[EM] Multiple Winner Elections

[LAYTON Craig]

Hi Moe,

you wrote:

>What are the best choice(s) of voting system(s)
>for a multiple winner election?
>
>I can believe there could be more than one depending
>on the type of election.
>
>For instance, we will have a 2 person co-chair in an organization,
>where the idea is to balance any opposing factions 
>as they will likely occur.
>
>What would be the best form of election?
>
>I know Approval could be used (taking the top two), 
>but it seems very easily for a faction to have a strategy
>of running multiple candidates.

Forest has a good Approval method, which is much more complicated than just
taking the top two.  What kind of method you can have largely depends on
what kind of resources you've got for counting the votes.  If you're hand
counting, you're really quite restricted on what you can do.

>Cumulative seems a little like overkill, and I'm not sure
>how well it stands up against other systems.

I don't think cumulative is a very acceptable PR system.  It has it's
advantages, but it isn't as good as quota-STV, list propotional
representation, or some hybrid methods (like Forest's advanced Approval
method).  Cumulative is probably better than simple STV, simple Approval,
block voting, limited voting etc...

>I don't see how we could possibly use any form
>of Proportional for this.

I agree, a form of list PR sounds impractical for this scenario.

>And I worry that STV is just as bad as IRV.

It isn't really as bad as IRV, depending on how you count it.  If your
resources are strictly limited, there's always simple STV (knock off the
candidate with the lowest number of votes untill there are 2 left).  This
does have significant problems, especially if you expect one candidate to
get alot of votes and/or a close race for 2nd place.  

You can improve it significantly by adding a droop quota, which will be the
total number of votes, divided by 3 (number of candidates +1), plus one
(ignoring any remaining fraction).  Any candidate who gets this number of
votes is declared elected.  If no candidate has a quota, eliminate the
candidates with the least number of number 1 votes, and transfer those votes
to the number 2 candidate on each ballot.  Continue until a candidate has a
quota.

When a candidate has a quota, you need to distribute the candidate's surplus
votes (ie, if the quota is 300, the candidate gets 400, there are 100
surplus votes to distribute).  The simplest way to distribute is to take a
sample (100 votes at random) and distribute to the next candidate down on
the ballot.  This is okay, with a decent number of votes.  With a small
number of votes, sampling errors are magnified.  This is the best system
that you can count by hand.

For a better distribution of surplus votes, you give every vote a fractional
value.  If the quota is 100, for instance, and the candidate has 200 votes,
then each vote is immediately worth .5. You distribute all the votes, and
keep counting.  With a smallish number of votes, it is possible to do this
by hand (with a calculator), but it is time consuming, and errors can be
made.  If you're doing it by hand, you go through all the votes and mark .5
on them, before distribution.  From now on, when counting the piles of
votes, you need to note what each vote is worth, rather than just counting
votes.  If they get marked again by another fraction, then you have to
multiply them together to get the new value of the vote (although, with only
two candiates, you would only mark ballots once, so it would be relatively
simple to do this count by hand.)

>Please let me know of the best alternative methods we may use, and
>if we did use the system above, should we rank the votes, or use
>something similar to approval voting, etc., for the actual ballot
>and ballot counting.

I'll think about your second scenario.  Do you have a certain number of
seats to be won by affiliated candidates, and a certain number by
unaffiliated candidates?  If not, what do you mean by saying that the top
unaffiliated candidates would be elected first?

Craig