View source for Score voting

{{Short description|Single-winner rated voting system}}
{{Lead too short|date=August 2024}}{{Electoral systems sidebar|expanded=Single-winner}}
'''Score voting''', sometimes called '''range voting''', is an [[electoral system]] for single-seat elections. Voters give each candidate a numerical score, and the candidate with the highest average score is elected.<ref>{{Cite news |url = https://electology.org/score-voting |title = Score Voting |date = 2015-05-21 |newspaper = The Center for Election Science |quote = Simplified forms of score voting automatically give skipped candidates the lowest possible score for the ballot they were skipped. Other forms have those ballots not affect the candidate's rating at all. Those forms not affecting the candidates rating frequently make use of quotas. Quotas demand a minimum proportion of voters rate that candidate in some way before that candidate is eligible to win. |access-date = 2016-12-10 }}</ref> Score voting includes the well-known [[approval voting]] (used to calculate [[approval ratings]]), but also lets voters give partial (in-between) approval ratings to candidates.<ref name=":0">{{Cite journal |last1 = Baujard |first1 = Antoinette |last2 = Igersheim |first2 = Herrade |last3 = Lebon |first3 = Isabelle |last4 = Gavrel |first4 = Frédéric |last5 = Laslier |first5 = Jean-François |date = 2014-06-01 |title = Who's favored by evaluative voting? An experiment conducted during the 2012 French presidential election |url = https://halshs.archives-ouvertes.fr/halshs-01090234/file/1430.pdf |journal = Electoral Studies |volume = 34 |pages = 131–145 |doi = 10.1016/j.electstud.2013.11.003 |quote = voting rules in which the voter freely grades each candidate on a pre-defined numerical scale. .. also called utilitarian voting |access-date = 2019-12-22 |archive-date = 2021-04-10 |archive-url = https://web.archive.org/web/20210410223035/https://halshs.archives-ouvertes.fr/halshs-01090234/file/1430.pdf |url-status = dead }}</ref>

== Usage ==

=== Political use ===

==== Historical ====
A crude form of score voting was used in some elections in ancient [[Sparta]], by measuring how loudly the crowd shouted for different candidates.<ref>James S. Fishkin: The Voice of the People: Public Opinion & Democracy, Yale University Press 1995</ref><ref>{{Cite book|last1= Girard |first1=C. |chapter= Going from Theory to Practice: The Mixed Success of Approval Voting | title=Handbook on Approval Voting |pages=15–17 |url=https://archive.org/details/handbookonapprov00lasl | url-access=limited | date=2010 |publisher=Springer Berlin Heidelberg | isbn=9783642028380 | editor-last=Laslier|editor-first=Jean-François| editor-last2=Sanver | editor-first2=M. Remzi | series=Studies in Choice and Welfare|language=en|doi=10.1007/978-3-642-02839-7_3}}</ref><ref name="spartashout">{{cite news |url = https://query.nytimes.com/gst/fullpage.html?res=9406E7DB163FF931A35755C0A9679C8B63&sec=technology&spon=&pagewanted=2 |title = Adding Up the Costs of Cyberdemocracy |access-date = 2009-10-03 |newspaper = New York Times |first = Alexander |last = Stille |date = 2001-06-02 }}</ref> This has a modern-day analog of using [[Clap-o-meter|clapometers]] in some television shows and the judging processes of some athletic competitions.

Beginning in the 13th century, the [[Republic of Venice]] elected the [[Doge of Venice]] using a multi-stage process with multiple rounds of score voting. This may have contributed to the Republic's longevity, being partly responsible for its status as the longest-lived [[democracy]] in world history.<ref>{{Cite journal |last=Lines |first=Marji |year=1986 |title=Approval Voting and Strategy Analysis: A Venetian Example |journal=Theory and Decision |volume=20 |issue=2 |pages=155–172 |doi=10.1007/BF00135090 |s2cid=121512308}}</ref><ref>{{cite conference |last1=Mowbray |first1=Miranda |last2=Gollmann |first2=Dieter |date=July 2007 |title=Electing the Doge of Venice: analysis of a 13th Century protocol |url=http://www.hpl.hp.com/techreports/2007/HPL-2007-28R1.pdf |conference=IEEE Computer Security Foundations Symposium |location=Venice, Italy |archive-url=https://ghostarchive.org/archive/20221009/http://www.hpl.hp.com/techreports/2007/HPL-2007-28R1.pdf |archive-date=October 9, 2022 |url-status=live}}</ref> Score voting was used in [[Greece|Greek]] legislative elections beginning in 1864, during which time it had a [[Multi-party system|many-party system]]; it was replaced with [[party-list proportional representation]] in 1923.<ref name="mavrogordatos">{{Cite book |last=Mavrogordatos |first=George Th. |url=http://archive.org/details/bub_gb_MbSifRqxM1EC |title=Stillborn Republic: Social Coalitions and Party Strategies in Greece 1922{{endash}}1936 |date=1983 |publisher=University of California Press |pages=351–352 |language=en}}</ref>

According to Steven J. Brams, approval was used for some elections in 19th century England.<ref>{{cite speech |url=http://www.nyu.edu/gsas/dept/politics/faculty/brams/normative_turn.pdf |title=The Normative Turn in Public Choice |page=4 |date=April 1, 2006 |access-date=May 8, 2010 |first=Steven J. |last=Brams |event=Presidential Address to Public Choice Society |location=New Orleans, Louisiana |archive-url=https://web.archive.org/web/20100531093534/http://www.nyu.edu/gsas/dept/politics/faculty/brams/normative_turn.pdf |archive-date=May 31, 2010}}</ref>

==== Current ====
Score voting is used to elect candidates who represent parties in [[Latvia]]'s [[Saeima]] (parliament) in an [[open list]] system.<ref>{{Cite web |title=14. SAEIMAS VĒLĒŠANAS |url=https://sv2022.cvk.lv/pub/en/elected-deputies#deputati |access-date=2024-04-30 |website=sv2022.cvk.lv}}</ref>

The [[United Nations Secretary-General selection|selection process]] for the [[Secretary-General of the United Nations]] uses a variant on a three-point scale ("Encourage", "Discourage", and "No Opinion"), with [[permanent members of the United Nations Security Council]] holding a veto over any candidate.<ref>{{cite web |title=The "Wisnumurti Guidelines" for Selecting a Candidate for Secretary-General |url=http://www.unsgselection.org/files/WisnumurtiGuidelinesSelectingCandidateSecretary-General.pdf |url-status=dead |archive-url=https://web.archive.org/web/20080227114317/http://www.unsgselection.org/files/WisnumurtiGuidelinesSelectingCandidateSecretary-General.pdf |archive-date=February 27, 2008 |access-date=November 30, 2007}}</ref><ref>{{Cite web |last=Tharoor |first=Shashi |date=October 21, 2016 |title=The inside Story of How I Lost the Race for the UN Secretary-General's Job in 2006 |url=http://www.openthemagazine.com/article/cover-story/the-inside-story-of-how-i-lost-the-race-for-the-un-secretary-generals-job-in-2006-shashi-tharoor |archive-url=https://web.archive.org/web/20190721215655/http://www.openthemagazine.com/article/cover-story/the-inside-story-of-how-i-lost-the-race-for-the-un-secretary-generals-job-in-2006-shashi-tharoor |archive-date=July 21, 2019 |access-date=March 6, 2019 |website=OPEN Magazine |language=en}}</ref>

Proportional score voting was used in [[Swedish elections]] in the early 20th century, prior to being replaced by [[party-list proportional representation]]. It is still used for local elections.
{|class="wikitable floatright"
|+ On a score ballot, the voter scores all the candidates.
! style="background-color:#e6e6ff" | Governor<br />Candidates
! style="background-color:#e6e6ff" |
! style="background-color:#e6e6ff" | Score each candidate by filling in<br />a number (0 is worst; 9 is best)
|-
|1: Candidate A || → ||	style="font-size:17pt; font-family:Calibri" | <span style="color:#dc2300">⓿</span>①②③④⑤⑥⑦⑧⑨
|-
|2: Candidate B	|| → ||	style="font-size:17pt; font-family:Calibri" | ⓪①②③④⑤⑥⑦⑧<span style="color:#dc2300">❾</span>
|-
|3: Candidate C	|| → || style="font-size:17pt; font-family:Calibri" | ⓪①②③④⑤⑥<span style="color:#dc2300">❼</span>⑧⑨
|}

In 2018, [[Fargo, North Dakota]], passed a local ballot initiative adopting [[approval voting]] for the city's local elections, becoming the first US city to adopt the method.<ref name="Fargo approves">[https://ivn.us/2018/11/06/one-americas-famous-towns-becomes-first-nation-adopt-approval-voting/ One of America's Most Famous Towns Becomes First in the Nation to Adopt Approval Voting] {{Webarchive|url=https://web.archive.org/web/20181107185459/https://ivn.us/2018/11/06/one-americas-famous-towns-becomes-first-nation-adopt-approval-voting/|date=November 7, 2018}}, accessed November 7, 2018</ref><ref name="Fargo votes">{{cite web |last=Moen |first=Mike |date=June 10, 2020 |title=Fargo Becomes First U.S. City to Try Approval Voting |url=https://www.publicnewsservice.org/2020-06-10/civic-engagement/fargo-becomes-first-u-s-city-to-try-approval-voting/a70495-1 |access-date=December 3, 2020 |work=Public News Service}}</ref><ref name=":1">{{Cite web |last=Piper |first=Kelsey |date=November 15, 2018 |title=This city just approved a new election system never tried before in America |url=https://www.vox.com/future-perfect/2018/11/15/18092206/midterm-elections-vote-fargo-approval-voting-ranked-choice |access-date=July 8, 2020 |website=Vox |language=en}}</ref>

Score voting is used by the [[List of state Green Parties in the United States#Utah|Green Party of Utah]] to elect officers, on a 0–9 scale.<ref>{{Cite news |date=2017-06-27 |title=Utah Green Party Hosts Dr. Stein; Elects New Officers |url=http://independentpoliticalreport.com/2017/06/utah-green-party-hosts-dr-stein-elects-new-officers/ |access-date=2017-09-14 |work=Independent Political Report |language=en-US |quote=Using the following Range Voting System, the Green Party of Utah elected a new slate of officers}}</ref>

The [[Pirate Party Germany]] uses variants of score voting such as Reweighted Range Voting (RRV) in some of its internal elections.<ref>{{Cite web |title=BPT 2014.1 – Wahlverfahren |url=https://wiki.piratenpartei.de/Bundesparteitag_2014.1/WahlordnungAV |access-date=2024-02-23 |quote=§2.1 - Bewertungswahl (range voting) … §2.2 - Proportionale Bewertungswahl (reweighted range voting) … §2.3 - Bewertungswahl mit Quorum … §2.4 - Mehrheits-Benotung |trans-quote=§2.3 Score Voting with Quorum … §2.4 Majority Score Voting.}}</ref><ref>{{Cite web |title=Bundesparteitag 2014.1 – Protokoll |url=https://wiki.piratenpartei.de/Bundesparteitag_2014.1/Protokoll |access-date=2024-02-23 |quote=Das Wahlverfahren nach Wahlordnung Par. 2.1 wird beschlossen. |trans-quote=The voting method according to election rules §2.1 (Score Voting) was adopted.}}</ref> The system has been used in the [[Bavaria|Bavarian]] branch for selecting candidates for the [[State list (Germany)|Bundestag list]],<ref>{{Cite web |title=Protokoll zur Aufstellungsversammlung Landeliste Bayern zur BTW 2025 |url=https://wiki.piratenpartei.de/Datei:2024-09-08_Protokoll_AV_BY_Bundestagswahl_2025.pdf |access-date=2024-02-23 |quote=Bewertungswahl für Plätze 4-X. Bewertungszahlen von 0-10. Reihenfolge wird durch den Schnitt festgelegt. Das Quorum sind 5 im Schnitt. Wer unter 5 im Schnitt fällt wird nicht in die Liste aufgenommen. |trans-quote=Score voting for places 4-X. Scores from 0-10. The ranking is determined by the average score. The quorum is 5 on average. Candidates scoring below 5 on average are not included in the list.}}</ref> and in the [[North Rhine-Westphalia|NRW]] branch for general decision-making and internal elections.<ref>{{Cite web |title=Satzung der Piratenpartei NRW |url=https://www.piratenpartei-nrw.de/landesverband/satzung/ |access-date=2024-02-23 |quote=Gibt es mehr als eine Option bei einer Abstimmung, so wird eine verbundene Einzelwahl zusammen mit einer Bewertungswahl durchgeführt. Bei der Bewertungswahl kann jeder Option unabhängig Null bis K Punkte (Ganzzahlen) vergeben werden. |trans-quote=If there is more than one option in a vote, a combined individual vote together with a score voting system is used. In score voting, each option can independently be assigned between zero and K points (integers).}}</ref>

=== Non-political use ===

Members of [[Arbitration Committee of the English Wikipedia|Wikipedia's Arbitration Committee]] are elected based on a three-point scale ("Support", "Neutral", "Oppose").<ref>{{Diff|en:Wikipedia:Arbitration_Committee_Elections_December_2017|diff=|oldid=832933245|label=}}{{Circular reference|date=January 2025}}</ref>

Non-governmental uses of score voting are common, such as in [[Likert scale]]s for [[customer satisfaction]] surveys and mechanism involving users rating a product or service in terms of "stars" (such as rating movies on [[IMDb]], products at [[Amazon.com|Amazon]], apps in the iOS or [[Google Play]] stores, etc.). Judged sports such as [[gymnastics]] generally rate competitors on a numeric scale.

A multi-winner proportional variant called [[Thiele's voting rules|Thiele's method]] or reweighted range voting is used to select five nominees for the [[Academy Award for Best Visual Effects]] rated on a 0–10 scale.<ref>{{Cite web |url = https://www.oscars.org/sites/oscars/files/89aa_rules.pdf#page=32 |title = 89TH ANNUAL ACADEMY AWARDS OF MERIT |date = 2016 |at = RULE TWENTY-TWO SPECIAL RULES FOR THE VISUAL EFFECTS AWARD |quote = Five productions shall be selected using reweighted range voting to become the nominations for final voting for the Visual Effects award. }}</ref>

==Example==
{{Tenn voting example}}
Suppose that 100 voters each decided to grant from 0 to 10 points to each city such that their most liked choice got 10 points, and least liked choice got 0 points, with the intermediate choices getting an amount proportional to their relative distance.
<!--
Distance table from Wolfram Alpha:
            | Memphis  | Knoxville | Nashville | Chattanooga
Memphis     | 0 mi     | 345.1 mi  | 194.2 mi  | 268.1 mi
Knoxville   |          |   0   mi  | 159.5 mi  |  96.2 mi
Nashville   |          |           |   0   mi  | 115.2 mi
Chattanooga |          |           |           |   0   mi
-->

{| class="wikitable" border="1" style="empty-cells: show; text-align:right;"
|-
!Voter from/<br />City Choice
!Memphis
!Nashville
!Chattanooga
!Knoxville
!Total
|-
!Memphis
|420 (42 × 10)
|0 (26 × 0)
|0 (15 × 0)
|0 (17 × 0)
|'''420'''
|-
!Nashville
|168 (42 × 4)
|260 (26 × 10)
|90 (15 × 6)
|85 (17 × 5)
|'''{{Green tick}} 603'''
|-
!Chattanooga
|84 (42 × 2)
|104 (26 × 4)
|150 (15 × 10)
|119 (17 × 7)
|'''457'''
|-
!Knoxville
|0 (42 × 0)
|52 (26 × 2)
|90 (15 × 6)
|170 (17 × 10)
|'''312'''
|}
Nashville, the capital in real life, likewise wins in the example.

For comparison, note that traditional first-past-the-post would elect Memphis, even though most citizens consider it the worst choice, because 42% is larger than any other single city. [[Instant-runoff voting#Tennessee capital election|Instant-runoff voting]] would elect the 2nd-worst choice (Knoxville), because the central candidates would be eliminated early (and Chattanooga voters preferring Knoxville above Nashville). In [[approval voting]], with each voter selecting their top two cities, Nashville would win because of the significant boost from Memphis residents.

==Properties==
Score voting allows voters to express preferences of varying strengths, making it a [[rated voting]] system.

Score voting is not vulnerable to the [[monotonicity criterion|less-is-more paradox]], i.e. raising a candidate's rating can never hurt their chances of winning. Score also satisfies the [[participation criterion]], i.e. a candidate can never lose as a result of voters turning out to support them. Score voting satisfies [[independence of irrelevant alternatives]], and does not tend to exhibit [[spoiler effect]]s.

It does not satisfy the [[Condorcet criterion]], i.e. the method does not always agree with the [[majority rule]]. However, when voters all vote strategically, basing their votes on [[Opinion poll|polling]] or past [[election]] results, the majority-preferred candidate will win.<ref>Laslier, J.-F. (2006) [http://halshs.archives-ouvertes.fr/docs/00/12/17/51/PDF/stratapproval4.pdf "Strategic approval voting in a large electorate"], ''IDEP Working Papers'' No. 405 (Marseille, France: Institut d'Économie Publique)</ref>

==Strategy==
{{See also|Tactical voting#Score voting}}
Ideal score [[strategic voting|voting strategy]] for well-informed voters is generally identical to their optimal [[approval voting]] strategy; voters will want to give their least and most favorite candidates a minimum and a maximum score, respectively. The game-theoretical analysis shows that this claim is not fully general, but holds in most cases.<ref>{{cite journal |title = Preference intensity representation: strategic overstating in large elections |journal =  Social Choice and Welfare |volume = 42|pages = 313–340  |last1 = Nunez |first1 = Matias |last2 = Laslier |first2 = Jean-François |year = 2014 |issue = 2 |doi = 10.1007/s00355-013-0728-0 |s2cid = 5738643 |url = https://hal.archives-ouvertes.fr/hal-00917099/file/overstateREVIEW20120928.pdf }}</ref> Another strategic voting tactic is given by the weighted mean utility theorem, maximum score for all candidates preferred compared to the expected winners weighted with winning probability and minimum score for all others.<ref>Approval Voting, Steven J. Brams, Peter C. Fishburn, 1983</ref>

Papers have found that "experimental results support the concept of bias toward unselfish outcomes in large elections." The authors observed what they termed ethical considerations dominating voter behavior as pivot probability decreased. This would imply that larger elections, or those perceived as having a wider margin of victory, would result in fewer tactical voters.<ref>{{cite journal |jstor = 27798496 |title = Moral Bias in Large Elections: Theory and Experimental Evidence |journal = The American Political Science Review |volume = 103 |issue = 2 |pages = 175–192 |last1 = Feddersen |first1 = Timothy |last2 = Gailmard |first2 = Sean |last3 = Sandroni |first3 = Alvaro |year = 2009 |doi = 10.1017/S0003055409090224 |s2cid = 55173201 }}</ref>

How voters precisely grade candidates is a topic that is not fully settled, although experiments show that their behavior depends on the grade scale, its length, and the possibility to give negative grades.<ref name=":Baujardetal2014">{{Cite journal |last1 = Baujard |first1 = Antoinette |last2 = Igersheim |first2 = Herrade |last3 = Lebon |first3 = Isabelle |last4 = Gavrel |first4 = Frédéric |last5 = Laslier |first5 = Jean-François |title = How voters use grade scales in evaluative voting|journal = European Journal of Political Economy  |volume = 55 |pages = 14–28 |doi = 10.1016/j.ejpoleco.2017.09.006 |year = 2014|url = https://halshs.archives-ouvertes.fr/halshs-01618039/file/1729.pdf }}</ref>

[[STAR voting]] (Score Then Automatic Runoff) is a variant proposed to address some concerns about strategic exaggeration in score voting. Under this system, each voter may assign a score (from 0 to the maximum) to any number of candidates. Of the two highest-scoring candidates, the winner is the one most voters ranked higher.<ref>{{Cite news |title=Equal Vote Coalition |url=http://equal.vote |access-date=2017-04-05}}</ref> The runoff step was introduced to mitigate the incentive to exaggerate ratings in ordinary score voting.<ref>{{Cite web |date=2016-12-08 |title=Score Runoff Voting: The New Voting Method that Could Save Our Democratic Process |url=https://ivn.us/2016/12/08/score-runoff-voting/ |access-date=2017-04-05 |website=IVN.us}}</ref><ref>{{Cite news |title=Strategic SRV? - Equal Vote Coalition |url=http://equal.vote/strategic_srv |access-date=2017-04-05 |work=Equal Vote Coalition}}</ref>

==Advocacy==

Albert Heckscher was one of the earliest proponents, advocating for a form of score voting he called the "immanent method" in his 1892 dissertation, in which voters assign any number between -1 and +1 to each alternative, simulating their individual deliberation.<ref>{{Cite journal |last = Lagerspetz |first = Eerik |date = 2014-06-01 |title = Albert Heckscher on collective decision-making |journal = Public Choice |language = en |volume = 159 |issue = 3–4 |pages = 327–339 |doi = 10.1007/s11127-014-0169-z |s2cid = 155023975 |issn = 0048-5829 }}</ref><ref>{{Cite book |title=Social choice and democratic values |first=Eerik |last=Lagerspetz |isbn=9783319232614 |eissn=2197-8530 |doi=10.1007/978-3-319-23261-4 |publisher=Springer International |publication-place=Cham, Switzerland |pages=109 |oclc=930703262 |publication-date=2015-11-26}}</ref><ref>{{Cite book |url = https://books.google.com/books?id=gpQEtAEACAAJ |title = Bidrag til Grundlæggelse af en Afstemningslære: om Methoderne ved Udfindelse af Stemmeflerhed i Parlamenter |last = Heckscher |first = Albert Gottlieb |date = 1892 |language = da }}</ref>

Currently, score voting is advocated by [[The Center for Election Science]].{{citation needed|date=July 2024}} Since 2014, the Equal Vote Coalition advocates a variant method ([[STAR voting|STAR]]) with an extra second evaluation step to address some of the criticisms of traditional score voting.<ref>{{Cite news |url = https://www.equal.vote/about |title = About The Equal Vote Coalition |work = Equal Vote Coalition |access-date = 2018-03-29 }}</ref><ref>{{Cite web|url=https://www.starvoting.us/|title=STAR Voting campaign|access-date=2019-09-02}}</ref>

==See also==
* [[Borda count]]
*[[Cardinal voting]]
* [[List of democracy and elections-related topics]]
* [[Consensus decision-making]]
* [[Decision making]]
* [[Democracy]]
* [[Implicit utilitarian voting]]
* [[Utilitarian social choice rule]]
* [[Majority judgment]] — similar rule based on [[median]]s instead of [[average]]s

==Notes==
{{reflist}}

==External links==
* [https://rangevoting.org/ The Center for Range Voting] and its [https://rangevoting.org/MotPlusMenu.html simplified introductory homepage]
* [https://electionscience.org/ The Center for Election Science] includes an [https://electionscience.org/library/score-voting/ article on Score Voting]
* [https://www.equal.vote/ Equal Vote Coalition], which promotes a [[STAR voting]], a variant of score voting, in the United States
* [http://bolson.org/voting/essay.html Simulation of various voting models for close elections] Article by Brian Olson.
* {{cite news |first = Michael |last = Mechanic |author2 = William Poundstone |title = The verdict is in: our voting system is a loser |url = https://www.motherjones.com/interview/2008/01/verdict-is-in-our%20voting-system-is-a-loser.html |work = Mother Jones |publisher = The Foundation for National Progress |date = 2007-01-02 |access-date = 2008-02-04 |author2-link = William Poundstone |archive-date = 2008-02-09 |archive-url = https://web.archive.org/web/20080209121523/http://www.motherjones.com/interview/2008/01/verdict-is-in-our%20voting-system-is-a-loser.html |url-status = dead }}

{{voting methods}}

[[Category:Electoral systems]]
[[Category:Single-winner electoral systems]]
[[Category:Cardinal electoral systems]]
[[Category:Monotonic electoral systems]]
[[Category:Utilitarianism]]