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# Combined approval voting

Combined approval voting (CAV) is an electoral system where each voter may express approval, disapproval, or indifference toward each candidate.[1] The winner is the most-approved candidate.

It is a cardinal system, a variation of score and approval voting, and is also known as dis&approval voting,[2][3] balanced approval voting (BAV),[4][5] approval with abstention option (AWAO),[6] true weight voting (TWV1),[7][8] or evaluative voting (EV)[9] (though the latter can also be used for variants with more than 3 values.) It has also been called net approval voting[10][11][12] (though this term has a different definition in the context of approval-based committee selection).[13][14]

## Procedure

A ballot that treats blanks as abstentions, showing support for two candidates, opposition to two candidates, and abstention from one.

Ballots contain a list of candidates, with 3 options next to each: "approve"/"disapprove"/"abstain", "for"/"against"/"neutral", or similar.[2] The ballot warns that blanks for a candidate are scored as "indifferent" votes.[2] 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's also possible to use ballots with 2 options, "approve"/"disapprove" and treat blanks as abstentions.[15]

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.[2] 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.[2][3]

## History

CAV has been independently invented many times. It was originally proposed by Dan Felsenthal in 1989.[1] Claude Hillinger introduced the same concept in 2004 under the name "Evaluative Voting".[9] Alcantud and Laruelle gave it the name "Dis&approval voting" in 2012.[2][16]

## Properties

As this is mathematically equivalent to 3-level score voting,[17] it shares the same properties. For instance, it is always safe for a voter to approve their honest favorite (the favorite betrayal criterion).[9]

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.[18]

Unlike other score voting scales, CAV is compatible with existing voting machines that can handle voting for/against ballot initiatives.[15]

## References

1. ^ a b Felsenthal, Dan S. (1989). "On combining approval with disapproval voting". Behavioral Science. 34 (1): 53–60. doi:10.1002/bs.3830340105. ISSN 0005-7940. 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)
2. Alcantud, José Carlos R.; Laruelle, Annick (2013-09-06). "Dis&approval voting: a characterization". Social Choice and Welfare. 43 (1): 1–10. doi:10.1007/s00355-013-0766-7. hdl:10366/127275. ISSN 0176-1714. S2CID 253844191. 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.
3. ^ a b "To approve or not to approve: this is not the question - Mapping Ignorance". Mapping Ignorance. Retrieved 2018-06-27.
4. ^ "Can Less be Better?". Negative Vote Association. 2018-01-22. Retrieved 2020-02-28. The sum is computed for each candidate and the winner is the candidate with the largest net vote.
5. ^ Cohen, Paul (2014-05-29). "Article: What Might be the Best Voting System?". OpEdNews. Archived from the original on 2018-06-16. Retrieved 2020-02-28. the votes For and Against each candidate are tallied and a net vote for each candidate is computed as the difference
6. ^ "Highlights of the Answers To Everything". AnswersToEverything. April 8, 2020. Retrieved 2020-04-11. Disapprovals are subtracted from approvals for each candidate, and candidate with highest margin of net-approval wins.
7. ^ Minet, Roy A. (2020-02-19). "Follow-on Election Simulation Leads to Definitive Proposal" (PDF). p. 3. TWV1 allows voters only three score values: -1, 0, and +1.
8. ^ Minet, Roy A. (2019-11-23). "Election Simulation Sheds New Light On Voting Methods" (PDF). p. 9. the Candidate having the highest positive (or least negative) total is the winner
9. ^ a b c Claude, Hillinger (2004-06-01). "Voting and the Cardinal Aggregation of Judgments". epub.ub.uni-muenchen.de. doi:10.5282/ubm/epub.353. Retrieved 2018-06-27. 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.
10. ^ cestith (2018-06-08). "What is net approval voting?". Hacker News. Retrieved 2020-02-29. you vote up, down, or neutral on each candidate. The candidate with the most approvals minus specific disapprovals wins.
11. ^ "Demosthenes' Game: Perhaps a Way Out". Retrieved 2020-02-29. 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.
12. ^ Kronos, Donald Arthur (2011-12-08). "An Easier Solution - A NET APPROVAL VOTING SYSTEM". Facebook. Retrieved 2020-02-29. 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.
13. ^ Dey, Palash; Misra, Neeldhara; Narahari, Y. (2015-11-13). "On Choosing Committees Based on Approval Votes in the Presence of Outliers". arXiv:1511.04190 [cs.MA].
14. ^ Faliszewski, Piotr; Slinko, Arkadii; Talmon, Nimrod (2017-11-17). "The Complexity of Multiwinner Voting Rules with Variable Number of Winners". arXiv:1711.06641 [cs.GT].
15. ^ a b Ossipoff, Mike (August 2005). "Endorsement of Range Voting from Mike Ossipoff". RangeVoting.org. Archived from the original on 2017-11-20. Retrieved 2018-06-27. If no mark indicates a 0 rating, then -1,0,1 could be implemented with the same ballots and count machinery used in our initiative voting, in which we can vote yes or no on a list of initiatives.
16. ^ LARUELLE, Annick. "Research Project at the University of Cergy-Pontoise - Collective decision-making" (PDF).
17. ^ William., Poundstone (2008). Gaming the vote : why elections aren't fair (and what we can do about it) (1st ed.). New York: Hill and Wang. pp. 248. ISBN 9780809048939. OCLC 156818830. 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.
18. ^ Baujard, Antoinette; Gavrel, Frédéric; Igersheim, Herrade; Laslier, Jean-François; Lebon, Isabelle (2018). "How voters use grade scales in evaluative voting". European Journal of Political Economy. 55: 14–28. doi:10.1016/j.ejpoleco.2017.09.006. ISSN 0176-2680.