Michel Balinski and Rida LarakiAuthors

Assign a selection of words to numbers ("yes" and "no" becomes 1, 0)

Each candidate has a vector which holds the votes each voter gave. The column in the vector corresponds to the voter.

Sort and take the median to determine the majority rating for each candidate.

The winner is whoever has the highest majority grade.

Where ties occur: remove one vote of the tied grade from each candidate who has tied on this grade. So if there there are three candidates with scores [C, B, B], remove a single B vote from the last two and recalculate them. Repeat the process until no ties occur.

Background

If judges are asked to assign points to different elements of a wine, they are found to work from a conclusive rating backward to fill out the form.

Approval Voting (voting yes or no on each candidate) is a degenerate form of Majority Approval, using only the symbols "yes" (1) and "no" (0.)

2006 Wine competition used "For you, this wine is: Excellent, Very Good, Good, Average, Mediocre."

French 2007 elections used grades "For you, this candidate is: Exceptional, Accomplished, Capable, Average, Limited, or Incompetent."

Voters appear to shun the highest and lowest ratings on a ballot.