Kotze-Pereira transformation
Replace any ballot which rates the C candidates with scores S1≥S2≥S3≥...≥SC
by these C weighted approval (meaning with {0,1}-scores only) ballots (1,1,1,...,1,1) with weight SC (1,1,1,...,1,0) with weight SC-1-SC ... (1,1,0,...,0,0) with weight S2-S3 (1,0,0,...,0,0) with weight S1-S2
Note: the candidates were ordered by decreasing scores on the ballot under consideration. That assures that all the weights come out positive. For example, the score ballot (9,5,3) in a three-candidate election would be replaced by 3×(1,1,1) + 2×(1,1,0) + 4×(1,0,0).
This "replacement of score ballots with weighted approval ballots" idea was invented by Toby Pereira. A "ballot with weight w" is to be interpreted the same as "w voters cast that ballot." This transform converts scores into approvals so that any method that uses approval ballots can be converted to a method that uses score ballots without having to individually define how to do so for each method.