Proportional representation: Difference between revisions

'''Proportional[[Voting Representation'''theorists]] ('''PR''')frequently isdebate which systems can be called "proportional representation", and consider the levels of proportionality achieved by various systems from "low proportional" to "high proportional". The concept of "proportional representation" can be quantified as a measure of the outcome of an election where there are multiple parties and multiple members are elected, and the representatives are demographically similar to the voting population. It is one of many [[types of representation]] in a [[W:Representative government|representative government]].

: <math>\mathrm{LSq} = \sqrt{ \frac{1}{2} \sum_{i=1}^n ( V_i-S_i ) ^2}</math>&nbsp;&nbsp;{{sfn|Gallagher|1991|p=40}}

=== [[Proportionality for Solid Coalitions]] Criterion ===

Whenever more than a [[Hare Quota]] of the voters gives max support to a single candidate and min support to every other candidate, that candidate is guaranteed to win regardless of how any of the other voters vote. This is explicitly formalized for approval ballots as [[Justified_representation#Proportional_justified_representation | Proportional justified representation ]].

There is an intermediate system in Uruguay ("[[Wikipedia:Ley de Lemas|intermediateLey systemde Lemas]] 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.<ref>{{citationCite neededjournal|last=Taylor|first=Phillip B.|date=May1955-02-01|title=The 2015Electoral System in Uruguay|url=https://www.journals.uchicago.edu/doi/10.2307/2126402|journal=The Journal of Politics|volume=17|issue=1|pages=19–42|doi=10.2307/2126402|issn=0022-3816}}</ref>

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|date=May 2015}}

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.<ref name=DMstvPdf>{{cite web|last1=Mollison|first1=Denis|title=Fair votes in practice STV for Westminster|url=http://www.macs.hw.ac.uk/~denis/signif.pdf|publisher=[[Heriot Watt University]]|access-date=3 June 2014}}</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|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.<ref name=tidemanSTV/> 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,<ref name=forder/>{{rp|50}} and STV has, for this reason, sometimes been labelled "quasi proportional".<ref name=AusOVC/>{{rp|83}} While this may be true when considering districts in isolation, results {{em|overall}} are proportional. In Ireland, with particularly small magnitudes, results are "highly proportional".<ref name=ideaEsd/>{{rp|73}}<ref name=ideaGallagher/> In the [[Wikipedia:1997 Irish general election|1997 Irish general election]], 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.<ref name=laver/> STV has also been described as the {{em|most}} proportional system.<ref name=AusOVC/>{{rp|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.<ref>{{Cite news |title=Referendum 2011: A look at the STV system |url=http://www.nzherald.co.nz/nz/news/article.cfm?c_id=1&objectid=10762976 |publisher=The New Zealand Herald |date=1 Nov 2011 |access-date=21 Nov 2014 |location=Auckland|work=[[The New Zealand Herald]] }}</ref><ref>{{cite magazine |title=Change the Way We Elect? Round Two of the Debate |url=https://thetyee.ca/Views/2009/04/30/STV2/ |magazine=The Tyee |date=30 Apr 2009 |access-date=21 Nov 2014 |location=Vancouver}}</ref> Conversely, widely respected candidates can win election with relatively few first preferences by benefitting from strong subordinate preference support.<ref name=DMstvPdf/>

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 [[Wikipedia:Australian Senate|Australian Senate]], most state upper houses, the [[Tasmania|Tasmanian]] lower house and the Capital Territory assembly. 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<ref name=prsaHC/> – 95% and more of voters use the above-the-line option, making the system, in all but name, a party list system.<ref name=uwaAbove>{{cite web|title=Above the line voting |url=http://elections.uwa.edu.au/glossaryc.lasso?CondensedGlossary=abovethelinevoting |publisher=University of Western Australia |access-date=21 Nov 2014|location=Perth}}</ref><ref name=abcGlossaryGVT>{{cite web |title=Glossary of Election Terms |url=http://www.abc.net.au/elections/federal/2010/guide/glossary.htm#group_voting_ticket |publisher=Australian Broadcasting Corporation|access-date=21 Nov 2014|location=Sydney}}</ref><ref>{{cite journal |last1=Hill|first1=I.D.|date=November 2000 |title=How to ruin STV |journal=Voting Matters |issue=12 |url = http://www.votingmatters.org.uk/ISSUE12/P7.htm |access-date=10 August 2013}}</ref> 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.<ref name=anthonyGreen04>{{cite web|last=Green|first=Anthony|title=Above or below the line? Managing preference votes|url=http://www.onlineopinion.com.au/view.asp?article=3359&page=0 |publisher=On Line Opinion|date=20 April 2005|access-date=21 Nov 2014 |location=Australia}}</ref><ref name=ersDog>{{cite web|last=Terry|first=Chris|title=Serving up a dog's breakfast|url=http://devers2.speedster-it.com/blog/serving-up-a-dogs-breakfast|publisher=[[Electoral Reform Society]]|date=5 April 2012|access-date=21 Nov 2014|location=London|archive-url=https://web.archive.org/web/20171007220903/http://devers2.speedster-it.com/blog/serving-up-a-dogs-breakfast|archive-date=7 October 2017|url-status=dead}}</ref> 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".<ref name=AusOVC>{{cite book|title=The Australian Electoral System: Origins, Variations, and Consequences |date=2006|publisher=[[UNSW Press]] |location=Sydney |isbn=978-0868408583 |author=David M. Farrell |author2=Ian McAllister}}</ref>{{rp|86}}

As a result of a parliamentary commission investigating the 2013 election, from 2016 the system has been considerably reformed (see [[Wikipedia:2016 Australian federal election|2016 Australian federal election]]), with group voting tickets (GVTs) abolished and voters no longer required to fill all boxes.

A mixed compensatory system is an electoral system that is [[mixed electoral system|mixed]], meaning that it combines 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> and that uses 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}}</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=May 13, 2010|publisher=Palgrave Macmillan|isbn=9780230281424}}</ref> 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. The most prominent mixed compensatory system is [[mixed member proportional representation]] (MMP), used in Germany since 1949. In MMP, the seats won by plurality are associated with single-member districts.

In asset voting,<ref name=smithMultisurv/><ref name=smithAssetMultiwin>{{cite web|last=Smith|first=Warren|title="Asset voting" scheme for multiwinner elections|url=http://rangevoting.org/WarrenSmithPages/homepage/multiwin.pdf|date=8 March 2005}}</ref> the voters vote for candidates and then the candidates negotiate amongst each other and reallocate votes amongst themselves. Asset voting was proposed by [[Lewis Carroll]] in 1884<ref>{{cite web |url=https://archive.org/details/ThePrinciplesOfParliamentaryRepresentation |title=The Principles of Parliamentary Representation |last=Dodgson |first=Charles |date=1884 |publisher=London: Harrison and Sons |access-date=28 June 2019 |quote=The Elector must understand that, in giving his vote to ''A'', he gives it to him as his absolute property, to use for himself, or to transfer to other Candidates, or to leave unused.}}</ref> and has been more recently independently rediscovered and extended by [[Warren D. Smith]] and [[Forest Simmons]].<ref name=smithAssetWeb>{{cite web|last=Smith|first=Warren|title=Asset voting – an interesting and very simple multiwinner voting system|url=http://rangevoting.org/Asset.html|access-date=4 April 2016}}</ref> As such, this method substitutes candidates' collective preferences for those of the voters.

Similar to [[Majority Judgment]] voting that elects single winners, Evaluative Proportional Representation (EPR) elects all the members of a legislative body. Both systems remove the qualitative wasting of votes.<ref>{{cite book|author= M. Balinski & R. Laraki|year=2010|title=Majority Judgment. |publisher=MIT |isbn=978-0-262-01513-4}}</ref> Each citizen grades the fitness for office of as many of the candidates as they wish as either Excellent (ideal), Very Good, Good, Acceptable, Poor, or Reject (entirely unsuitable). Multiple candidates may be given the same grade by a voter. Using EPR, each citizen elects their representative at-large for a city council. For a large and diverse state legislature, each citizen chooses to vote through any of the districts or official electoral associations in the country. Each voter grades any number of candidates in the whole country. Each elected representative has a different voting power (a different number of weighted votes) in the legislative body. This number is equal to the total number of votes given exclusively to each member from all citizens. Each member's weighted vote results from receiving one of the following from each voter: their highest grade, highest remaining grade, or proxy vote. No citizen's vote is "[[wasted vote|wasted]]"<ref>{{cite journal |first1=Stephen |last1=Bosworth |first2=AnderAnders |last2=Corr |first3=Stevan |last3=Leonard |name-list-style=amp |title=Legislatures Elected by Evaluative Proportional Representation (EPR): an Algorithm |url=http://www.jpolrisk.com/legislatures-elected-by-evaluative-proportional-representation-epr-an-algorithm-v2/|journal=Journal of Political Risk |volume=7 |number=8 |date=July 8, 2019 |access-date=August 19, 2019}}</ref> Unlike all the other proportional representation systems, each EPR voter, and each self-identifying minority or majority is quantitatively represented with exact proportionality. Also, like Majority Judgment, EPR reduces by almost half both the incentives and possibilities for voters to use Tactical Voting. {{See also|Tactical voting#Majority judgment}}

SystemsA designedfew tocities havein highthe levelsUnited ofStates Proportionaluse representationSTV, doincluding havePortland, someOR, historyAlbany, inCA, thePalm UnitedDesert, StatesCA, Cambridge, MA, and [https://fairvote.org/our-reforms/proportional-ranked-choice-voting-information/ a couple of others]. Many cities in the past, including New York, oncealso had used such systems for their city councils as a way to break up the Democratic Party monopolies on elective office. In Cincinnati, Ohio, a system was adopted in 1925 to get rid of Republican party dominance but was successfully overturned in 1957.

Many of the properties of these systems can be derived from their party list simplifications. The [[Balinski–Young theorem]] implies that not all desirable properties are possible in the same system. Theile type systems reduce to [[Highest averages method|divisor methods]] which means that adding voters or winners will not change results in undesirable ways. The other three reduce to [[Largest remainder methods]] which obey Quota Rules but adding voters or winners may change outcomes in undesirable ways. One such way is failure of [[Participation criterion]]. It is not clear which is a fundamentally better choice since Quota Rules are inanimatelyintimately tied with some definitions of proportionality.

Some common criticisms of [[STV]] (which would likely hold for many other nonpartisan PR methods) are that it is too complex in terms of filling out the ballot and tabulation, that it takes too long to count compared to partisan PR methods (many of which are [[Precinctprecinct-summable]] due to being based on [[FPTP]]), and that it can even make representatives parochialist and focused on representing their multi-member districts rather than the state or nation as a whole. Note that this last criticism is inapplicable when nonpartisan PR methods are proposed for a single national/statewide district, though this is usually not proposed or done (with the exception of some 21-seaters in Australia).

Due to the ambiguity and difficulty in the definition of Proportional Representation academic work often uses another more robust metric. This is the concept of a [[Stable Winner Set]]. The requirement that a system always produces a stable winner set when there exists one is definable in all possible systems. This makes it more useful than the concept of Proportional Representation which is typically tied to Partisan voting and as such cannot be defined for all systems. This concept evolved out of the economics field of Participatory[[participatory Budgeting but can be equally suitable in Social Choice Theorybudgeting]]. A less strict and more practicalweaker version of this is given by [[Justifiedjustified representation]].

Almost all sequential PR methods can have a single-winner method done to elect the final seat; this is because at that point there is only one seat left to elect. See [[Single transferable vote#Deciding the election of the final seat]] for an example. [[Condorcet methods]] and [[STAR voting]] can be made to work with PR methods in this way.

** [https://www.fairvote.org/proportional_representation_libraryarchives/proportional-representation-library/ FairVote]