Greg Nisbet wrote:
So far the following multiwinner methods have been suggested or I know of:
CPOSTV
Schulze STV
QBS (this is what I meant by Proportional Borda, sorry!)
http://en.wikipedia.org/wiki/Quota_Borda_system
QanythingS (look at the description of QBS, it effectively allows a
black box single winner method to be used in place of Borda Count).
Naive Adaptations -- you can do this with just about anything. Not
proportional at all but enh.
STV various ballot transfer rules
IRNRSTV (**)
BordaSTV (**)
Sainte-Lague (and the 1.4 divisor variant)
Largest Rem (various quotas)
D'hondt
All party-flavored methods can be made with open/closed/free lists too
so its great.
SNTV
Limited vote
Block vote
Preferential Block
RRV
PAV
PRV
Cumulative vote
Districted crap
MMP (combination of districted crap and some party alloc.)
Asset Voting (*)
Forest Simmons' methods:
http://www.rangevoting.org/cgi-bin/DoPassword.cgi (I'll include a copy
of the page at the bottom if you don't feel like joining CRV)
I already suggested QPQ, but I think I forgot to mention some others my
simulation program (or a previous vote-counting program) includes.
D'Hondt without lists:
This is a multiwinner method that can be paired with any Condorcet
method. First, elect the winner of that method. Second, redo the
Condorcet matrix, so that all preferences below the winner is
downweighted by f(1). E.g, if A wins and C > B > A > D > E, then D > E
has half the strength of C > E. Run the method again. Remove the winner
from the output social ordering and whoever placed first to the list of
winners.
Next round, downweight the preferences below one or more winners by
f(x), where x is how many winners the highest-ranked candidate of the
pair is below. E.g if A and E are winners and we encounter a ballot of
the type B > A > D > E > F > C, then
B > E has strength f(0)
D > F has strength f(0) * f(1)
F > C has strength f(0) * f(1) * f(2).
Continue in this manner until you have all the winners.
For D'Hondt, f(0) = 1, f(1) = 1/2, f(2) = 1/3.. etc. Sainte-Laguë is
probably better. You could also use additive weighting.
CFPRM: See
http://listas.apesol.org/pipermail/election-methods-electorama.com/2002-November/008855.html
===================
I do need some single winner methods as well to test for QanythingS,
districted crap, and naive crap. I'm not suggesting all [insert large
number] that we have ever discussed. FPTP and Range make the list.
Schulze too. Any other suggestions? (I'd like to limit it to about ten
if that's OK).
A trick here is to make "envelopes" which transform one method into
another. For instance, Eliminate-* (combine with FPTP to get IRV, or
with Borda to get Baldwin), and Average-Eliminate-* (combine with FPTP
to get Carey's Q method).
But if you want to keep the number down.. add one simple Condorcet
method to see if the complexity matters. Say, minimax. Also, Borda (or
some other simple weighted positional method). If you'll support
approval cutoff ballot formats, you could have one or two of those:
UncAAO and MDDA, perhaps Condorcet//Approval.
=======================================
Puzzle #15 (open – multiwinner EP & PR voting systems):
[snip]
That's interesting, and not quite what I thought the method was like
beforehand. It makes sense that the array is limited by the number of
candidates, since ultimately, opinion space can't be rendered any more
accurately.
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