An Approval method that requires finalists to be the favorite of a significant number of voters.
Simpler than Ranked Choice, more complex than Approval Voting, and likely superior to both, state legislatures will be more likely to go for this one.
Favorite - Approval Grading (A-C)
A grade of "A" indicates a voter's one favorite candidate.
A grade of "C" indicates basic approval.
No limit on C grades.
Up to half of the candidates having the fewest "A" grades are eliminated - but keep a minimum of three finalists.
A and C grades are added together to determine the total Approval vote.
The finalist having the most total Approval votes will be the winner.
Use a simple Vote-for-2 nonpartisan primary to qualify three to five, with a Favorite / Approval general election. (Vote-for-2 is a compromise of Favorite and Approval.)
The Majority Criterion could be used to bypass the approval evaluation, and award the win to any candidate who gets an "A" grade from over half of the voters. This will reduce the likelihood of a candidate being defeated by another who is preferred by fewer voters. (No approval winner could ever beat a first-choice majority winner without using lower-rank votes cast by the majority voting bloc, which many would see as illogical or unfair.) (Note that all majority winners are also Condorcet winners, unbeatable in head-to-head matchups.)
Majority Reject, indicated with a grade of "F," can be used for added precision in a Vote-for-2 primary, or in a single-ballot Favorite / Approval election.
Favorite - Approval Grading (A-B-C)
To cautiously whittle down a large number of candidates (and for Ranking enthusiasts), add a grade of "B," for one, 2nd-favorite candidate.
For 6 or more candidates.
"A" grades eliminate the minimum number of candidates that will leave a maximum of 2/3 remaining. (If 7, 8, or 9 candidates, eliminate 3.)
A grades plus B grades (Vote-for-2) eliminate up to 1/2 of the remaining field, to a minimum of 3 remaining.
A + B + C grades (Approval) determine the winner.
Note that saving the total Approval check for the last step will discourage dishonest voting. (If "C" grades didn't affect the outcome of the final, there would be no consequence in using "Cs" to stack the final field with unpopular rivals.)
Comparison With Other Methods
Approval Voting determines the most popular candidate, under a strict definition of "popular:" approved by the largest number of voters.
Approval Voting is often criticized for ignoring preference, or not allowing a designation of Favorite.
Favorite / Approval Grading and Instant Runoff both involve ranking, though the evaluations differ.
Instant Runoff relies heavily upon Favorite votes, while often ignoring many 2nd-choice and lower preferences.
Contrary to popular belief, Instant Runoff elections do involve vote-splitting, a flaw shared with a basic choose-one election.
These aspects of Instant Runoff cause an occasional, but inevitable error: elimination of the most preferred candidate in 3rd place. (It's because an instant runoff only works perfectly when there are two candidates being compared.)
Favorite / Approval Grading puts less priority on Favorite votes, and ensures that the most popular of the top three favorites will win.
Though it lacks the quasi-scientific appearance of precision of Instant Runoff, Favorite / Approval Grading is likely to more accurately approximate the will of the people, while using a simpler and less costly evaluation.