[EM] Proportional Representation beyond STV?
Alex Small
asmall at physics.ucsb.edu
Tue Jul 8 23:05:02 PDT 2003
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
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