Editing Proportional representation (section)

==PR electoral systems==

=== Party-based systems ===

==== Party list PR ====
{{Main|Party-list proportional representation}}

Party list proportional representation is an electoral system in which seats are first allocated to parties based on vote share, and then assigned to party-affiliated candidates on the parties' [[electoral list]]s. This system is used in many countries, including [[Finland]] (open list), [[Latvia]] (open list), [[Sweden]] (open list), [[Israel]] (national closed list), [[Brazil]] (open list), [[Kazakhstan]] (closed list), [[Nepal]] (closed list) as 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 of the European Union|member states]] use open lists; but most large EU countries use closed lists, so that the majority of EP seats are distributed by those.<ref>As counted from the table in {{cite web |url=http://www.wahlrecht.de/ausland/europa.htm |title=Wahlsysteme in den EU-Mitgliedstaaten |language=de |website=Europawahlrecht |access-date=May 5, 2025}}</ref> Local lists were used to elect the [[Italian Senate]] during the second half of the 20th century. Some common types of electoral lists are:

* [[Closed list]] systems, where 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.<ref>{{cite web |title=Party List PR |url=http://www.electoral-reform.org.uk/party-list |publisher=Electoral Reform Society |access-date=23 May 2016}}</ref><ref>{{cite book |title=Fixing Canadian Democracy |first=Gordon |last=Gibson |url=https://books.google.com/books?id=y7hFz5GawkcC&q=closed+list+PR&pg=PA58 |publisher=The Fraser Institute |page=76 |date=2003 |isbn=9780889752016}}</ref> A party is allocated seats in proportion to the number of votes it receives.<ref>{{cite book |last1=Gallagher |first1=Michael |last2=Mitchell |first2=Paul |date=2005 |title=The Politics of Electoral Systems |location=Oxford, New York |publisher=Oxford University Press |page=11 |isbn=978-0-19-925756-0}}</ref>
* [[Ley de Lemas]], an intermediate system used in 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|date=May 2015}}
* [[Open list]] systems, where voters may vote, depending on the model, for one person, or for two or more, or vote for a party list but 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 each list is determined by the number of votes that the list receives or that the candidates on the list receive.<ref name="auto3">{{cite journal |first=Michal |last=Smrek |title=Mavericks or Loyalists? Popular Ballot Jumpers and Party Discipline in the Flexible-List PR Context |journal=[[Political Research Quarterly]]  |date=2023 |volume=76 |issue=1 |pages=323–336 |doi=10.1177/10659129221087961 }}</ref>
* [[Localized list]] systems, where 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 a [[FPTP]] system.
* Two-tier party list systems, as in Denmark, Norway, and Sweden. These operate similarly to [[Mixed-member proportional representation|mixed-member proportional]] systems or additional member systems. For example, [[Folketing#Constitutional requirements|Denmark]] 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. It is cast for an individual candidate or for a party list on the district ballot. To determine district winners, parties are allocated district seats based on their district vote shares. Candidates in the district are apportioned their share of their party's district list vote plus their individual votes, and the most-popular are elected to fill their party's seats. 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.<ref name="denmark">{{cite web |title=The Parliamentary Electoral System in Denmark |url=http://www.thedanishparliament.dk/Publications/The%20Parliamentary%20Electoral%20System%20in%20DK.aspx |publisher=Ministry of the Interior and Health |location=Copenhagen |access-date=1 September 2014 |date=2011 |archive-date=23 November 2017 |archive-url=https://web.archive.org/web/20171123004726/http://www.thedanishparliament.dk/Publications/The%20Parliamentary%20Electoral%20System%20in%20DK.aspx}}</ref><ref>{{cite web |title=The main features of the Norwegian electoral system |url=http://www.regjeringen.no/en/dep/kmd/information-campaigns/election_portal/the-electoral-system/the-norwegian-electoral-system.html?id=456636 |publisher=Ministry of Local Government and Modernisation |location=Oslo |access-date=1 September 2014 |date=6 July 2017}}</ref><ref>{{cite web |title=The Swedish electoral system |url=http://www.val.se/sprak/engelska/general_information/index.html |publisher=Election Authority |location=Stockholm |access-date=1 September 2014 |date=2011 |archive-url=https://web.archive.org/web/20140818233057/http://www.val.se/sprak/engelska/general_information/index.html |archive-date=18 August 2014}}</ref>

==== Mixed systems ====
There are [[mixed electoral system]]s combining a plurality/majority formula with a proportional formula<ref name="ACEMixSys">{{cite web |last1=ACE Project Electoral Knowledge Network |title=Mixed Systems |url=https://aceproject.org/ace-en/topics/es/esd/esd03/default |access-date=29 June 2016}}</ref> or using the proportional component to compensate for disproportionality caused by the plurality/majority component.<ref name="MassicotteSearch">{{cite report |first1=Louis |last1=Massicotte |title=In Search of Compensatory Mixed Electoral System for Québec |url=https://www.institutions-democratiques.gouv.qc.ca/publications/mode_scrutin_rapport_en.pdf |date=2004 |access-date=29 December 2023 |archive-date=24 December 2019 |archive-url=https://web.archive.org/web/20191224070656/https://www.institutions-democratiques.gouv.qc.ca/publications/mode_scrutin_rapport_en.pdf}}</ref><ref name="BochslerTerritory">{{cite book |first1=Daniel |last1=Bochsler |title=Territory and Electoral Rules in Post-Communist Democracies |chapter=Chapter 5, How Party Systems Develop in Mixed Electoral Systems |chapter-url=https://books.google.com/books?id=qkCBDAAAQBAJ |date=13 May 2010 |publisher=Palgrave Macmillan |isbn=9780230281424}}</ref>

The most prominent mixed compensatory system is [[mixed-member proportional representation]] (MMP). It combines a single-district vote, usually [[First-past-the-post voting|first-past-the-post]], with a compensatory regional or nationwide party list proportional vote. For example, suppose that a party wins 10 seats based on [[plurality voting|plurality]], but requires 15 seats in total to obtain its proportional share of an elected body. A fully proportional mixed compensatory system would award this party 5 compensatory (PR) seats, raising the party's seat count from 10 to 15. MMP has the potential to produce proportional or moderately proportional election outcomes, depending on a number of factors such as the ratio of FPTP seats to PR seats, the existence or nonexistence of extra compensatory seats to make up for [[overhang seat]]s, and electoral thresholds.<ref name="IfesElecSys">{{cite web |title=Electoral Systems and the Delimitation of Constituencies |url=http://www.ifes.org/publications/electoral-systems-and-delimitation-constituencies |date=2 July 2009 |publisher=[[International Foundation for Electoral Systems]]}}</ref><ref name="MoserMixedElec">{{cite journal |title=Mixed electoral systems and electoral system effects: controlled comparison and cross-national analysis |date=December 2004 |volume=23 |issue=4 |pages=575–599 |last1=Moser |first1=Robert G. |doi=10.1016/S0261-3794(03)00056-8 |journal=Electoral Studies}}</ref><ref name="MassicotteMixedElecSys">{{cite journal |title=Mixed electoral systems: a conceptual and empirical survey |date=September 1999 |volume=18 |issue=3 |pages=341–366 |last1=Massicotte |first1=Louis |doi=10.1016/S0261-3794(98)00063-8 |journal=Electoral Studies}}</ref> It was invented for the German [[Bundestag]] after the Second World War, and has spread to [[Lesotho]], [[Bolivia]], [[New Zealand]] and [[Thailand]]. The system is also used for the [[Scottish Parliament]] where it is called the [[additional member system]].<ref name="ersAMS">{{cite web |title=Additional Member System |url=http://www.electoral-reform.org.uk/additional-member-system |access-date=16 October 2015 |publisher=[[Electoral Reform Society]] |location=London}}</ref>

Voters typically have two votes, one for their district representative and one for the party list. The list vote usually determines how many seats are allocated to each party 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 the party's overall list vote. Before apportioning list seats, all list votes for parties which failed to reach the threshold are discarded. If eliminated parties lose seats in this manner, then the seat counts for parties that achieved the threshold improve. Any direct seats won by independent candidates are subtracted from the parliamentary total used to apportion list seats.<ref>{{cite web |title=MMP Voting System |url=http://www.elections.org.nz/voting-system/mmp-voting-system |publisher=[[Electoral Commission (New Zealand)|Electoral Commission New Zealand]] |location=Wellington |access-date=10 August 2014 |date=2011}}</ref>

Proportionality of MMP can be compromised if the ratio of list to district seats is too low, as it may then not be possible to completely compensate district seat disproportionality. 

Another factor can be how [[overhang seat]]s 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.<ref>{{cite news |title=Deutschland hat ein neues Wahlrecht |url=http://www.zeit.de/politik/deutschland/2013-02/bundestag-wahlrecht-beschluss |publisher=[[Zeit Online]] |language=de |date=22 February 2013}}</ref> Lesotho, Scotland and Wales do not increase the size of parliament at all, even if there are overhang seats. In 2012, a New Zealand parliamentary commission proposed abandoning compensation for overhang seats, and so fixing the size of parliament. At the same time, it proposed abolishing the single-seat threshold (the go-around past the electoral threshold used by some small parties to get their due share of seats). It was expected that such seats would be overhang seats. If that was done without abolishing overhang compensation, it would have increased the size of parliament further through the overhang compensation. The commission also proposed reducing the electoral threshold from 5 percent to 4 percent. It was expected that proportionality would not suffer from these changes.<ref name="ideaEsd" /><ref name="NZ2012EC">{{cite web |title=Report of the Electoral Commission on the Review of the MMP Voting System |url=http://www.elections.org.nz/events/past-events-0/2012-mmp-review/results-mmp-review |publisher=[[Electoral Commission (New Zealand)|Electoral Commission New Zealand]] |location=Wellington |access-date=10 August 2014 |date=2011 |archive-url=https://web.archive.org/web/20140707151142/http://www.elections.org.nz/events/past-events-0/2012-mmp-review/results-mmp-review |archive-date=7 July 2014}}</ref>

Similarly to MMP, [[Mixed single vote|mixed single vote systems]] (MSV) use a proportional formula for allocating seats on the compensatory tier, but voters only have one vote that functions on both levels. MSV may use a positive vote transfer system, where unused votes are transferred from the lower tier to the upper, compensatory tier, where only these are used in the proportional formula. Alternatively, the MMP (seat linkage) algorithm can be used with a mixed single vote to "top-up" to a proportional result. With MSV, the similar requirements as in MMP apply to guarantee an overall proportional result.

[[Parallel voting]] (MMM) systems use proportional formulas to allocate seats on a proportional tier separately from other tiers. Certain systems, like [[scorporo]] use a proportional formula after combining results of a parallel list vote with transferred votes from lower tiers (using negative or positive vote transfer).

Another mixed system is [[dual-member proportional representation]] (DMP). It is a single-vote system that elects two representatives in every district.<ref>{{Cite thesis |last=Graham |first=Sean |date=2016 |title=Dual-Member Mixed Proportional: A New Electoral System for Canada |publisher=University of Alberta |url=https://era.library.ualberta.ca/items/e3ab993a-d264-4d30-b819-290ab5fd6b62 |access-date=10 August 2022 |doi=10.7939/R3-QPPP-B676}}</ref> 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|FPTP 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 [[mixed-member proportional representation|MMP]] used in the German state of [[Baden-Württemberg]].<ref>{{cite news |first=Antony |last=Hodgson |title=Why a referendum on electoral reform would be undemocratic |url=https://thetyee.ca/Opinion/2016/01/21/Why-Referendum-on-Electoral-Reform-Undemocratic/ |work=[[The Tyee]] |date=21 January 2016}}</ref> 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 [[Single transferable vote|STV]] in that all elected representatives, including those who receive compensatory seats, serve their local districts. Invented in 2013 in the [[Provinces and Territories of Canada|Canadian province]] of [[Alberta]], DMP received attention on [[Prince Edward Island]] where it appeared on a [[2016 Prince Edward Island electoral reform referendum|2016 plebiscite]] as a potential replacement for FPTP,<ref>{{cite news |first=Kerry |last=Campbell |title=P.E.I. electoral reform committee proposes ranked ballot |url=http://www.cbc.ca/news/canada/prince-edward-island/pei-electoral-reform-1.3537355 |work=[[CBC News]] |date=15 April 2016}}</ref> but was eliminated on the third round.<ref>{{cite web |author=Elections PEI |title=Plebiscite Results |url=http://www.electionspei.ca/plebisciteresults |date=7 November 2016 |access-date=26 October 2017 |archive-url=https://web.archive.org/web/20161108134958/http://www.electionspei.ca/plebisciteresults |archive-date=8 November 2016}}</ref><ref>{{cite news |first=Susan |last=Bradley |title=P.E.I. plebiscite favours mixed member proportional representation |url=http://www.cbc.ca/news/canada/prince-edward-island/mixed-member-proportional-representation-in-plebiscite-1.3840172 |work=[[CBC News]] |date=7 November 2016}}</ref> It was also one of three proportional voting system options on a [[2018 British Columbia electoral reform referendum|2018 referendum]] in [[British Columbia]].<ref>{{cite web |first=David |last=Eby |title=How We Vote: 2018 Electoral Reform Referendum Report and Recommendations of the Attorney General |url=https://engage.gov.bc.ca/app/uploads/sites/271/2018/05/How-We-Vote-2018-Electoral-Reform-Referendum-Report-and-Recommendations-of-the-Attorney-General.pdf |date=30 May 2018 |access-date=9 June 2018 |archive-url=https://web.archive.org/web/20180831060310/https://engage.gov.bc.ca/app/uploads/sites/271/2018/05/How-We-Vote-2018-Electoral-Reform-Referendum-Report-and-Recommendations-of-the-Attorney-General.pdf |archive-date=31 August 2018}}</ref><ref>{{cite news |first=Justin |last=McElroy |title=Know your voting systems: three types of electoral reform on B.C.'s ballot |url=http://www.cbc.ca/news/canada/british-columbia/pr-electoral-reform-questions-1.4688604?cmp=rss |work=[[CBC News]] |date=2 June 2018}}</ref><ref>{{cite web |publisher=[[Elections BC]] |title=2018 Referendum on Electoral Reform: Voting Results Available |date=20 December 2018 |url=https://elections.bc.ca/news/2018-referendum-on-electoral-reform-voting-results-available/ |access-date=1 November 2020}}</ref>

==== Biproportional apportionment ====
{{Main|Biproportional apportionment}}

Biproportional [[apportionment (politics)|apportionment]] aims to achieve proportionality in two dimensions, for example: proportionality by region and proportionality by party. There are several mathematical methods to attain biproportionality.

One method is called [[iterative proportional fitting]] (IPF). It was proposed for elections by the mathematician [[Michel Balinski]] in 1989, and first used by the city of [[Zürich]] for its council elections in February 2006, in a modified form called "new Zürich apportionment" (''Neue Zürcher Zuteilungsverfahren''). Zürich had had to modify its party list PR system after the Swiss Federal Court ruled that its smallest [[Ward (electoral subdivision)|wards]], as a result of population changes over many years, unconstitutionally disadvantaged smaller political parties. With biproportional apportionment, the use of open party lists has not 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 Zürich 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 of Switzerland|cantons]].<ref name="pukZna">{{Cite journal |last=Pukelsheim |first=Friedrich |date=September 2009 |title=Zurich's New Apportionment |url=http://www.uni-augsburg.de/pukelsheim/2008e-en.pdf |journal=German Research |volume=31 |issue=2 |pages=10–12 |doi=10.1002/germ.200990024 |access-date=10 August 2014 |ref=ZurichNA}}</ref><ref name="balinskiFMV">{{Cite journal |last=Balinski |first=Michel |author-link=Michel Balinski |date=February 2008 |title=Fair Majority Voting (or How to Eliminate Gerrymandering) |url=http://www.maa.org/programs/maa-awards/writing-awards/fair-majority-voting-or-how-to-eliminate-gerrymandering |journal=The American Mathematical Monthly |volume=115 |issue=2 |pages=97–113 |doi=10.1080/00029890.2008.11920503 |access-date=10 August 2014 |ref=FMV |s2cid=1139441}}</ref>

Balinski has proposed another variant called [[fair majority voting]] (FMV) to replace single-winner plurality/majoritarian electoral systems, in particular the system used for the [[US House of Representatives]]. FMV introduces proportionality without changing the method of voting, the number of seats, or the{{snd}}possibly gerrymandered{{snd}}district boundaries. Seats would be apportioned to parties in a proportional manner at the [[U.S. state|state]] level.<ref name="balinskiFMV" /> In a related 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{{snd}} unlikely to be acceptable to the electorate, the authors concede{{snd}} but this effect could be substantially reduced by incorporating a third, regional, apportionment tier, or by specifying minimum thresholds.<ref>{{Cite journal |last1=Akartunalı |first1=Kerem |last2=Knight |first2=Philip A. |date=June 2017 |title=Network models and biproportional rounding for fair seat allocations in the UK elections |journal=Annals of Operations Research |publisher=[[University of Strathclyde]] |volume=253 |issue=1 |pages=1–19 |doi=10.1007/s10479-016-2323-0 |s2cid=30623821 |issn=0254-5330 |doi-access=free }}</ref>

=== Candidate-based systems ===

==== Single transferable vote ====
{{Main|Single transferable vote}}

The single transferable vote (STV), also called [[Ranked voting|ranked choice voting]], is a [[ranked voting|ranked system]]: voters rank candidates in order of preference. Voting districts usually elect three to seven representatives; each voter casts just one vote. The count is cyclic, electing or eliminating candidates and transferring votes until all seats are filled. A candidate whose tally reaches a [[Droop quota|quota]], the minimum vote that guarantees election, is declared elected. 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 voters' preferences. If there are no surplus votes to transfer and there are still seats to fill, the least popular candidate is eliminated, those votes being transferred to their next preference at full value. The votes are transferred according to the next marked preference. Any votes that cannot be transferred are moved to a pile labelled exhausted or non-transferable.{{Citation needed|date=May 2025}}

The count continues until all the seats are filled or until there is only one more candidate than the number of remaining open seats. At that point all of them except the least popular candidate are declared elected, even if they do not have quota.

The transfer of votes of eliminated candidates is simple{{snd}}the transfer of surplus votes is more involved. There are various methods for transferring surplus votes.

Manual methods used in early times and still today in places where STV was adopted in early 20th century (Ireland and Malta) transfer surplus votes according to a randomly selected sample, or transfer only a segment of the votes held by the successful candidate as surplus, selected based on the next usable marked preference.

Other more recent methods transfer all votes held by successful candidate at a fraction of their value (the fraction derived by the surplus divided by the candidate's tally) and with reference to all the marked preferences on the ballots, not just the next usable preference. They may need the use of a computer.

The different methods may not produce the same result in all respects. But the front runners in the first count before any transfers are conducted are all or mostly elected in the end under any STV variant, so the various methods of transfers all produce much the same result.

Some variants of STV allow transfers to already elected or eliminated candidates, and these, too, can require a computer.<ref name="tidemanSTV">{{cite journal |last1=Tideman |first1=Nicolaus |author-link=Nicolaus Tideman |date=1995 |title=The Single Transferable Vote |journal=Journal of Economic Perspectives |volume=9 |issue=1 |pages=27–38 |doi=10.1257/jep.9.1.27 |doi-access=free}}</ref><ref>{{cite journal |last1=O’Neill |first1=Jeffrey C. |date=July 2006 |title=Comments on the STV Rules Proposed by British Columbia |url=http://www.votingmatters.org.uk/ISSUE22/INDEX.HTM |journal=Voting Matters |issue=22 |access-date=10 August 2013}}</ref>

In effect, the method produces groups of voters of much the same size so the overall effect is to reflect the diversity of the electorate, each substantial group electing one or more representatives that the group had voted for.

In Cambridge, under STV, 90 percent of voters see their vote help to elect a candidate, more than 65 percent of voters see their first choice candidate elected, and more than 95 percent of voters see one of their top three choices win.<ref>[http://www.nationalcivicleague.org/wp-content/uploads/2021/12/Model-City-Charter%E2%80%949th-Edition.pdf Model City Charter] National Civic League. 9th edition. 2021</ref>

Other reports claim that 90 percent 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.<ref name="DMstvPdf" /> Another source states that, when STV was used between 1925 and 1955 in Cincinnati, 90 percent of voters saw their first choice elected or their vote used to elect a secondary preference, with about 60 to 74 percent of voters seeing their first choice elected, even if their vote was not used to elect that person because it was transferred on as a surplus vote.<ref>{{Cite book |last=Barber |title=Proportional Representation and Electoral Reform in Ohio |pages=191}}</ref>

Political parties are not necessary; all other prominent PR electoral systems presume that parties reflect voters wishes, which many believe gives power to parties.<ref name="tidemanSTV" /> STV satisfies the [[Comparison of electoral systems|electoral system criterion]] ''[[proportionality for solid coalitions]]''{{snd}} a solid coalition for a set of candidates is the group of voters that rank all those candidates above all others{{snd}} and is therefore considered a system of proportional representation.<ref name="tidemanSTV" />

However, the small district magnitude used in STV elections (usually 5 to 9 seats, but sometimes rising to 21) has been criticized as impairing proportionality, especially when more parties compete than there are seats available,<ref name="forder" />{{rp|50}} and STV has, for this reason, sometimes been labelled "quasi proportional".<ref name="AusOVC">{{cite book |first1=David M. |last1=Farrell |title=The Australian Electoral System: Origins, Variations, and Consequences |first2=Ian |last2=McAllister |date=2006 |publisher=[[UNSW Press]] |isbn=978-0868408583 |location=Sydney}}</ref>{{rp|83}}

While this may be true when considering districts in isolation, results {{em|overall}} are usually more proportional.

Even though Ireland has particularly small magnitudes (3 to 5 seats), results of STV elections are "highly proportional".<ref name="ideaEsd" />{{rp|73}}<ref name="ideaGallagher" /> In [[1997 Irish general election|1997]], the average magnitude was 4. Eight parties gained representation, four of them with less than 3% of first-preference votes nationally. Six independent candidates also won election.<ref name="laver" />

There have been claims made that STV handicaps certain extreme candidates because, to gain transfers based on back-up 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.<ref>{{Cite news |date=1 November 2011 |title=Referendum 2011: A look at the STV system |work=[[The New Zealand Herald]] |publisher=The New Zealand Herald |location=Auckland |url=http://www.nzherald.co.nz/nz/news/article.cfm?c_id=1&objectid=10762976 |access-date=21 November 2014}}</ref> This argument is made from the high natural threshold STV provides with low district magnitude.<ref>{{cite magazine |date=30 April 2009 |title=Change the Way We Elect? Round Two of the Debate |url=https://thetyee.ca/Views/2009/04/30/STV2/ |magazine=The Tyee |location=Vancouver |access-date=21 November 2014}}</ref>

Conversely, widely respected candidates can win election even if they receive relatively few first preferences. They do this by benefiting from strong subordinate preference support. Of course, they must have enough initial support so that they are not in the bottom rung of popularity or they will be eliminated when the field of candidate is thinned.<ref name="DMstvPdf" />

[[Lewis Carroll|Charles Dodgson]] (Lewis Carroll), the polymath logician and author, developed a passionate interest<ref>{{citation |last=McLean |first=Iain |chapter=Voting |editor-first1=Robin |editor-last1=Wilson |editor-first2=Amirouche |editor-last2=Moktefi |title=The Mathematical World of Charles L. Dodgson (Lewis Carroll)  |publisher=Oxford |date=2019 |edition=Online Oxford Academic}}</ref> in voting methods. He believed RCV/STV to be fundamentally flawed, particularly regarding the allocation of "surplus" votes. His novel solution was to let the candidates themselves caucus and "club" votes together through the process of a negotiated consensus.<ref>{{cite web |title=Negotiated Consensus |url=https://gregblonder.medium.com/negotiated-consensus-bfde8bde5a20 |work=Medium |last=Blonder |first=Greg |date=21 October 2024 |access-date=5 May 2025}}</ref> As he stated:<ref>{{cite book |first=C. L. |last=Dodgson |author-link=Lewis Carroll |title=The Principles of Parliamentary Representation: Supplement |publisher=Oxford |date=1885 |p=7 |url=https://ia801308.us.archive.org/26/items/principlesofparl00carr/principlesofparl00carr_jpg.pdf}}</ref>

<blockquote>May I, in conclusion, point out that the method advocated in my pamphlet (where each elector names one candidate only, and the candidates themselves can, after the numbers are announced, club their votes, so as to bring in others besides those already announced as returned) would be at once perfectly simple and perfectly equitable in its result?</blockquote>

However, his entreaties to [[Robert Gascoyne-Cecil, 3rd Marquess of Salisbury|Lord Salisbury]], leader of the Conservative Party and future prime minister, to adopt "clubbing" were rejected in 1884<ref>{{cite book |last=Poundstone |first=William |title=Gaming the Vote: Why Elections Aren't Fair (and What We Can Do About It) |publisher=Hill and Wang |location=New York |date=2008 |isbn=9780809048922}}</ref> as "too sweeping a change". Subsequently, he joined with [[Thomas Hare (political reformer)|Thomas Hare]] and several Conservative and Liberal members of Parliament to found the Proportional Representation Society (later the [[Electoral Reform Society]]) and to pursue STV.

==== Proportional approval voting ====
{{Main|Proportional approval voting}}

Systems can be devised that aim at proportional representation but are based on approval votes on individual candidates (not parties). Such is the idea of [[proportional approval voting]] (PAV). It satisifes an adaptation of PR called [[extended justified representation]] (EJR).<ref>{{cite arXiv |eprint=1611.08691 |class=cs.GT |first1=Markus |last1=Brill |first2=Jean-François |last2=Laslier |title=Multiwinner Approval Rules as Apportionment Methods |last3=Skowron |first3=Piotr |year=2016}}</ref>

When there are many seats to be filled, as in a legislature, counting ballots under PAV may not be feasible, so sequential variants have been used, such as [[sequential proportional approval voting]] (SPAV). SPAV was used briefly in Sweden during the early 1900s.<ref name="AzizGaspers2014">{{cite book |last1=Aziz |first1=Haris |title=Proceedings of the 2015 International Conference on Autonomous Agents and Multiagent Systems |first2=Serge |last2=Gaspers |first3=Joachim |last3=Gudmundsson |first4=Simon |last4=Mackenzie |first5=Nicholas |last5=Mattei |first6=Toby |last6=Walsh |year=2014 |isbn=978-1-4503-3413-6 |pages=107–115 |chapter=Computational Aspects of Multi-Winner Approval Voting |arxiv=1407.3247v1}}</ref> The vote counting procedure occurs in rounds. The first round of SPAV is identical to [[approval voting]]. All ballots are added with equal weight, and the candidate with the highest overall score is elected. In all subsequent rounds, ballots that support candidates who have already been elected are added with a reduced weight. Thus, voters who support none of the winners in the early rounds are increasingly likely to elect one of their preferred candidates in a later round. The procedure has been shown to yield proportional outcomes especially when voters are loyal to distinct groups of candidates (e.g. political parties).<ref>{{Cite journal |last1=Faliszewski |first1=Piotr |last2=Skowron |first2=Piotr |last3=Szufa |first3=Stanisław |last4=Talmon |first4=Nimrod |date=8 May 2019 |title=Proportional Representation in Elections: STV vs PAV |url=https://dl.acm.org/doi/10.5555/3306127.3331972 |journal=Proceedings of the 18th International Conference on Autonomous Agents and MultiAgent Systems |series=AAMAS '19 |location=Richland, SC |publisher=International Foundation for Autonomous Agents and Multiagent Systems |pages=1946–1948 |isbn=978-1-4503-6309-9}}</ref><ref>{{Cite book |last1=Lackner |first1=Martin |last2=Skowron |first2=Piotr |title=Multi-Winner Voting with Approval Preferences |series=SpringerBriefs in Intelligent Systems |year=2023 |doi=10.1007/978-3-031-09016-5 |arxiv=2007.01795 |isbn=978-3-031-09015-8 |s2cid=244921148}}</ref>

Reweighted range voting (RRV) uses the same method as [[sequential proportional approval voting]] but uses a [[Score voting|score ballot]].{{citation needed|date=March 2024}} Reweighted range voting was used for the nominations in the Visual Effects category for recent Academy Award Oscars from 2013 through 2017,<ref name="oscars2017Rules">{{cite web |title=89th Annual Academy Awards of Merit for Achievements during 2017 |url=https://www.oscars.org/sites/oscars/files/89aa_rules.pdf |access-date=4 April 2016}}</ref><ref name="oscars2012RulesRule22">{{cite web |title=Rule Twenty-Two: Special Rules for the Visual Effects Award |url=http://www.oscars.org/awards/academyawards/rules/rule22.html |archive-url=https://web.archive.org/web/20120914153856/http://www.oscars.org/awards/academyawards/rules/rule22.html |archive-date=14 September 2012 |access-date=4 April 2016}}</ref> and is used in the city of [[Berkeley, California]], for sorting the priorities of the city council.<ref>{{Cite web |last=Sargent |first=Felix |date=19 June 2019 |title=Opinion: Berkeley's City Council's switch to 're-weighted range voting' adds fairness to the system |url=https://www.berkeleyside.org/2019/06/19/opinion-berkeleys-city-councils-switch-to-re-weighted-range-voting-adds-fairness-to-the-system |access-date=11 May 2022 |website=Berkeleyside}}</ref>