Combined approval voting#Properties
{{Short description|Single-winner electoral system}}
Combined approval voting (CAV) is an electoral system where each voter may express approval, disapproval, or indifference toward each candidate.{{Cite journal|last=Felsenthal|first=Dan S.|date=1989|title=On combining approval with disapproval voting|journal=Behavioral Science|language=en|volume=34|issue=1|pages=53–60|doi=10.1002/bs.3830340105|issn=0005-7940|quote=k candidates ... each voter under CAV has k votes and can, with respect to each candidate, either cast one vote in favor of this candidate, or cast one vote against this candidate, or abstain from voting for this candidate. The outcome of a CAV ballot is the candidate with the largest net vote total (algebraic sum of votes in favor and votes against)}} The winner is the candidate with the highest score, which is determined by subtracting the number of approval votes by the number of disapproval votes.
It is a cardinal system and a variant of score voting. It has also been referred to as dis&approval voting,{{Cite journal|last1=Alcantud|first1=José Carlos R.|last2=Laruelle|first2=Annick|author2-link=Annick Laruelle|date=2013-09-06|title=Dis&approval voting: a characterization|journal=Social Choice and Welfare|language=en|volume=43|issue=1|pages=1–10|doi=10.1007/s00355-013-0766-7|issn=0176-1714|quote=The three levels have the following interpretation: 1 means approval, 0 means indifference, abstention or ‘do not know’, and -1 means disapproval. ... We investigate the ‘dis&approval rule’, that selects the candidates who obtain the largest difference between the number of positive votes and the number of negative votes.|hdl=10366/127275|s2cid=253844191 |hdl-access=free}}{{Cite news|url=https://mappingignorance.org/2014/01/31/to-approve-or-not-to-approve-this-is-not-the-question/|title=To approve or not to approve: this is not the question - Mapping Ignorance|work=Mapping Ignorance|access-date=2018-06-27|language=en-US}} balanced approval voting (BAV),{{Cite web|url=https://www.negativevote.org/news/pid_1/84.html?lang=en|title=Can Less be Better?|date=2018-01-22|website=Negative Vote Association|language=en|access-date=2020-02-28|quote=The sum is computed for each candidate and the winner is the candidate with the largest net vote.}}{{Cite web|url=https://www.opednews.com/articles/What-Might-be-the-Best-Vot-by-Paul-Cohen-Polarization_Voting-Laws-State_Voting-Reform-140529-132.html&series=326|title=Article: What Might be the Best Voting System?|last=Cohen|first=Paul|date=2014-05-29|website=OpEdNews|url-status=live|archive-url=https://web.archive.org/web/20180616014810/https://www.opednews.com/articles/What-Might-be-the-Best-Vot-by-Paul-Cohen-Polarization_Voting-Laws-State_Voting-Reform-140529-132.html%26series%3D326|archive-date=2018-06-16|access-date=2020-02-28|quote=the votes For and Against each candidate are tallied and a net vote for each candidate is computed as the difference}} approval with abstention option (AWAO),{{Cite web|url=https://a2e-highlights.net/|title=Highlights of the Answers To Everything|date=April 8, 2020|website=AnswersToEverything|language=en-US|access-date=2020-04-11|quote=Disapprovals are subtracted from approvals for each candidate, and candidate with highest margin of net-approval wins.}} true weight voting (TWV1),{{Cite web|url=http://royminet.org/wp-content/uploads/2020/03/FollowOnSimLeadsToFirmProposal.pdf|title=Follow-on Election Simulation Leads to Definitive Proposal|last=Minet|first=Roy A.|date=2020-02-19|page=3|quote=TWV1 allows voters only three score values: -1, 0, and +1.}}{{Cite web|url=http://royminet.org/wp-content/uploads/2019/12/ElectionSimulationShedsLight.pdf|title=Election Simulation Sheds New Light On Voting Methods|last=Minet|first=Roy A.|date=2019-11-23|page=9|quote=the Candidate having the highest positive (or least negative) total is the winner}} or evaluative voting (EV){{Cite journal|url=http://epub.ub.uni-muenchen.de/353/|title=Voting and the Cardinal Aggregation of Judgments|last=Claude|first=Hillinger|date=2004-06-01|website=epub.ub.uni-muenchen.de|doi=10.5282/ubm/epub.353 |language=en|access-date=2018-06-27|quote=The alternative that maximizes the sum wins. ... I argue for a three valued scale for general elections. ... with the scale (-1 (against), 0 (neutral), +1 (for)). In a committee of experts a more differentiated rule, EV-5, with the scale (-2,- 1,0,+1,+2) may be appropriate. ... A great advantage of EV is that the voter has no strategic incentive to withdraw his vote from the candidates he likes best.}} (though the latter can also be used for variants with more than 3 values.) It has also been called net approval voting{{Cite web|url=https://news.ycombinator.com/item?id=17213149|title=What is net approval voting?|last=cestith|date=2018-06-08|website=Hacker News|access-date=2020-02-29|quote=you vote up, down, or neutral on each candidate. The candidate with the most approvals minus specific disapprovals wins.}}{{Cite web|url=https://demosthenesgame.blogspot.com/2007/05/perhaps-way-out.html|title=Demosthenes' Game: Perhaps a Way Out|language=en|access-date=2020-02-29|quote=Just two lines in the ballot: who you're for, and who you're against. The difference between 'for' and 'against' votes gives the candidate's net approval vote. Highest net approval vote wins.}}{{Cite web|url=https://www.facebook.com/notes/occupy-hunger-strike/an-easier-solution-a-net-approval-voting-system/229304087140661|title=An Easier Solution - A NET APPROVAL VOTING SYSTEM|last=Kronos|first=Donald Arthur|date=2011-12-08|website=Facebook|access-date=2020-02-29|quote=able to indicate approval or disapproval of any number of candidates ... as additive votes to show approval and subtractive votes to show disapproval, where the candidate shown to have the highest net approval is the winner.}} (though this term has a different definition in the context of approval-based committee selection).{{cite arXiv|last1=Dey|first1=Palash|last2=Misra|first2=Neeldhara|last3=Narahari|first3=Y.|date=2015-11-13|title=On Choosing Committees Based on Approval Votes in the Presence of Outliers|eprint=1511.04190|class=cs.MA}}{{cite arXiv|last1=Faliszewski|first1=Piotr|last2=Slinko|first2=Arkadii|last3=Talmon|first3=Nimrod|date=2017-11-17|title=The Complexity of Multiwinner Voting Rules with Variable Number of Winners|eprint=1711.06641|class=cs.GT}}
Procedure
File:Balanced Approval ballot.svg
Ballots contain a list of candidates, with three options next to each: "approve"/"disapprove"/"abstain", "for"/"against"/"neutral", or similar. The ballot warns that blanks for a candidate are scored as "indifferent" votes. Voters express their opinion of each candidate, and the votes are summed, with support = +1 and opposition = −1. The candidate with the largest score is the winner.
It is also possible to use ballots with two options, "approve"/"disapprove" and treat blanks as abstentions.{{cn|date=March 2024}}
Unlike approval voting, in which non-approval could mean either disapproval or indifference, CAV allows explicit expression of disapproval, which is hoped to increase turnout, and reduce spoiled/blank ballots and insincere votes for unviable candidates. Some jurisdictions allow a "none of the above" option to express disapproval of all candidates, but ballots that allow disapproval of specific candidates are otherwise rare.
History
CAV has been independently invented many times. It was originally proposed by Dan Felsenthal in 1989. Alcantud and Laruelle gave it the name "Dis&approval voting" in 2012.{{Cite web|url=https://iea.u-cergy.fr/_resources/Chercheurs%2520invit%25C3%25A9s/2017/LARUELLE_Projet.pdf|title=Research Project at the University of Cergy-Pontoise - Collective decision-making|last=LARUELLE|first=Annick}}
Properties
As this is mathematically equivalent to 3-level score voting,{{Cite book|title=Gaming the vote : why elections aren't fair (and what we can do about it)|last=William.|first=Poundstone|date=2008|publisher=Hill and Wang|isbn=9780809048939|edition=1st|location=New York|pages=[https://archive.org/details/gamingvotewhyele00poun/page/248 248]|oclc=156818830|quote=A three-valued system called "evaluative voting" has been proposed by D. S. Felsenthal, Claude Hillinger, and Mike Ossipoff. ... Mathematically, this is no different from allowing votes of 0, I, or 2.|url-access=registration|url=https://archive.org/details/gamingvotewhyele00poun/page/248}} it shares the same properties. For instance, it is always safe for a voter to approve their honest favorite (the favorite betrayal criterion).
While a (-1, 0, +1) scale is mathematically identical to a (0, 1, 2) scale, there are psychological differences between the two, and the introduction of negative ratings (combined with the change in scoring blanks as middle grades rather than lowest grades) changes the scores that candidates receive in each system. Studies of French voters in 2012 found that, while the highest-rated candidate was the same under either system, and the grades of "exclusive" (polarizing) candidates were relatively unchanged, there were slight increases in the scores of "inclusive" (broadly-liked) candidates, and large increases in the scores of lesser-known candidates.{{Cite journal|last1=Baujard|first1=Antoinette|last2=Gavrel|first2=Frédéric|last3=Igersheim|first3=Herrade|last4=Laslier|first4=Jean-François|last5=Lebon|first5=Isabelle|title=How voters use grade scales in evaluative voting|url=https://halshs.archives-ouvertes.fr/halshs-01618039/document|journal=European Journal of Political Economy|volume=55|pages=14–28|doi=10.1016/j.ejpoleco.2017.09.006|issn=0176-2680|year=2018}}