[EM] New PR method

[Diego Santos]

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
-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://lists.electorama.com/pipermail/election-methods-electorama.com/attachments/20090218/9efb2637/attachment-0003.htm>