Chris Benham said: > My second idea is this: Elect the CW (completed however), and then > depending on how many seats there are to be filled, fractionally mark > down some of the ballots according to their contribution to electing the > winner, and taking into account the "wasted" vote. Repeat until the > desired number of candidates are elected. The details of exactly which > ballots to mark down by exactly how much I haven't yet thought about, > but I shouldn't think it is a huge problem.
Some sort of fractional system seems necessary when generalizing single-winner methods (be it IRV, Condorcet, Approval, etc.) to multi-winner races. I'm not sure how to do this in Condorcet, although I seem to recall some posts on this subject a while ago. My best guess: Each time a candidate is elected, determine a "runner-up", i.e. the candidate who would have been elected had our latest winner not also been in the running. Anybody who preferred the newly elected candidate to the runner-up has his ballot marked down by a factor n/(n+1) where n is the number who are now elected. Of course, I haven't thought this through very carefully yet. I put PR systems into 3 main categories: 1) Fractional systems: Generalizations of single-winner methods that involve marking down ballots after a candidate has been elected. STV, Proportional Approval Voting, and Condorcet PR all fit into this category. 2) Plurality systems: SNTV, cumulative voting, limited vote, etc. Just give the voters N votes, specify the maximum number of votes they can give a single candidate, and elect the top S candidates, where S is the number of seats. 3) List systems. Personally, I prefer simplicity over sophistication for public elections, so my preference is list systems for explicitly partisan multi-winner races, and plurality systems for ostensibly non-partisan multi-winner races. But I see virtues in fractional systems when the number of winners is 2 or 3. Alex ---- Election-methods mailing list - see http://electorama.com/em for list info
