Combined approval voting

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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] or evaluative voting (EV)[4] (though the latter can also be used for variants with more than 3 values.)


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.[5]

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]


CAV has been independently invented several times. It was originally proposed by Dan Felsenthal in 1989.[1] Claude Hillinger introduced the same concept in 2004 under the name "Evaluative Voting".[4] Alcantud and Laruelle gave it the name "Dis&approval voting" in 2016.[2][6]


As this is mathematically equivalent to 3-level score voting,[7] it shares the same properties. For instance, it is always safe for a voter to approve their honest favorite (the favorite betrayal criterion).[4]

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.[8]

Unlike other score voting scales, CAV is compatible with existing voting machines that can handle voting for/against ballot initiatives.[5]


  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. ^ a b c d e f 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. ISSN 0176-1714. 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. ^ a b c Claude, Hillinger (2004-06-01). "Voting and the Cardinal Aggregation of Judgments". 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.
  5. ^ a b Ossipoff, Mike (August 2005). "Endorsement of Range Voting from Mike Ossipoff". 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.
  6. ^ LARUELLE, Annick. "Research Project at the University of Cergy-Pontoise - Collective decision-making" (PDF).
  7. ^ 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. p. 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.
  8. ^ Baujard, Antoinette; Gavrel, Frédéric; Igersheim, Herrade; Laslier, Jean-François; Lebon, Isabelle (September 2017). "How voters use grade scales in evaluative voting". European Journal of Political Economy. doi:10.1016/j.ejpoleco.2017.09.006. ISSN 0176-2680.