Content deleted Content added
m →top: fixed links Tags: Mobile edit Mobile app edit Android app edit App full source |
|||
| (27 intermediate revisions by 18 users not shown) | |||
Line 1:
{{Short description|Single-winner electoral system}}
{{Use mdy dates|date=June 2024}}
{{Electoral systems sidebar|expanded=Single-winner}}{{Lead too short|date=August 2024}}[[File:Approval ballot.svg|thumb|On an [[approval ballot]], the voter can select any number of candidates.]]
'''Approval voting''' is a single-winner [[electoral system]] in which voters mark all the candidates they support, instead of just [[Plurality voting|choosing one]]. The candidate with the highest approval rating is elected. Approval voting is currently in use for government elections in [[St. Louis|St. Louis,
== Effect on elections ==
Research by [[Social choice theory|social choice theorists]] [[Steven Brams]] and [[Dudley R. Herschbach]] found that approval voting would increase voter participation, prevent minor-party candidates from being spoilers, and reduce negative campaigning.<ref>{{cite journal |last1=Brams |first1=Steven J. |last2=Herschbach |first2=Dudley R. |year=2001 |title=The Science of Elections |journal=Science |volume=292 |issue=5521 |pages=1449 |doi=10.1126/science.292.5521.1449 |jstor=3083781 |pmid=11379606 |s2cid=28262658}}</ref> Brams' research concluded that approval can be expected to elect [[Majority preferred candidate|majority-preferred candidates]] in practical election scenarios, avoiding the [[center squeeze]] common to [[Instant-runoff voting|ranked-choice voting]] and [[
One study showed that approval would not have chosen the same two winners as plurality voting ([[Jacques
In the actual election, Le Pen lost by an overwhelming margin in the runoff, 82.2% to 17.8%, a sign that the true top two candidates had not been found. In the approval voting survey primary, Chirac took first place with 36.7%, compared to Jospin at 32.9%. Le Pen, in that study, received 25.1% and so would not have made the cut to the second round. In the real primary election, the top three were Chirac, 19.9%, Le Pen, 16.9%, and Jospin, 16.2%.<ref>{{cite web |last1=Laslier |first1=Jean-François |last2=Vander Straeten |first2=Karine |date=April 2003 |title=Approval Voting: An Experiment during the French 2002 Presidential Election |url=http://www.lse.ac.uk/collections/VPP/VPPpdf_Wshop2/jflkvdscaen.pdf |archive-url=https://web.archive.org/web/20050507223548/http://www.lse.ac.uk/collections/VPP/VPPpdf_Wshop2/jflkvdscaen.pdf |archive-date=May 7, 2005 |access-date=July 8, 2014 |page=6}}</ref> A study of various
=== Operational impacts ===
Line 15:
* '''Simple to tally—'''Approval ballots can be counted by some existing machines designed for plurality elections, as ballots are cast, so that final tallies are immediately available after the election, with relatively few if any upgrades to equipment.
* '''Just one round—'''Approval can remove the need for multiple rounds of voting, such as a [[
* '''Avoids
== Usage ==
Line 22:
=== Current electoral use ===
====Latvia====
The [[Saeima|Latvian parliament]] uses a modified version of approval voting within [[open list proportional representation]], in which voters can cast either positive (approval) votes, negative votes or neither for any number of candidates.<ref>{{Cite web |title=How do elections work in Latvia? |url=https://www.electoral-reform.org.uk/how-do-elections-work-in-latvia/|access-date=28 July 2024 |website=Electoral Reform Society |language=en}}</ref>
====United States====
;Missouri
In November 2020, [[St. Louis, Missouri]], passed Proposition D with 70% voting to authorize a variant of approval ([[unified primary]]) for municipal offices.<ref name="St. Louis approves">{{cite web |last= |first= |date=November 4, 2020 |title=St. Louis Voters Approve Nonpartisan Elections |url=https://www.usnews.com/news/best-states/missouri/articles/2020-11-04/st-louis-voters-approve-nonpartisan-elections |url-status=live |archive-url=https://web.archive.org/web/20210614075134/https://www.usnews.com/news/best-states/missouri/articles/2020-11-04/st-louis-voters-approve-nonpartisan-elections |archive-date=June 14, 2021 |access-date=December 3, 2020 |work=U.S. News & World Report}}</ref> In 2021, the [[2021 St. Louis mayoral election|first mayoral election with approval voting]] saw Tishaura Jones and Cara Spencer move on to the general with 57% and 46% support. Lewis Reed and Andrew Jones were eliminated with 39% and 14% support, resulting in an average of 1.6 candidates supported by each voter in the 4 person race.<ref>{{cite news |last=Clancy |first=Sam |date=March 2, 2021 |title=Tishaura Jones, Cara Spencer advance to general election in race for St. Louis Mayor |url=https://www.ksdk.com/article/news/politics/elections/tishaura-jones-cara-spencer-st-louis-mayor-race/63-34335593-223a-431b-ac63-b17eb2495841 |work=KSDK |location=St. Louis, MO |access-date=May 22, 2024}}
;North Dakota
Line 40:
It is also used in internal elections by the [[American Solidarity Party]];<ref>{{cite web|url=https://solidarity-party.org/16112120-b9ec-4746-9bff-c2d18e7662b9/|title=Vice-Chair's Remarks|last1=Covich|first1=Skylar|website=American Solidarity Party|url-status=dead|archive-url=https://web.archive.org/web/20180622032935/https://solidarity-party.org/16112120-b9ec-4746-9bff-c2d18e7662b9/|archive-date=June 22, 2018|access-date=June 21, 2018}}</ref> the [[Green party|Green Parties]] of [[Green Party of Texas|Texas]]<ref>{{Cite web|url=http://www.txgreens.org/platform#reform|title=Platform|publisher=Green Party of Texas|access-date=January 31, 2017|quote=We support switching to a preferential voting method, such as approval voting.}}</ref><ref>{{Cite web|url=http://www.txgreens.org/by_laws|title=By-Laws|publisher=Green Party of Texas|url-status=dead|archive-url=https://web.archive.org/web/20170129154828/http://www.txgreens.org/by_laws|archive-date=January 29, 2017|access-date=January 31, 2017|quote=The Co-Chair, Treasurer, and Secretary positions shall be filled by using approval voting.}}</ref> and [[Green Party of Ohio|Ohio]];<ref>{{Cite web|url=http://www.ohiogreens.org/event/ohio-green-party-presidential-nominating-convention-columbus-results|title=Ohio Green Party Presidential Nominating Convention (Columbus)|publisher=Ohio Green Party|access-date=January 31, 2017|quote=We have agreed to use "approval voting" as opposed to "instant runoff voting" to make the Ohio Green Party choice for president|archive-date=February 26, 2021|archive-url=https://web.archive.org/web/20210226172609/http://www.ohiogreens.org/event/ohio-green-party-presidential-nominating-convention-columbus-results|url-status=dead}}</ref> the [[Libertarian National Committee]];<ref>{{Cite web |date=October 4, 2020 |title=MEETING MINUTES LIBERTARIAN NATIONAL COMMITTEE |url=https://lpedia.org/w/images/f/fa/LNC-MEETING_2020-10-04_FINAL.pdf#page=10 |archive-url=https://ghostarchive.org/archive/20221009/https://lpedia.org/w/images/f/fa/LNC-MEETING_2020-10-04_FINAL.pdf#page=10 |archive-date=October 9, 2022 |url-status=live |quote=VOTING METHOD: Approval Voting per OpaVote. Vote for as many candidates as desired.}}</ref> the [[Libertarian Party (United States)|Libertarian parties]] of [[Libertarian Party of Texas|Texas]],<ref>{{Cite news|url=http://www.lptexas.org/state-platform|title=State Platform|access-date=January 31, 2017|url-status=dead|archive-url=https://web.archive.org/web/20170130003731/http://www.lptexas.org/state-platform|archive-date=January 30, 2017|publisher=Libertarian Party of Texas|quote=We also believe that all races should be decided by Approval Voting}}</ref> [[Libertarian Party of Colorado|Colorado]],<ref>{{Cite web |title=Document:Colorado State Party Bylaws 2021 |url=https://lpedia.org/wiki/Document:Colorado_State_Party_Bylaws_2021 |access-date=September 24, 2022 |website=LPedia |quote=For any partisan offices, Convention Delegates shall vote by approval voting}}</ref><ref>{{Cite web |title=Colorado Convention 2018 |url=https://lpedia.org/wiki/Colorado_Convention_2018 |access-date=September 24, 2022 |work=LPedia |language=en |quote=All candidates were selected by approval voting via standing vote.}}</ref> [[Arizona Libertarian Party|Arizona]],<ref>{{Cite web |title=Bylaws |url=https://azlp.org/about/bylaws/ |access-date=September 24, 2022 |website=Arizona Libertarian Party |language=en-US |quote=The remaining Delegates … shall be elected by approval voting … should there be more Delegate Candidates than allotted seats.}}</ref> and [[Libertarian Party of New York|New York]];<ref>{{Cite web |date=November 7, 2021 |title=Rules of the Libertarian Party |url=https://lpny.org/wp-content/uploads/sites/24/2021/11/LPNY-RULES-2021-11-07.pdf#page=10 |archive-url=https://ghostarchive.org/archive/20221009/https://lpny.org/wp-content/uploads/sites/24/2021/11/LPNY-RULES-2021-11-07.pdf#page=10 |archive-date=October 9, 2022 |url-status=live |website=Libertarian Party of New York |quote=All elections shall be held with approval voting}}</ref> [[Alliance 90/The Greens]] in Germany;<ref>{{Cite web |date=January 18, 2017 |title=Grüne München: Satzung |trans-title=Statutes of the city association - Alliance 90/The Greens Munich-City District Association |url=https://www.gruene-muenchen.de/partei/satzung/ |url-status=dead |archive-url=https://web.archive.org/web/20170118171623/https://www.gruene-muenchen.de/partei/satzung/ |archive-date=January 18, 2017 |access-date=March 5, 2023 |language=de |quote=Delegierte für Bundes, Landes- und Bezirksversammlungen werden per Zustimmungsblockwahl gewählt. Jede*r Stimmberechtigte hat so viele Stimmen, wie Bewerber*innen zur Wahl stehen, und kann jeder*m Bewerber*in eine oder keine Stimme geben.}}</ref> and the [[Czech Pirate Party|Czech]]<ref>{{Cite web|title=Jednací řád celostátního fóra|url=https://wiki.pirati.cz/rules/jdr|access-date=November 16, 2021|website=Pirati.CZ|language=cs}}</ref> and [[German Pirate Party]]<!-- with a 50% threshold requirement? -->.<ref>{{Cite web|url=http://wiki.piratenpartei.de/Bundesparteitag_2010.1/Gesch%C3%A4ftsordnung#Wahlen_zu_Vorstand_und_Schiedsgericht|title=Bundesparteitag 2010.1/Geschäftsordnung|publisher=[[German Pirate Party]]|language=de|access-date=June 24, 2018}}</ref><ref>{{Cite web |title=Election Data from the German Pirate Party (Piratenpartei) |url=https://sites.google.com/a/electology.org/www/pirate-elections-germany |url-status=dead |archive-url=https://web.archive.org/web/20190219005345/https://sites.google.com/a/electology.org/www/pirate-elections-germany |archive-date=February 19, 2019 |access-date=September 24, 2022 |publisher=The Center for Election Science}}</ref>
Approval has been adopted by several societies: the Society for Social Choice and Welfare (1992),<ref>{{cite web |url=http://www.unicaen.fr/recherche/mrsh/sites/all/themes/simpler2/scw/statutesSCW.pdf |archive-url=https://ghostarchive.org/archive/20221009/http://www.unicaen.fr/recherche/mrsh/sites/all/themes/simpler2/scw/statutesSCW.pdf |archive-date=October 9, 2022 |url-status=live |title=Statutes of the Society for Social Choice and Welfare |publisher=Society for Social Choice and Welfare |access-date=January 28, 2020}}</ref> [[Mathematical Association of America]] (1986),<ref>{{cite web|url=http://www.maa.org/about-maa/governance/governance-documents/bylaws#article9 |title=MAA Bylaws |publisher=[[Mathematical Association of America]] |date=August 7, 2010 |access-date=November 6, 2014}}</ref> the [[American Mathematical Society]],<ref>{{cite web|url=https://www.ams.org/notices/201508/rnoti-p931a.pdf |archive-url=https://ghostarchive.org/archive/20221009/https://www.ams.org/notices/201508/rnoti-p931a.pdf |archive-date=October 9, 2022 |url-status=live |title=2015 American Mathematical Society Elections |publisher=[[American Mathematical Society]] |access-date=August 19, 2015}}</ref> the Institute of Management Sciences (1987) (now the [[Institute for Operations Research and the Management Sciences]]),<ref>{{cite web |url=https://www.informs.org/content/download/363531/3797055/file/Constitution%20and%20Bylaws%20August%202017.pdf |archive-url=https://ghostarchive.org/archive/20221009/https://www.informs.org/content/download/363531/3797055/file/Constitution%20and%20Bylaws%20August%202017.pdf |archive-date=October 9, 2022 |url-status=live |title=Constitution of the Institute for Operations Research and the Management Sciences |publisher=Institute for Operations Research and the Management Sciences |date=August 2017 |page=7}}</ref> the [[American Statistical Association]] (1987),<ref>{{cite web|url = https://www.amstat.org/asa/files/pdfs/ABT-Bylaws.pdf |title = Bylaws of the American Statistical Association |date = September 19, 2018 |access-date = January 28, 2020 |publisher=[[American Statistical Association]]}}</ref> and the [[Institute of Electrical and Electronics Engineers]] (1987).
Steven Brams' analysis of the 5-candidate 1987 Mathematical Association of America presidential election shows that 79% of voters cast a ballot for one candidate, 16% for 2 candidates, 5% for 3, and 1% for 4, with the winner earning the approval of 1,267 (32%) of 3,924 voters.<ref name="theory to practice"/><ref>{{Cite book|title=Handbook on Approval Voting|url=https://archive.org/details/handbookonapprov00lasl|url-access=limited|last1=Brams|first1=Steven J.|last2=Fishburn|first2=Peter C.|chapter=Going from Theory to Practice: The Mixed Success of Approval Voting |date=2010 |publisher=Springer Berlin Heidelberg|isbn=9783642028380|editor-last=Laslier|editor-first=Jean-François|series=Studies in Choice and Welfare|pages=[https://archive.org/details/handbookonapprov00lasl/page/n37 19]–37|language=en|doi=10.1007/978-3-642-02839-7_3|editor-last2=Sanver|editor-first2=M. Remzi}}</ref> The IEEE board in 2002 rescinded its decision to use approval. IEEE Executive Director Daniel J. Senese stated that approval was abandoned because "few of our members were using it and it was felt that it was no longer needed."<ref name="theory to practice">{{cite conference |last1=Brams |first1=Steven J. |last2=Fishburn |first2=Peter C. |title=Going from Theory to Practice: The Mixed Success of Approval Voting |work=Annual Meeting of the American Political Science Association |publisher=[[American Political Science Association]] |access-date=May 8, 2010| url= http://www.nyu.edu/gsas/dept/politics/faculty/brams/theory_to_practice.pdf | date=August 2003 |archive-url=https://web.archive.org/web/20181218010629/http://www.nyu.edu/gsas/dept/politics/faculty/brams/theory_to_practice.pdf |archive-date=December 18, 2018}}</ref> Approval voting was used for Dartmouth Alumni Association elections for seats on the College Board of Trustees, but after some controversy<ref name="verbum">{{cite news |url=https://www.thedartmouth.com/article/2009/04/verbum-ultimum-making-amends |title=Verbum Ultimum: Making Amends |date=April 3, 2009 |work=The Dartmouth}}</ref> it was replaced with traditional runoff elections by an alumni vote of 82% to 18% in 2009.<ref>{{cite web |url=https://alumni.dartmouth.edu/content/dartmouth-alumni-association-election-results-new-executive-committee-elected-constitutional |title=Dartmouth Alumni Association Election Results: New Executive Committee Elected; Constitutional Amendment Passes |date=May 9, 2009 |publisher=Dartmouth Office of Alumni Relations}}</ref> Dartmouth students started to use approval voting to elect their student body president in 2011. In the first election, the winner secured the support of 41% of voters against several write-in candidates.<ref>{{cite web |url=http://thelittlegreenblog.blogspot.com/2011/04/hix-12-dartmouth-student-body-both.html |last=Bruschi |first=Nathan |title=Hix '12, Dartmouth Student Body, both shafted in student election |date=April 16, 2011 |work=The Little Green Blog}}</ref> In 2012, Suril Kantaria won with the support of 32% of the voters.<ref>{{cite news |url=https://www.thedartmouth.com/article/2012/04/kantaria-danford-win-student-assembly-elections |title=Kantaria, Danford win Student Assembly elections |last=Shkuratov |first=Marina |date=April 16, 2012 |work=The Dartmouth}}</ref> In 2013, 2014 and 2016, the winners also earned the support of under 40% of the voters.<ref>{{cite news |url=https://www.thedartmouth.com/article/2013/04/ferrari-zhu-elected-to-lead-student-assembly |title=Ferrari, Zhu elected to lead Student Assembly |date=April 15, 2013 |last=Riordan |first=Michael |work=The Dartmouth}}</ref><ref name="Dennis, Cunningham to lead Assembly">{{cite news |url=https://www.thedartmouth.com/article/2014/04/dennis-cunningham-to-lead-assembly |title=Dennis, Cunningham to lead Assembly |last=McGahan |first=Sara |date=April 15, 2014 |work=The Dartmouth}}</ref><ref name="thedartmouth.com">{{cite web |url=https://www.thedartmouth.com/article/2016/04/harrington-wins-student-assembly-president-election |title=Harrington will be Student Assembly president |last=Jiang |first=Heyi |date=April 17, 2016 |work=The Dartmouth}}</ref> Results reported in ''The Dartmouth'' show that in the 2014 and 2016 elections, more than 80 percent of voters approved of only one candidate.<ref name="Dennis, Cunningham to lead Assembly"/><ref name="thedartmouth.com"/> Students replaced approval voting with plurality voting before the 2017 elections.<ref>[https://static1.squarespace.com/static/5b397fa0e2ccd1b58ab7a317/t/5b3bf00f0e2e72d1275f0e3d/1530654736431/DartmouthSAConstitution.pdf], Dartmouth student constitution</ref>
===Historical===
[[file:The story of the greatest nations, from the dawn of history to the twentieth century - a comprehensive history, founded upon the leading authorities, including a complete chronology of the world, and (14765071792).jpg|300px|thumb|Rows of [[secret ballot|secret]] approval vote boxes from early 1900s [[Greece]], where the voter drops a marble to the right or left of the box, through a tube, one for each candidate standing]]
[[Robert J. Weber]] coined the term "Approval Voting" in 1971.<ref name=":0">{{citation|title=Approval Voting|first1=Steven J.|last1=Brams|author1-link=Steven Brams|first2=Peter C.|last2=Fishburn|author2-link=Peter C. Fishburn|page=xv|publisher=Springer-Verlag|year=2007|isbn=978-0-387-49895-9|url=https://books.google.com/books?id=e7h7evxSclIC&pg=PR5}}</ref> It was more fully published in 1978 by political scientist [[Steven Brams]] and mathematician [[Peter Fishburn]].<ref>{{Cite journal | doi = 10.2307/1955105 |last1=Brams |first1=Steven |last2=Fishburn |first2=Peter | year = 1978 | title = Approval Voting | jstor = 1955105| journal = American Political Science Review | volume = 72 | issue = 3 | pages = 831–847 |s2cid=251092061 }}</ref>
<span id="Historical_use">Historically, several voting methods that incorporate aspects of approval have been used:</span>
Line 58 ⟶ 62:
== Strategic voting ==
{{See also|
=== Overview ===
Line 98 ⟶ 102:
==== Dichotomous preferences ====
Approval avoids the issue of multiple sincere votes in special cases when voters have [[dichotomous preferences]]. For a voter with dichotomous preferences, approval is [[Strategyproofness|strategyproof]].{{sfn|Brams|Fishburn|1983|p=31}} When all voters have dichotomous preferences and vote the sincere, strategy-proof vote, approval is guaranteed to elect
Having dichotomous preferences means that a voter has bi-level preferences for the candidates. All of the candidates are divided into two groups such that the voter is indifferent between any two candidates in the same group and any candidate in the top-level group is preferred to any candidate in the bottom-level group.{{sfn|Brams|Fishburn|1983|p=16–17}} A voter that has strict preferences between three candidates—prefers A to B and B to C—does not have dichotomous preferences.
Being strategy-proof for a voter means that there is a unique way for the voter to vote that is a strategically best way to vote, regardless of how others vote. In approval, the strategy-proof vote, if it exists, is a sincere vote.{{sfn|Brams|Fishburn|1983|p=29}}
==== Approval threshold ====
Line 113 ⟶ 118:
Voting strategy under approval is guided by two competing features of approval. On the one hand, approval fails the [[later-no-harm criterion]], so voting for a candidate can cause that candidate to win instead of a candidate more preferred by that voter. On the other hand, approval satisfies the [[monotonicity criterion]], so not voting for a candidate can never help that candidate win, but can cause that candidate to lose to a less preferred candidate. Either way, the voter can risk getting a less preferred election winner. A voter can balance the risk-benefit trade-offs by considering the voter's cardinal utilities, particularly via the [[von Neumann–Morgenstern utility theorem]], and the probabilities of how others vote.
A [[Tactical voting#Myerson-Weber strategy|rational voter model]] described by [[Roger Myerson|Myerson]] and Weber specifies an approval strategy that votes for those candidates that have a positive prospective rating.<ref name=":2">{{Cite journal | doi = 10.2307/2938959 |last1=Myerson |first1=R. |last2=Weber |first2=R. J. | year = 1993 | title = A theory of Voting Equilibria | jstor = 2938959| journal = American Political Science Review | volume = 87 | issue = 1| pages = 102–114 |url=http://www.kellogg.northwestern.edu/research/math/papers/782.pdf |archive-url=https://ghostarchive.org/archive/20221009/http://www.kellogg.northwestern.edu/research/math/papers/782.pdf |archive-date=October 9, 2022 |url-status=live | hdl = 10419/221141 |s2cid=143828854 | hdl-access = free }}</ref> This strategy is optimal in the sense that it maximizes the voter's [[Utility#Expected utility|expected utility]], subject to the constraints of the model and provided the number of other voters is sufficiently large.
An optimal approval vote always votes for the most preferred candidate and not for the least preferred candidate, which is a [[dominant strategy]]. An optimal vote can require supporting one candidate and not voting for a more preferred candidate if there 4 candidates or more, e.g. the third and forth choices are correlated to gain or lose decisive votes together; however, such situations are inherently unstable, suggesting such strategy should be rare.<ref>{{Cite journal | last1=Dutta |first1=B |last2=De Sinopoli |first2=F. | last3=Laslier |first3= J.-F.| year = 2006 | title = Approval voting: three examples | journal = International Journal of Game Theory | volume = 35 | pages = 27–38 |doi=10.1007/s00182-006-0053-2 |s2cid=801286 | citeseerx=10.1.1.365.8090 }}</ref>
Other strategies are also available and coincide with the optimal strategy in special situations. For example:
* Vote for the candidates that have above average utility. This strategy coincides with the optimal strategy if the voter thinks that all pairwise ties are equally likely.{{sfn|Brams|Fishburn|1983|p=85}}
* Vote for any candidate that is more preferred than the expected winner and also vote for the expected winner if the expected winner is more preferred than the expected runner-up. This strategy coincides with the optimal strategy if there are three or fewer candidates or if the pivot probability for a tie between the expected winner and expected runner-up is sufficiently large compared to the other pivot probabilities. This strategy, if used by all voters, implies at equilibrium the election of the Condorcet winner whenever it exists.<ref name=":3">{{Cite journal | last1=Laslier |first1= J.-F.| year = 2009 | title = The Leader rule: a model of strategic approval voting in a large electorate | journal = Journal of Theoretical Politics | volume = 21 | issue=1 | pages = 113–136 |doi= 10.1177/0951629808097286|s2cid= 153790214}}</ref>
*Vote for the most preferred candidate only. This strategy coincides with the optimal strategy when the best candidate is either much better than all others (i.e. is the only one with a positive expected value).{{sfn|Brams|Fishburn|1983|p=74, 81}}
*If all voters are rational and cast a strategically optimal vote based on a common knowledge of how all other voters vote except for small-probability, statistically independent errors, then the winner will be the Condorcet winner, if one exists.<ref name=":4">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'Economie Publique)</ref>
=== Strategy examples ===
Line 192 ⟶ 197:
===Dichotomous cutoff===
{{more citations needed section|date=June 2019}}
As this voting method is cardinal rather than ordinal, it is possible to model voters in a way that does not simplify to an ordinal method. Modelling voters with a 'dichotomous cutoff' assumes a voter has an immovable approval cutoff, while having meaningful cardinal preferences. This means that rather than voting for their top 3 candidates, or all candidates above the average approval
For example, in this scenario, voters are voting for candidates with approval above 50% (bold signifies that the voters voted for the candidate):
Line 313 ⟶ 318:
== Compliance with voting system criteria ==
{{
Most of the mathematical criteria by which voting systems are compared were formulated for voters with ordinal preferences. In this case, approval voting requires voters to make an additional decision of where to put their approval cutoff (see examples above). Depending on how this decision is made, approval satisfies different sets of criteria.
There is no ultimate authority on which criteria should be considered, but the following are criteria that many voting theorists accept and consider desirable:
{| class="wikitable" style="text-align:center"
|- style="font-size:90%;"
! '''Voting model:'''
![[Sincere favorite criterion|Sincere favorite]]
![[Gibbard's theorem|Strategyproof]]
|-
! [[Impartial anonymous culture|Zero information]]<ref name=":2" />
|{{No}} ▼
|{{Yes}}
|{{No}}
|{{No}}
|{{No}}
|{{Yes}}
|{{Yes}}
|{{No}}
|-
!Leader rule<ref name=":3" />
▲|{{No}}
|-▼
![[Trembling hand perfect equilibrium|Trembling hand equilibrium]]▼
|{{Yes}}
|{{Yes}}
|{{Yes}}
|{{No}}
|
| |
|{{Yes}}
|{{No}}
▲|-
|{{Yes}}
|{{Yes}}
|{{Yes}}
|{{No}}
|
| |
|{{Yes}}
|{{No}}
|-
! [[Dichotomous preferences
|
| | | | | | |{{Yes}}
|}
Line 365 ⟶ 373:
* [[Multiwinner approval voting]] — multiple candidates may be elected, instead of just one.
* [[Fractional approval voting]] — the election outcome is a distribution - assigning a fraction to each candidate.
* [[Score voting]] (also called range voting) — is simply approval voting where voters can give a wider range of scores than 0 or 1 (e.g. 0-5 or
* [[Combined approval voting]] — form of score voting with three levels that uses a scale of (-1, 0, +1) or (0, .5, 1).
* [[D21 – Janeček method]] — limited to two approval and one negative vote per voter.
* [[Unified primary]] — a nonpartisan primary that uses approval voting for the first round.
== Notes ==
<references group="note" />
== References ==
{{Reflist|30em}}
| |||