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 a voting method into a different voting method.