czech Republic||Party list, 5% threshold|
|"Denmark||Party list, 2% threshold|
|"Dominican Republic||Party list|
|"El Salvador||Party list|
|"Equatorial Guinea||Party list|
|"Estonia||Party list, 5% threshold|
|"European Union||Varies between Member States|
|"Germany||"Mixed-member proportional representation, 5% (or 3 district winners) threshold|
|"Greece||Reinforced proportionality, 3% threshold|
|"Hong Kong||Party list on all 5 geographical constituents and one functional constituent (District Council (Second)), total 40 seats|
|"Hungary||"Mixed-member proportional representation, 5% threshold or higher|
|"Indonesia||Party list, 3.5% threshold|
|"Ireland||"Single transferable vote (For "Dáil only)|
|"Israel||Party list, 3.25% threshold|
|"Italy||Party list, 10% threshold for coalitions, and 4% for individual parties|
|"Kyrgyzstan||Party list, 5% threshold|
|"Latvia||Party list, 5% threshold|
|"Lesotho||"Mixed-member proportional representation|
|"Liechtenstein||Party list, 8% threshold|
|"Malta||"Single transferable vote|
|"Mexico||"Mixed-member proportional representation|
|"Moldova||Party list, 6% threshold|
|"New Zealand||"Mixed-member proportional representation, 5% (or 1 district winner) threshold|
|"Northern Ireland||"Single transferable vote|
|"Norway||Party list, 4% national threshold|
|"Poland||Party list, 5% threshold or more|
|"Romania||"Mixed-member proportional representation|
|"Russia||"Mixed-member proportional representation|
|"San Marino||"Semi-proportional representation, 3.5% threshold|
|"São Tomé and Príncipe||Party list|
|"Serbia||Party list, 5% threshold or less|
|"Sint Maarten||Party list|
|"Slovakia||Party list, 5% threshold|
|"Slovenia||Party list, 4% threshold|
|"South Africa||Party list|
|"Spain||Party list, 3% threshold in small constituencies|
|"Sri Lanka||Party list|
|"Sweden||Party list, 4% national threshold or 12% in a district|
|"Turkey||Party list, 10% threshold|
|"Venezuela||"Mixed-member proportional representation|
- Amy, Douglas J. (1993). Real Choices/New Voices: The Case for Proportional Representation Elections in the United States. Columbia University Press.
- Batto, Nathan F.; Huang, Chi; Tan, Alexander C.; Cox, Gary (2016). Mixed-Member Electoral Systems in Constitutional Context: Taiwan, Japan, and Beyond. Ann Arbor: University of Michigan Press.
- Pilon, Denis (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.
- Linton, Martin; Southcott, Mary (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.
- Hickman, John; Little, Chris (November 2000). "Seat/vote proportionality in Romanian and Spanish parliamentary elections". Journal of Southern Europe and the Balkans Online. "Taylor and Francis. 2 (2): 197–212. "doi:10.1080/713683348.
- Galasso, Vincenzo; Nannicini, Tommaso (December 2015). "So closed: political selection in proportional systems". "European Journal of Political Economy. "Elsevier. 40 (B): 260–273. "doi:10.1016/j.ejpoleco.2015.04.008.
- "Apportionment (politics)
- "Hare quota
- "Index of politics articles
- "Interactive representation
- "Sainte-Laguë method
- "Semi-proportional representation
- "Direct representation
- "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.
- "Electoral System Design: the New International IDEA Handbook". "International Institute for Democracy and Electoral Assistance. 2005. Retrieved 9 April 2014.
- "Fair Voting/Proportional Representation". "FairVote. Retrieved 9 April 2014.
- "Electoral Systems". "ACE Electoral Knowledge Network. Retrieved 9 April 2014.
- "Voting systems made simple". London: "Electoral Reform Society. Retrieved 28 July 2014.
- "Electoral Systems and the Delimitation of Constituencies". "International Foundation for Electoral Systems. 2 Jul 2009.
- Moser, Robert G. (Dec 2004). "Mixed electoral systems and electoral system effects: controlled comparison and cross-national analysis". Electoral Studies. 23 (4): 575–599. "doi:10.1016/S0261-3794(03)00056-8.
- Massicotte, Louis (Sep 1999). "Mixed electoral systems: a conceptual and empirical survey". Electoral Studies. 18 (3): 341–366. "doi:10.1016/S0261-3794(98)00063-8.
- "Elections in Wales". "Cardiff University.
- "Where else is MMP used?". Wellington: "Electoral Commission New Zealand. 2011. Retrieved 10 Aug 2014.
- "Additional Member System". London: "Electoral Reform Society. Retrieved 16 October 2015.
- Pukelsheim, Friedrich (September 2009). "Zurich's New Apportionment" (PDF). German Research. "Wiley Online Library. 31 (2). Retrieved 10 August 2014.
- ACE Project: The Electoral Knowledge Network. "Electoral Systems Comparative Data, Table by Country". Retrieved 20 November 2014.
- Gallagher, Michael. "Ireland: The Archetypal Single Transferable Vote System" (PDF). Retrieved 26 October 2014.
- 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.
- Amy, Douglas J. "A Brief History of Proportional Representation in the United States". "FairVote. Retrieved 16 October 2015.
- ACE Project Electoral Knowledge Network. "The Systems and Their Consequences". Retrieved 26 September 2014.
- "Forder, James (2011). The case against voting reform. Oxford: "Oneworld Publications. "ISBN "978-1-85168-825-8.
- Colin Rallings; Michael Thrasher. "The 2005 general election: analysis of the results" (PDF). Electoral Commission, Research, Electoral data. London: "Electoral Commission. Retrieved 29 March 2015.
- Norris, Pippa (1997). "Choosing Electoral Systems: Proportional, Majoritarian and Mixed Systems" (PDF). "Harvard University. Retrieved 9 April 2014.
- "Election 2015 - BBC News". BBC. Retrieved 11 May 2015.
- Roberts, Iain (29 June 2010). "People in broad church parties should think twice before attacking coalitions". "Liberal Democrat Voice. Retrieved 29 July 2014.
- "Why Proportional Representation? A look at the evidence" (PDF). Fair Vote Canada. Retrieved 8 April 2016.
- Amy, Douglas J. "Single Transferable Vote Or Choice Voting". "Mount Holyoke College. Retrieved 9 April 2014.
- "Electoral Reform Society's evidence to the Joint Committee on the Draft Bill for House of Lords Reform". "Electoral Reform Society. 21 October 2011. Retrieved 10 May 2015.
- Harris, Paul (20 November 2011). "'America is better than this': paralysis at the top leaves voters desperate for change". The Guardian. Retrieved 17 November 2014.
- Krugman, Paul (19 May 2012). "Going To Extreme". The Conscience of a Liberal, Paul Krugman Blog. "The New York Times Co. Retrieved 24 Nov 2014.
- Mollison, Denis. "Fair votes in practice STV for Westminster" (PDF). "Heriot Watt University. Retrieved 3 June 2014.
- "Democrats' Edge in House Popular Vote Would Have Increased if All Seats Had Been Contested". "FairVote. Retrieved 7 July 2014.
- Amy, Douglas J (2002). Real Choices / New Voices, How Proportional Representation Elections Could Revitalize American Democracy. "Columbia University Press. "ISBN "9780231125499.
- Mollison, Denis (2010). "Fair votes in practice: STV for Westminster". "Heriot-Watt University. Retrieved 3 June 2014.
- 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.
- "Office for Democratic Institutions and Human Rights (11 July 2014). "Hungary, Parliamentary Elections, 6 April 2014: Final Report". "OSCE.
- "Voting Counts: Electoral Reform for Canada" (PDF). Law Commission of Canada. 2004. p. 22.
- "Report of the Hansard Society Commission on Electoral Reform" (PDF). "Hansard Society. London. 1976.
- "Single Transferable Vote". London: "Electoral Reform Society. Retrieved 28 July 2014.
- Humphreys, John H (1911). Proportional Representation, A Study in Methods of Election. London: Methuen & Co.Ltd.
- "Electoral systems, district magnitude". "ACE Electoral Knowledge Network. Retrieved 9 April 2014.
- Laver, Michael (1998). "A new electoral system for Ireland?" (PDF). The Policy Institute, "Trinity College, Dublin.
- "Joint Committee on the Constitution" (PDF). Dublin: Houses of the "Oireachtas. July 2010.
- "National projections" (PDF). Monopoly Politics 2014 and the Fair Voting Solution. "FairVote. Retrieved 9 July 2014.
- Lubell, Maayan (Mar 11, 2014). "Israel ups threshold for Knesset seats despite opposition boycott". "Thomson Reuters. Retrieved 10 July 2014.
- "Party Magnitude and Candidate Selection". "ACE Electoral Knowledge Network.
- O'Kelly, Michael. "The fall of Fianna Fáil in the 2011 Irish general election". "Significance. "Royal Statistical Society, "American Statistical Association.
- Kestelman, Philip (March 1999). "Quantifying Representativity". Voting matters. London: The McDougall Trust (10). Retrieved 10 August 2013.
- Hill, I D (May 1997). "Measuring proportionality". Voting matters. London: The McDougall Trust (8).
- Dunleavy, Patrick; Margetts, Helen (2004). "How proportional are the 'British AMS' systems?". Representation: Journal of Representative Democracy. 40 (4): 317–329. Retrieved 25 November 2014.
- As counted from the table in http://www.wahlrecht.de/ausland/europa.htm [in German]; "Vorzugsstimme(n)" means "open list".
- "Party List PR". Electoral Reform Society. Retrieved 23 May 2016.
- Gordon Gibson (2003). Fixing Canadian Democracy. The Fraser Institute. p. 76.
- Gallagher, Michael; Mitchell, Paul (2005). The Politics of Electoral Systems. Oxford, New York: Oxford University Press. p. 11. "ISBN "0-19-925756-6.
- "The Parliamentary Electoral System in Denmark". Copenhagen: Ministry of the Interior and Health. 2011. Retrieved 1 Sep 2014.
- "The main features of the Norwegian electoral system". Oslo: Ministry of Local Government and Modernisation. Retrieved 1 Sep 2014.
- "The Swedish electoral system". Stockholm: Election Authority. 2011. Retrieved 1 Sep 2014.
- "Tideman, Nicolaus (1995). "The Single Transferable Vote". Journal of Economic Perspectives. American Economic Association. 9 (1): 27–38. "doi:10.1257/jep.9.1.27.
- O’Neill, Jeffrey C. (July 2006). "Comments on the STV Rules Proposed by British Columbia". Voting matters. London: The McDougall Trust (22). Retrieved 10 August 2013.
- David M. Farrell; Ian McAllister (2006). The Australian Electoral System: Origins, Variations, and Consequences. Sydney: "UNSW Press. "ISBN "978-0868408583.
- "Referendum 2011: A look at the STV system". Auckland: The New Zealand Herald. 1 Nov 2011. Retrieved 21 Nov 2014.
- "Change the Way We Elect? Round Two of the Debate". Vancouver: The Tyee. 30 Apr 2009. Retrieved 21 Nov 2014.
- "The Hare-Clark System of Proportional Representation". Melbourne: Proportional Representation Society of Australia. Retrieved 21 Nov 2014.
- "Above the line voting". Perth: University of Western Australia. Retrieved 21 Nov 2014.
- "Glossary of Election Terms". Sydney: Australian Broadcasting Corporation. Retrieved 21 Nov 2014.
- Hill, I.D. (November 2000). "How to ruin STV". Voting matters. London: The McDougall Trust (12). Retrieved 10 August 2013.
- Green, Anthony (20 April 2005). "Above or below the line? Managing preference votes". Australia: On Line Opinion. Retrieved 21 Nov 2014.
- Terry, Chris (5 April 2012). "Serving up a dog's breakfast". London: "Electoral Reform Society. Retrieved 21 Nov 2014.
- Smith, Warren. "Asset voting – an interesting and very simple multiwinner voting system". Retrieved 4 April 2016.
- Smith, Warren (8 Mar 2005). ""Asset voting" scheme for multiwinner elections" (PDF). Retrieved 4 April 2016.
- Smith, Warren (8 Mar 2005). "Comparative survey of multiwinner election methods" (PDF). Retrieved 4 April 2016.
- Smith, Warren (6 Aug 2005). "Reweighted range voting – new multiwinner voting method" (PDF). Retrieved 4 April 2016.
- Kok, Jan; Smith, Warren. "Reweighted Range Voting – a Proportional Representation voting method that feels like range voting". Retrieved 4 April 2016.
- Ryan, Ivan. "Reweighted Range Voting – a Proportional Representation voting method that feels like range voting". Retrieved 4 April 2016.
- "89TH ANNUAL ACADEMY AWARDS OF MERIT FOR ACHIEVEMENTS DURING 2017" (PDF). Retrieved 4 April 2016.
- "Rule Twenty-Two: Special Rules for the Visual Effects Award". Retrieved 4 April 2016.
- ACE Project Electoral Knowledge Network. "Mixed Systems". Retrieved 29 June 2016.
- "Additional-member system: Politics". "Encyclopedia Britannica. Retrieved 24 Mar 2016.
- "Electoral Reform and Voting Systems". Politics.co.uk.
- "Mixed Member Proportional (MMP) System" (PDF).
- Amy, Douglas J. "How Proportional Representation Elections Work". "Mount Holyoke College. Retrieved 9 April 2014.
- "MMP Voting System". Wellington: "Electoral Commission New Zealand. 2011. Retrieved 10 Aug 2014.
- "Deutschland hat ein neues Wahlrecht" (in German). "Zeit Online. 22 February 2013.
- "Report of the Electoral Commission on the Review of the MMP Voting System". Wellington: "Electoral Commission New Zealand. 2011. Retrieved 10 Aug 2014.
- "Balinski, Michel (February 2008). "Fair Majority Voting (or How to Eliminate Gerrymandering)". The American Mathematical Monthly. Washington D.C.: "Mathematical Association of America. 115 (2). Retrieved 10 August 2014.
- Akartunali, Kerem; Knight, Philip A. (January 2014). "Network Models and Biproportional Apportionment for Fair Seat Allocations in the UK Elections" (PDF). "University of Strathclyde. Retrieved 10 August 2014.
- Sean Graham (April 4, 2016). "Dual-Member Mixed Proportional: A New Electoral System for Canada" (PDF).
- Antony Hodgson (Jan 21, 2016). "Why a referendum on electoral reform would be undemocratic". "The Tyee.
- PEI Special Committee on Democratic Renewal (April 15, 2016). "Recommendations in Response to the White Paper on Democratic Renewal - A Plebiscite Question" (PDF).
- Kerry Campbell (April 15, 2016). "P.E.I. electoral reform committee proposes ranked ballot". "CBC News.
- Teresa Wright (April 15, 2016). "Electoral reform plebiscite question will be a multi-option ballot". "The Guardian.
- Mitch McDonald (May 2, 2016). "Islanders can help change electoral system, says May". "Journal Pioneer.
- Adams, John (1776). "Thoughts on Government". The Adams Papers Digital Edition. Massachusetts Historical Society. Retrieved 26 July 2014.
- Hoag, Clarence; Hallett, George (1926). Proportional Representation. New York: The Macmillan Company.
- Madison, James. "Notes of Debates in the Federal Convention of 1787, Wednesday, June 6". TeachingAmericanHistory.org. Retrieved 5 August 2014.
- Wilson, James (1804). "Vol 2, Part II, Ch.1 Of the constitutions of the United States and of Pennsylvania – Of the legislative department, I, of the election of its members". The Works of the Honourable James Wilson. "Constitution Society. Retrieved 5 August 2014.
- "Constitution of the Commonwealth of Pennsylvania – 1790, art.I,§ VII, Of districts for electing Senators". "Duquesne University. Retrieved 9 December 2014.
- Hirczy de Miño, Wolfgang (1997). "Malta: Single-Transferable Vote with Some Twists". "ACE Electoral Knowledge Network. Retrieved 5 Dec 2014.
- "Adoption of Plan E". Welcome to the City of Cambridge. City of Cambridge, MA. Retrieved 25 November 2014.
- "Proportional Representation in Most Robust Democracies". Fair Vote: The Center for Voting And Democracy. Retrieved 22 January 2015.
- Jansen, Harold John (1998). "The Single Transferable Vote in Alberta and Manitoba" (PDF). "Library and Archives Canada. University of Alberta. Retrieved 23 March 2015.
- 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
- Election Districts Voting improves PR with overlapping districts elections for first past the post, alternative vote and single transferable vote voters
- 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.
- RangeVoting.org page on PR