Editing Proportional representation (section)

==== 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>