Combined approval voting (CAV) is anelectoral system where each voter may express approval, disapproval, or indifference toward each candidate.[1] 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 acardinal system and a variant ofscore voting. It has also been referred to asdis&approval voting,[2][3]balanced approval voting (BAV),[4][5]approval with abstention option (AWAO),[6]true weight voting (TWV1),[7][8] orevaluative voting (EV)[9] (though the latter can also be used for variants with more than 3 values.) It has also been callednet approval voting[10][11][12] (though this term has a different definition in the context ofapproval-based committee selection).[13][14]
Ballots contain a list of candidates, with three 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 is also possible to use ballots with two 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 ofall candidates, but ballots that allow disapproval of specific candidates are otherwise rare.[2][3]
CAV has been independently invented many times. It was originally proposed by Dan Felsenthal in 1989.[1] Alcantud andLaruelle gave it the name "Dis&approval voting" in 2012.[2][16]
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 (thefavorite 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/againstballot initiatives.<ref name=":3">
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 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.
The sum is computed for each candidate and the winner is the candidate with the largest net vote.
the votesFor andAgainst each candidate are tallied and a net vote for each candidate is computed as the difference
Disapprovals are subtracted from approvals for each candidate, and candidate with highest margin of net-approval wins.
TWV1 allows voters only three score values: -1, 0, and +1.
the Candidate having the highest positive (or least negative) total is the winner
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.
you vote up, down, or neutral on each candidate. The candidate with the most approvals minus specific disapprovals wins.
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.
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.
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.
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.