[EM] Multiwinner Methods Request

[Kristofer Munsterhjelm]

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.