This is the algorithm of my PR method. I replaced the elimination of candiates from my previous idea to "preference collapsing" after the questions from Kristofer Munsterhjelm:
1. Calculate the quota (e. g. Droop, Newland-Britton, etc.) 2. Count the sum of each candidate, initially set to zero. 3. In the first stage, add to the sum of each candidate the number of votes where this candiate is the first preference. 4. If some candidate reaches the quota at the first stage, this candidate is elected. Transfer the surplus votes like in Gregory STV. 5. If not, add the number of votes to each candidate where he/she is the second (2nd stage), third (3rd stage) and so on until some candidate reaches the quota. 6. Collapse the votes of the candidate with the least sum: the 1st and 2nd preferences are considered identically as 1st on new counts, the 3rd preference is considered 2nd, and so on. 6a. The same candidate cannot have his/her votes more than one time until some candidate is elected. 6b. If in some vote there is no more preferences to be collapsed, subtract this vote from the quota expression. 7. Go to 1. I used this example from http://lists.electorama.com/pipermail/election-methods-electorama.com/2003-August/010602.html: 5028 votes, 2 seats: 1248: A>E>B>C>D 1236: B>E>C>D>A 1224: C>E>D>B>A 1212: D>E>B>C>A 36: E>A>B>D>C 36: E>C>D>B>A 36: E>D>C>B>A Quota = 1676 1st stage - A: 1248, B: 1236, C: 1224, D: 1212, E: 108 2nd stage - A: 1284, B: 1236, C: 1260, D: 1248, E: 5028 E reaches the quota. B has the least sum and its votes are collapsed: 1248: A>E>B>C>D 1236: (B>E) >C>D>A 1224: C>E>D>B>A 1212: D>E>B>C>A 36: E>A>B>D>C 36: E>C>D>B>A 36: E>D>C>B>A 1st stage - A: 1248, B: 1236, C: 1224, D: 1212, E: 1344 2nd stage - A: 1284, B: 1236, C: 2496, D: 1248, E: 5028 E reaches the quota. D has the least sum and its votes are collapsed: 1248: A>E>B>C>D 1236: (B>E) >C>D>A 1224: C>E>D>B>A 1212: (D>E) >B>C>A 36: E>A>B>D>C 36: E>C>D>B>A 36: E>D>C>B>A 1st stage - A: 1248, B: 1236, C: 1224, D: 1212, E: 2556 E reaches the quota at the first stage, then it is elected. After tranfer of surplus votes: 1248: A>B>C>D 425.54: B>C>D>A 1224: C>D>B>A 417.28: D>B>C>A 12.39: A>B>D>C 12.39: C>D>B>A 12.39: D>C>B>A 1st stage - A: 1260.39, B: 425.54, C: 1236.39, D: 429.67 2nd stage - A: 1260.39, B: 2103.21, C: 1674.32, D: 1666.06 B and C reach the quota. A has the least sum and its votes are collapsed: 1248: (A>B) >C>D 425.54: B>C>D>A 1224: C>D>B>A 417.28: D>B>C>A 12.39: (A>B) >D>C 12.39: C>D>B>A 12.39: D>C>B>A 1st stage - A: 1260.39, B: 1685.93, C: 1236.39, D: 429.67 B reaches the quota at the first stage, then it is elected. Final outcome: {E, B}. Plain STV elects {B, C} ________________________________ Diego Santos
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