Combined approval voting

Combined approval voting (CAV) is an electoral system where each voter may express approval, disapproval, or indifference toward each candidate. The winner is the candidate with the highest average score.

It is a cardinal system and a variant on score voting. It has also been referred to as dis&approval voting or net approval voting.

Procedure
Ballots contain a list of candidates, with 3 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's also possible to use ballots with 2 options, "approve"/"disapprove" and treat blanks as abstentions.

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.

Properties
As this is mathematically equivalent to 3-level score voting, 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.