Proportional representation

From Wikipedia, the free encyclopedia
  (Redirected from Proportional voting)
Jump to: navigation, search

Proportional representation (PR) characterizes electoral systems by which divisions in an electorate are reflected proportionately in the elected body. If n% of the electorate support a particular political party, then roughly n% of seats will be won by that party. The essence of such systems is that all votes contribute to the result: not just a plurality, or a bare majority, of them. Proportional representation requires the use of multiple-member voting districts (also called super-districts); it is not possible using single-member districts alone.[1][2][3] In fact, the most proportional representation is achieved when just one super-district is used.

The two most widely used families of PR electoral systems are party list PR and single transferable vote (STV).[4][5] Mixed member proportional representation (MMP), also known as the Additional Member System, is a hybrid Mixed Electoral System that uses party list PR as its proportional component. MMP has the potential to be proportional or semi-proportional depending on a number of factors such as the ratio of first past the post (FPTP) seats to PR seats, the existence or nonexistence of compensatory seats to make up for overhang seats, and election thresholds.[6][7][8][9]

With party list PR, political parties define candidate lists and voters vote for a list. The relative vote for each list determines how many candidates from each list are actually elected. Lists can be "closed" or "open"; open lists allow voters to indicate individual candidate preferences and vote for independent candidates. Voting districts can be small (as few as two candidates per district in Chile) or as large as a province or an entire nation.

The single transferable vote uses small districts, with voters ranking individual candidates in order of preference. During the count, as candidates are elected or eliminated, surplus or discarded votes that would otherwise be wasted are transferred to other candidates according to the preferences. STV enables voters to vote across party lines and to elect independent candidates.

Mixed member proportional representation (MMP), also called the additional member system (AMS), is a hybrid, two-tier, mixed member system [2]:118[10] combining a non-proportional Plurality/Majoritarian election and a compensatory regional or national party list PR one. Voters have two votes, one for their single-member district and one for the party list, the party list vote determining the balance of the parties in the elected body.[2][11] Biproportional apportionment, first used in Zurich in 2006, is a two-tier method for adjusting an election's result to achieve overall proportionality.[12]

Some form of proportional representation is used for national lower house elections in 94 countries, party list PR, being used in 85 countries, is the most widely used.[13] MMP is used in seven lower houses, and STV, despite long being advocated by political scientists,[2]:71 is used in only two: Ireland, since independence in 1922,[14] and Malta, since 1921.[15]

As with all electoral systems, there are overlapping and contentious claims in terms of its advantages and disadvantages.[16]

Advantages and disadvantages[edit]

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.[1]

Many academic political theorists agree with Mill,[17] that in a representative democracy the representatives should represent all segments of society.


PR tries to resolve the unfairness of Plurality/Majoritarian 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 UK elections can win formal control of the parliament with as little as 35% of votes (2005 UK general election). In Canada, majority governments are regularly formed by parties with the support of under 40% of votes cast. Coupled with turnout levels in the electorate of less than 60%, this can lead to a party forming a majority government by convincing as few as one quarter of the electorate to vote for it. In the 2005 general election, for example, the Labour Party under Tony Blair won a comfortable parliamentary majority with the votes of only 21.6% of the total electorate.[18]:3 But PR systems with a high electoral threshold, or other features that reduce proportionality, are not necessarily much fairer: in the Turkish general election, 2002, using an open list system with a 10% threshold, 46% of votes were wasted.[2]:83

Plurality/Majoritarian systems can also disproportionately benefit regional parties that can win districts where they have a strong following, while other parties with national support but no strongholds, like the Greens, win few or no seats. An example is the Bloc Québécois in Canada that won 52 seats in the 1993 federal election, all in Quebec, on 18% of the national vote, while the Progressive Conservatives collapsed to two seats on 16% spread nationally.[19] Similarly, in the 2015 UK General Election, the Scottish National Party gained 56 seats, all in Scotland, with a 4.7% share of the vote while the UK Independence Party, with 12.6% of the national vote, gained only a single seat.[20]

Election of minor parties[edit]

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.[2]:58

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,[2]:59 but these problems can be limited, as in the modern German Bundestag, by the introduction of higher threshold limits for a party to gain parliamentary representation.

Another criticism is that the dominant parties in plurality systems, often looked on as "coalitions" or as "broad churches",[21] can fragment under PR as the election of candidates from smaller groups becomes possible. Israel, again, and Brazil and Italy are examples.[2]:59,89 However, research shows, in general, there is only a marginal increase in the number of parties in parliament.[22]

Open list systems and STV, the only PR system which does not require political parties,[23] enable independent candidates to be elected. In Ireland, on average, about six independent candidates have been elected each parliament.[24]


The election of smaller parties gives rise to the principal objection to PR systems, that they almost always result in coalition governments.[2]:59[17]

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 policies 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/are adopted. Most importantly, the ability of voters to vote a party in disfavour out of power is curtailed.[17]

All these disadvantages, the PR opponents contend, 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.[17] However, the US experience shows that this is not necessarily so, and that a two-party system can result in a "drift to extremes", hollowing out the centre,[25] or, at least, in one party drifting to an extreme.[26]

Nevertheless, on average, compared to countries using plurality systems, governments elected with PR accord more closely with the median voter and the citizens are more content with democracy.[22]

Voter participation[edit]

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;[27] in the 2012 US House elections 45 districts (10% of all districts) were uncontested by one of the two dominant parties.[28] Voters who know their preferred candidate cannot win have little incentive to vote, and if they do their vote has no effect, it is "wasted".[2]:10

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.[19] On average about 8% more women are elected.[22]

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. Compared to countries with plurality electoral systems, voter turnout improves and the population is more involved in the political process.[2][19][22]


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 (gerrymandering). To compound the problem, boundaries have to be periodically re-drawn to accommodate population changes. Even apolitically drawn boundaries can unintentionally produce the effect of gerrymandering, reflecting naturally occurring concentrations.[29]:65 PR systems with their multiple-member districts are less prone to this – research suggests five-seat districts are immune to gerrymandering.[29]:66 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.[27][30]

Mixed member systems are susceptible to gerrymandering for the local seats that remain a part of such systems. Under MMM, there is no compensation for the effects that such gerrymandering might have. Under MMP, the use of compensatory list seats makes gerrymandering less of an issue. However, its effectiveness in this regard depends upon the features of the system, including the size of the regional districts, the relative share of list seats in the total, and opportunities for collusion that might exist. A striking example of how the compensatory mechanism can be undermined can be seen in the 2014 Hungarian parliamentary election, where the leading party, Fidesz, combined gerrymandering and decoy lists, which resulted in a two-thirds parliamentary majority from a 45% vote.[31][32] This is an example of how MMP can result in semi-proportional representation.

Link between constituent and representative[edit]

It is generally accepted that a particular advantage of plurality of majoritarian electoral systems, such as first-past-the-post, is the geographic link between representatives and their constituents.[2]:36[33]:65[34]:21 A notable disadvantage of PR is that, as its multiple member districts are larger, this link is weakened if not completely lost.[2]:82 Party list PR systems with large districts, especially those without delineated districts such as the Netherlands and Israel, lack a geographic link between residents and their constituents. With smaller districts, in particular with STV, there are counter-arguments: about 90% of voters can consult a representative they voted for, someone whom they might think more sympathetic to their problem - one could say: with whom they have a closer link;[27][29]:212 constituents have a choice of representative so they can consult one with particular expertise in the topic at issue.[29]:212[35] With multiple member districts, prominent candidates are more able to be elected in their home constituencies, which they know and can represent authoritatively, so there is less need to parachute them into constituencies in which they are strangers and thus less than ideal representatives.[36]:248–250 Mixed member PR systems incorporate single-member districts to preserve the link,[2]:95 although, because up to half the parliamentary seats are list rather than district seats, the districts are necessarily up to twice as large as with a single member system.[34]:32

Wider benefits to society[edit]

Wider benefits from PR have been identified in societies using it as compared to those using FPTP, including higher scores on the UN Human Development Index, a measure of health, education, and personal security, higher economic growth, less inequality, and better environmental protection.[22]

Attributes of PR systems[edit]

District magnitude[edit]

Academics agree that the most important influence on proportionality is an electoral district's magnitude, the number of representatives elected from the district. Proportionality improves as the magnitude increases.[2] Scholars recommend voting districts of between three and seven members.[37]

At one extreme, the Chilean binomial voting electoral 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.[2]:79

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.[2]:83

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.[38] In 2010, a parliamentary constitutional committee recommended a minimum magnitude of four.[39] Nonetheless, despite relatively low magnitudes Ireland has generally experienced highly proportional results.[2]:73

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.[40] 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.[27]

Minimum threshold[edit]

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 representatives and the fewer the votes wasted.[2]

All electoral systems have thresholds, either formally defined or as a mathematical consequence of the parameters of the election.[2]:83

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%.[2] Israel has raised its threshold from 1% (before 1992) to 1.5% (up to 2004), 2% (in 2006) and 3.25% in 2014.[41]

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).[27] The need to attract second preferences tends to promote consensus and disadvantage extremes.

Party magnitude[edit]

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.[42]

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.[27] The same effect may have contributed to the collapse of Fianna Fáil in the 2011 Irish general election.[43]


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[edit]

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.[44][45]

Deviation from proportionality denotes the proportion of malappointment in a democratic process. The deviation is a mathematical relationship between the percentage of votes obtained by a political party and the percentage of parliamentary seats allocated to it. It is calculated by subtracting each party's vote share from its seat share, adding up the absolute values (ignoring any negative signs), and dividing by two.[46]:4–6

PR electoral systems[edit]

Party list PR[edit]

This system is used in many countries, including Finland (local list), Latvia (open list), Sweden (open list), Israel (national closed list), Brazil (open list), Nepal (Closed list) adopted in 2008 in first CA election, the Netherlands (open list), Russia (closed list), South Africa (closed list), Democratic Republic of the Congo (open list), and Ukraine (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.[47] Local lists were used to elect the Italian Senate during the second half of the 20th century.

Closed list PR[edit]

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.[48][49] A party is allocated seats in proportion to the number of votes it receives.[50]

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[edit]

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[edit]

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[edit]

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.[51][52][53]

Single transferable vote[edit]

The single transferable vote (STV), also called choice voting,[3][54] is a ranked 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.[55][56]

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.[27] Political parties are not necessary; all other PR electoral systems presume that parties reflect voters wishes, and so give power to parties.[55] STV satisfies the electoral 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.[55] 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,[17]:50 and STV has, for this reason, sometimes been labelled "quasi proportional".[57]: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".[2]:73[14] 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.[38] STV has also been described as the most proportional system.[57]: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.[58][59] Conversely, widely respected candidates can win election with relatively few first preferences by benefitting from strong subordinate preference support.[27]

Australian Senate STV[edit]

The term STV in Australia refers to the Senate electoral 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[60] – 95% and more of voters use the above-the-line option, making the system, in all but name, a party list system.[61][62][63] 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.[64][65] 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".[57]: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[edit]

Asset voting[edit]

In asset voting,[66][67][68] 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.[66]

Reweighted Range Voting[edit]

The Reweighted Range Voting (RRV)[68][69][70] procedure is (quoted from [71]):

  1. Each voter casts a ballot rating the candidates from 0 to M
  2. Each ballot is given a weight equal to: C/(C + sum of the scores given to all elected candidates on that ballot)
  3. Sum up all the ballots using those weightings
  4. The candidate with the highest score wins and is declared elected
  5. 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.[72][73]

Mixed electoral systems[edit]

Mixed systems combine different methods of vote apportionment, typically one majoritarian method and a second method based on proportionality.[74] 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[edit]

Mixed member proportional representation (MMP), known regionally as Additional Member System in the United Kingdom,[9][75][76][77] 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.[6][7][8][9] 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.[11][78] 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.[79]

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.[80] Lesotho, Scotland and Wales do not 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.[2][81]

Biproportional apportionment[edit]

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.[12][82]

Balinski has proposed another variant, fair majority voting (FMV), for plurality/majoritarian electoral 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.[82] 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.[83]

Dual member proportional representation[edit]

Dual member proportional representation (DMP) is a single-vote system that elects two representatives in every district.[84] 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.[85] 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.[86][87][88][89]


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.[90]

Mirabeau, speaking to the Assembly of Provence on January 30, 1789, was also an early proponent of a proportionally representative assembly:[91]

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.[91]

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",[92] 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".[93] The 1790 Constitution of Pennsylvania specified multiple-member districts for the state Senate and required their boundaries to follow county lines.[94]

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.[91]

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.[91]

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.[36]

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,[14] and Malta, since 1921, long before independence in 1966.[95] 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,[35] the Tasmanian (since 1907) and Australian Capital Territory assemblies, where the method is known as Hare-Clark,[60] and the city council in Cambridge, Massachusetts, (since 1941).[54][96]

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.[97]

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.[91]:223–234[98]

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[edit]

Countries by type of PR system[disputed ]

Detailed information on electoral 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.

Country Type
1 Albania Party list, 4% national threshold or 2.5% in a district
2 Algeria Party list
3 Angola Party list
4 Armenia For elections to National Assembly : two-tier party list.[99] 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.
5 Argentina Party list
6 Aruba Party list
7 Australia For Senate only, Single transferable vote
8 Austria Party list, 4% threshold
9 Belgium Party list, 5% threshold
10 Bénin Party list
11 Bhutan Party list
12 Bolivia Mixed-member proportional representation, 3% threshold
13 Bosnia and Herzegovina Party list
14 Brazil Party list
15 Bulgaria Party list, 4% threshold
16 Burkina Faso Party list
17 Burundi Party list, 2% threshold
18 Cambodia Party list
19 Cape Verde Party list
20 Chile Binomial voting
21 Colombia Party list
22 Costa Rica Party list
23 Croatia Party list, 5% threshold
24 Cyprus Party list
25 Czech Republic Party list, 5% threshold
26 Denmark Party list, 2% threshold
27 Dominican Republic Party list
28 El Salvador Party list
29 Equatorial Guinea Party list
30 Estonia Party list, 5% threshold
31 European Union Varies between Member States
32 Finland Party list
33 Germany Mixed-member proportional representation, 5% (or 3 district winners) threshold
34 Greece Reinforced proportionality, 3% threshold
35 Guatemala Party list
36 Guinea-Bissau Party list
37 Guyana Party list
38 Honduras Party list
39 Hong Kong Party list on all 5 geographical constituents and one functional constituent (District Council (Second)), total 40 seats
40 Hungary Mixed-member proportional representation, 5% threshold or higher
41 Iceland Party list
42 Indonesia Party list, 3.5% threshold
43 Iraq Party list
44 Ireland Single transferable vote (For Dáil only)
45 Israel Party list, 3.25% threshold
46 Italy Party list, 10% threshold for coalitions, and 4% for individual parties
47 Kazakhstan Party list
48 Kosovo Party list
49 Kyrgyzstan Party list, 5% threshold
50 Latvia Party list, 5% threshold
51 Lesotho Mixed-member proportional representation
52 Liechtenstein Party list, 8% threshold
53 Luxembourg Party list
54 Macedonia Party list
55 Malta Single transferable vote
56 Mexico Mixed-member proportional representation
57 Moldova Party list, 6% threshold
58 Mongolia Party list
59 Montenegro Party list
60 Morocco Party list
61 Mozambique Party list
62 Namibia Party list
63 Nepal Parallel voting
64 Netherlands Party list
65 New Zealand Mixed-member proportional representation, 5% (or 1 district winner) threshold
66 Nicaragua Party list
67 Northern Ireland Single transferable vote
68 Norway Party list, 4% national threshold
69 Paraguay Party list
70 Peru Party list
71 Philippines Parallel voting
72 Poland Party list, 5% threshold or more
73 Portugal Party list
74 Romania Mixed-member proportional representation
75 Russia Mixed-member proportional representation
76 Rwanda Party list
77 San Marino Semi-proportional representation, 3.5% threshold
78 São Tomé and Príncipe Party list
79 Serbia Party list, 5% threshold or less
80 Sint Maarten Party list
81 Slovakia Party list, 5% threshold
82 Slovenia Party list, 4% threshold
83 South Africa Party list
84 Spain Party list, 3% threshold in small constituencies
85 Sri Lanka Party list
86 Suriname Party list
87 Sweden Party list, 4% national threshold or 12% in a district
88 Switzerland Party list
89 Tunisia Party list
90 Turkey Party list, 10% threshold
91 Uruguay Party list
92 Venezuela Mixed-member proportional representation

See also[edit]


  1. ^ a b 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. 
  2. ^ a b c d e f g h i j k l m n o p q r s t u v w "Electoral System Design: the New International IDEA Handbook". International Institute for Democracy and Electoral Assistance. 2005. Retrieved 9 April 2014. 
  3. ^ a b "Fair Voting/Proportional Representation". FairVote. Retrieved 9 April 2014. 
  4. ^ "Electoral Systems". ACE Electoral Knowledge Network. Retrieved 9 April 2014. 
  5. ^ "Voting systems made simple". London: Electoral Reform Society. Retrieved 28 July 2014. 
  6. ^ a b "Electoral Systems and the Delimitation of Constituencies". International Foundation for Electoral Systems. 2 Jul 2009. 
  7. ^ a b Moser, Robert G. (December 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. 
  8. ^ a b Massicotte, Louis (September 1999). "Mixed electoral systems: a conceptual and empirical survey". Electoral Studies. 18 (3): 341–366. doi:10.1016/S0261-3794(98)00063-8. 
  9. ^ a b c "Elections in Wales". Cardiff University. 
  10. ^ "Where else is MMP used?". Wellington: Electoral Commission New Zealand. 2011. Retrieved 10 Aug 2014. 
  11. ^ a b "Additional Member System". London: Electoral Reform Society. Retrieved 16 October 2015. 
  12. ^ a b Pukelsheim, Friedrich (September 2009). "Zurich's New Apportionment" (PDF). German Research. Wiley Online Library. 31 (2). Retrieved 10 August 2014. 
  13. ^ ACE Project: The Electoral Knowledge Network. "Electoral Systems Comparative Data, Table by Country". Retrieved 20 November 2014. 
  14. ^ a b c Gallagher, Michael. "Ireland: The Archetypal Single Transferable Vote System" (PDF). Retrieved 26 October 2014. 
  15. ^ 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. 
  16. ^ ACE Project Electoral Knowledge Network. "The Systems and Their Consequences". Retrieved 26 September 2014. 
  17. ^ a b c d e Forder, James (2011). The case against voting reform. Oxford: Oneworld Publications. ISBN 978-1-85168-825-8. 
  18. ^ 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. 
  19. ^ a b c Norris, Pippa (1997). "Choosing Electoral Systems: Proportional, Majoritarian and Mixed Systems" (PDF). Harvard University. Retrieved 9 April 2014. 
  20. ^ "Election 2015 - BBC News". BBC. Retrieved 11 May 2015. 
  21. ^ Roberts, Iain (29 June 2010). "People in broad church parties should think twice before attacking coalitions". Liberal Democrat Voice. Retrieved 29 July 2014. 
  22. ^ a b c d e "Why Proportional Representation? A look at the evidence" (PDF). Fair Vote Canada. Retrieved 8 April 2016. 
  23. ^ Amy, Douglas J. "Single Transferable Vote Or Choice Voting". Mount Holyoke College. Retrieved 9 April 2014. 
  24. ^ "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. 
  25. ^ 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. 
  26. ^ 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. 
  27. ^ a b c d e f g h Mollison, Denis. "Fair votes in practice STV for Westminster" (PDF). Heriot Watt University. Retrieved 3 June 2014. 
  28. ^ "Democrats' Edge in House Popular Vote Would Have Increased if All Seats Had Been Contested". FairVote. Retrieved 7 July 2014. 
  29. ^ a b c d Amy, Douglas J (2002). Real Choices / New Voices, How Proportional Representation Elections Could Revitalize American Democracy. Columbia University Press. ISBN 9780231125499. 
  30. ^ Mollison, Denis (2010). "Fair votes in practice: STV for Westminster". Heriot-Watt University. Retrieved 3 June 2014. 
  31. ^ 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. 
  32. ^ Office for Democratic Institutions and Human Rights (11 July 2014). "Hungary, Parliamentary Elections, 6 April 2014: Final Report". OSCE. 
  33. ^ "Voting Counts: Electoral Reform for Canada" (PDF). Law Commission of Canada. 2004. p. 22. 
  34. ^ a b "Report of the Hansard Society Commission on Electoral Reform" (PDF). Hansard Society. London. 1976. 
  35. ^ a b "Single Transferable Vote". London: Electoral Reform Society. Retrieved 28 July 2014. 
  36. ^ a b Humphreys, John H (1911). Proportional Representation, A Study in Methods of Election. London: Methuen & Co.Ltd. 
  37. ^ "Electoral systems, district magnitude". ACE Electoral Knowledge Network. Retrieved 9 April 2014. 
  38. ^ a b Laver, Michael (1998). "A new electoral system for Ireland?" (PDF). The Policy Institute, Trinity College, Dublin. 
  39. ^ "Joint Committee on the Constitution" (PDF). Dublin: Houses of the Oireachtas. July 2010. 
  40. ^ "National projections" (PDF). Monopoly Politics 2014 and the Fair Voting Solution. FairVote. Retrieved 9 July 2014. 
  41. ^ Lubell, Maayan (March 11, 2014). "Israel ups threshold for Knesset seats despite opposition boycott". Thomson Reuters. Retrieved 10 July 2014. 
  42. ^ "Party Magnitude and Candidate Selection". ACE Electoral Knowledge Network. 
  43. ^ O'Kelly, Michael. "The fall of Fianna Fáil in the 2011 Irish general election". Significance. Royal Statistical Society, American Statistical Association. 
  44. ^ Kestelman, Philip (March 1999). "Quantifying Representativity". Voting matters. London: The McDougall Trust (10). Retrieved 10 August 2013. 
  45. ^ Hill, I D (May 1997). "Measuring proportionality". Voting matters. London: The McDougall Trust (8). 
  46. ^ 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. 
  47. ^ As counted from the table in [in German]; "Vorzugsstimme(n)" means "open list".
  48. ^ "Party List PR". Electoral Reform Society. Retrieved 23 May 2016. 
  49. ^ Gordon Gibson (2003). Fixing Canadian Democracy. The Fraser Institute. p. 76. 
  50. ^ Gallagher, Michael; Mitchell, Paul (2005). The Politics of Electoral Systems. Oxford, New York: Oxford University Press. p. 11. ISBN 0-19-925756-6. 
  51. ^ "The Parliamentary Electoral System in Denmark". Copenhagen: Ministry of the Interior and Health. 2011. Retrieved 1 Sep 2014. 
  52. ^ "The main features of the Norwegian electoral system". Oslo: Ministry of Local Government and Modernisation. Retrieved 1 Sep 2014. 
  53. ^ "The Swedish electoral system". Stockholm: Election Authority. 2011. Retrieved 1 Sep 2014. 
  54. ^ a b Amy, Douglas J. "A Brief History of Proportional Representation in the United States". FairVote. Retrieved 16 October 2015. 
  55. ^ a b c 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. 
  56. ^ 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. 
  57. ^ a b c David M. Farrell; Ian McAllister (2006). The Australian Electoral System: Origins, Variations, and Consequences. Sydney: UNSW Press. ISBN 978-0868408583. 
  58. ^ "Referendum 2011: A look at the STV system". Auckland: The New Zealand Herald. 1 Nov 2011. Retrieved 21 Nov 2014. 
  59. ^ "Change the Way We Elect? Round Two of the Debate". Vancouver: The Tyee. 30 Apr 2009. Retrieved 21 Nov 2014. 
  60. ^ a b "The Hare-Clark System of Proportional Representation". Melbourne: Proportional Representation Society of Australia. Retrieved 21 Nov 2014. 
  61. ^ "Above the line voting". Perth: University of Western Australia. Retrieved 21 Nov 2014. 
  62. ^ "Glossary of Election Terms". Sydney: Australian Broadcasting Corporation. Retrieved 21 Nov 2014. 
  63. ^ Hill, I.D. (November 2000). "How to ruin STV". Voting matters. London: The McDougall Trust (12). Retrieved 10 August 2013. 
  64. ^ Green, Anthony (20 April 2005). "Above or below the line? Managing preference votes". Australia: On Line Opinion. Retrieved 21 Nov 2014. 
  65. ^ Terry, Chris (5 April 2012). "Serving up a dog’s breakfast". London: Electoral Reform Society. Retrieved 21 Nov 2014. 
  66. ^ a b Smith, Warren. "Asset voting – an interesting and very simple multiwinner voting system". Retrieved 4 April 2016. 
  67. ^ Smith, Warren (8 Mar 2005). ""Asset voting" scheme for multiwinner elections" (PDF). Retrieved 4 April 2016. 
  68. ^ a b Smith, Warren (8 Mar 2005). "Comparative survey of multiwinner election methods" (PDF). Retrieved 4 April 2016. 
  69. ^ Smith, Warren (6 Aug 2005). "Reweighted range voting – new multiwinner voting method" (PDF). Retrieved 4 April 2016. 
  70. ^ Kok, Jan; Smith, Warren. "Reweighted Range Voting – a Proportional Representation voting method that feels like range voting". Retrieved 4 April 2016. 
  71. ^ Ryan, Ivan. "Reweighted Range Voting – a Proportional Representation voting method that feels like range voting". Retrieved 4 April 2016. 
  73. ^ "Rule Twenty-Two: Special Rules for the Visual Effects Award". Retrieved 4 April 2016. 
  74. ^ ACE Project Electoral Knowledge Network. "Mixed Systems". Retrieved 29 June 2016. 
  75. ^ "Additional-member system: Politics". Encyclopædia Britannica. Retrieved 24 Mar 2016. 
  76. ^ "Electoral Reform and Voting Systems". 
  77. ^ "Mixed Member Proportional (MMP) System" (PDF). 
  78. ^ Amy, Douglas J. "How Proportional Representation Elections Work". Mount Holyoke College. Retrieved 9 April 2014. 
  79. ^ "MMP Voting System". Wellington: Electoral Commission New Zealand. 2011. Retrieved 10 Aug 2014. 
  80. ^ "Deutschland hat ein neues Wahlrecht" (in German). Zeit Online. 22 February 2013. 
  81. ^ "Report of the Electoral Commission on the Review of the MMP Voting System". Wellington: Electoral Commission New Zealand. 2011. Retrieved 10 Aug 2014. 
  82. ^ a b 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. 
  83. ^ 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. 
  84. ^ Sean Graham (April 4, 2016). "Dual-Member Mixed Proportional: A New Electoral System for Canada" (PDF). 
  85. ^ Antony Hodgson (Jan 21, 2016). "Why a referendum on electoral reform would be undemocratic". The Tyee. 
  86. ^ PEI Special Committee on Democratic Renewal (April 15, 2016). "Recommendations in Response to the White Paper on Democratic Renewal - A Plebiscite Question" (PDF). 
  87. ^ Kerry Campbell (April 15, 2016). "P.E.I. electoral reform committee proposes ranked ballot". CBC News. 
  88. ^ Teresa Wright (April 15, 2016). "Electoral reform plebiscite question will be a multi-option ballot". The Guardian. 
  89. ^ Mitch McDonald (May 2, 2016). "Islanders can help change electoral system, says May". Journal Pioneer. 
  90. ^ Adams, John (1776). "Thoughts on Government". The Adams Papers Digital Edition. Massachusetts Historical Society. Retrieved 26 July 2014. 
  91. ^ a b c d e Hoag, Clarence; Hallett, George (1926). Proportional Representation. New York: The Macmillan Company. 
  92. ^ Madison, James. "Notes of Debates in the Federal Convention of 1787, Wednesday, June 6". Retrieved 5 August 2014. 
  93. ^ 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. 
  94. ^ "Constitution of the Commonwealth of Pennsylvania – 1790, art.I,§ VII, Of districts for electing Senators". Duquesne University. Retrieved 9 December 2014. 
  95. ^ Hirczy de Miño, Wolfgang (1997). "Malta: Single-Transferable Vote with Some Twists". ACE Electoral Knowledge Network. Retrieved 5 Dec 2014. 
  96. ^ "Adoption of Plan E". Welcome to the City of Cambridge. City of Cambridge, MA. Retrieved 25 November 2014. 
  97. ^ "Proportional Representation in Most Robust Democracies". Fair Vote: The Center for Voting And Democracy. Retrieved 22 January 2015. 
  98. ^ Jansen, Harold John (1998). "The Single Transferable Vote in Alberta and Manitoba" (PDF). Library and Archives Canada. University of Alberta. Retrieved 23 March 2015. 
  99. ^

Further reading[edit]


  • 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. 


External links[edit]