Editing Proportional representation (section)

==== 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>