This is an old version of the "Proportional runoff" algorithm. Please check out the new version
On this page, I want to present an idea for a simple vote counting system producing proportional rankings. It is also possible to use the system as a replacement for STV (single transferrable vote), by using the first ranks up to the number of seats.
Each ballot contains an ordered list of candidates. Let P be a big integer constant, e.g. 1000000. Proceed as follows:
Ballot distribution with quota Q:
The method is invulnerable to Woodall Free Riding, as the count is restarted after a candidate gets eliminated. However it is NOT invulnerable to Hylland Free Riding and Vote Management. There are other systems, which are much better in this regard, i.e. the more complicated Schulze STV method can prevent Hylland Free Riding and Vote Management, except in those cases where the droop proportionality would have been violated otherwise.
Log of counting:
Non-eliminated candidates: A; B; C Initial ballot weight: 1000000 Quota: 2222222 Used ballot weight: 740741 Remaining ballot weight: 1000000 - 740741 = 259259 Votes for candidate A: 0 + 2 * 740741 = 1481482 Votes for candidate B: 0 + 2 * 740741 = 1481482 Votes for candidate C: 0 + 3 * 740741 = 2222223 (passed) Used ballot weight: 148148 Remaining ballot weight: 259259 - 148148 = 111111 Votes for candidate A: 1481482 + 2 * 148148 = 1777778 Votes for candidate B: 1481482 + 5 * 148148 = 2222222 (passed) Votes for candidate C: 2222223 (passed) Used ballot weight: 111111 Remaining ballot weight: 111111 - 111111 = 0 Votes for candidate A: 1777778 + 4 * 111111 = 2222222 (passed) Votes for candidate B: 2222222 (passed) Votes for candidate C: 2222223 (passed) All candidates have passed. Ballot weight exhausted. No loser. Non-eliminated candidates: A; B; C Initial ballot weight: 1000000 Quota: 2222223 Used ballot weight: 740741 Remaining ballot weight: 1000000 - 740741 = 259259 Votes for candidate A: 0 + 2 * 740741 = 1481482 Votes for candidate B: 0 + 2 * 740741 = 1481482 Votes for candidate C: 0 + 3 * 740741 = 2222223 (passed) Used ballot weight: 148149 Remaining ballot weight: 259259 - 148149 = 111110 Votes for candidate A: 1481482 + 2 * 148149 = 1777780 Votes for candidate B: 1481482 + 5 * 148149 = 2222227 (passed) Votes for candidate C: 2222223 (passed) Used ballot weight: 111110 Remaining ballot weight: 111110 - 111110 = 0 Votes for candidate A: 1777780 + 4 * 111110 = 2222220 Votes for candidate B: 2222227 (passed) Votes for candidate C: 2222223 (passed) Ballot weight exhausted. Eliminating loser: A Non-eliminated candidates: B; C Initial ballot weight: 1000000 Quota: 3000000 Used ballot weight: 750000 Remaining ballot weight: 1000000 - 750000 = 250000 Votes for candidate B: 0 + 4 * 750000 = 3000000 (passed) Votes for candidate C: 0 + 3 * 750000 = 2250000 Used ballot weight: 250000 Remaining ballot weight: 250000 - 250000 = 0 Votes for candidate B: 3000000 (passed) Votes for candidate C: 2250000 + 3 * 250000 = 3000000 (passed) All candidates have passed. Ballot weight exhausted. No loser. Non-eliminated candidates: B; C Initial ballot weight: 1000000 Quota: 3000001 Used ballot weight: 750001 Remaining ballot weight: 1000000 - 750001 = 249999 Votes for candidate B: 0 + 4 * 750001 = 3000004 (passed) Votes for candidate C: 0 + 3 * 750001 = 2250003 Used ballot weight: 249999 Remaining ballot weight: 249999 - 249999 = 0 Votes for candidate B: 3000004 (passed) Votes for candidate C: 2250003 + 3 * 249999 = 3000000 Ballot weight exhausted. Eliminating loser: C Non-eliminated candidates: B Initial ballot weight: 1000000 Quota: 7000000 Used ballot weight: 1000000 Remaining ballot weight: 1000000 - 1000000 = 0 Votes for candidate B: 0 + 7 * 1000000 = 7000000 (passed) All candidates have passed. Ballot weight exhausted. No loser. Non-eliminated candidates: B Initial ballot weight: 1000000 Quota: 7000001 Used ballot weight: 1000000 Remaining ballot weight: 1000000 - 1000000 = 0 Votes for candidate B: 0 + 7 * 1000000 = 7000000 Ballot weight exhausted. Eliminating loser: B
I'd appreciate feedback on this idea (see Impressum).
(published 2011-11-08, last updated: 2011-12-11)