Multi-winner Condorcet, vs STV

Sorry, but I think we need to think again about our voting system for
the board elections. Condorcet is great for a single-winner election.
However AFAICT the current system for the multi-winner board elections
has a very undesirable majority-takes-all property.

I couldn't find a formal description of the process we use but as I
understand it, we use Condorcet to elect the first seat. Then we
remove the winner from the ballots and rerun Condorcet to elect the
2nd winner, etc.

If we imagine a polarised election, where there are four candidates on
one side A B C D and three candidates on the other side W X Y Z, and
three seats, and every ballot is either an ABCD-ballot (ranks every
ABCD above every WXYZ) or an WXYZ-ballot (ranks every WXYZ above every
ABCD) then a bare majority of ABCDs over WXYZs will get all three of
their candidates elected. This would be quite unfair; a better result
would be to elect two of A B C D and two of W X Y Z.

In less polarised elections we still have the problem that we get a
slate of winners who are very similar to each other. In the extreme
case, if the winning candidate had n identical twins, they would all
win, excluding anyone else. Surely this can't be what we want. We
Would rather have diversity, with minority viewpoints represented.

I don't have a clear suggestion for an improvement to Condorcet to fix
this problem. I did a bit of searching for multi-winner Condorcet and
it seems to be an open research problem.

I think therefore that we should probably hold the next board
elections using STV, which is an established and relatively
hard-to-game system which copes well with multiple-winner elections.

Ian.

Um, I forgot to change some of my threes to fours, in my example:

If we imagine a polarised election, where there are four candidates on
one side A B C D and four candidates on the other side W X Y Z, and
four seats, and every ballot is either an ABCD-ballot (ranks every
ABCD above every WXYZ) or an WXYZ-ballot (ranks every WXYZ above every
ABCD) then a bare majority of ABCDs over WXYZs will get all four of
their candidates elected. This would be quite unfair; a better result
would be to elect two of A B C D and two of W X Y Z.

Ian.

Ian is correct: using the top K Condorcet winners is a very poor
multiwinner election system, if the goal is to have proportional
representation.

Having studied this a bit, I would suggest that the best currently
available multiwinner election system for our purposes here, i.e., for
proportional representation, is Reweighted Range Voting, see

http://www.rangevoting.org/RRV.html

for details. Advantages: with RRV it is really simple to cast a valid
ballot, ballots can be quite expressive, it is easy to explain how to
vote, and it is quite simple to calculate the winners. The main
disadvantage (cannot do per-district tallying) is not a problem for us.

--Barak.

On Thu, Dec 10, 2009 at 09:15:11PM +0000, Barak A. Pearlmutter wrote:
> Ian is correct: using the top K Condorcet winners is a very poor
> multiwinner election system, if the goal is to have proportional
> representation.
>
>
> Having studied this a bit, I would suggest that the best currently
> available multiwinner election system for our purposes here, i.e., for
> proportional representation, is Reweighted Range Voting, see
>
> http://www.rangevoting.org/RRV.html
>
> for details. Advantages: with RRV it is really simple to cast a valid
> ballot, ballots can be quite expressive, it is easy to explain how to
> vote, and it is quite simple to calculate the winners. The main
> disadvantage (cannot do per-district tallying) is not a problem for us.

You claim "easy to explain how to vote".

Really?

How do I choose the numbers for giving my vote the maximum desired
effect?

> --Barak.

cu
Adrian

--

"Is there not promise of rain?" Ling Tan asked suddenly out
of the darkness. There had been need of rain for many days.
"Only a promise," Lao Er said.
Pearl S. Buck - Dragon Seed

Barak A. Pearlmutter writes ("Re: Multi-winner Condorcet, vs STV"):
> Having studied this a bit, I would suggest that the best currently
> available multiwinner election system for our purposes here, i.e., for
> proportional representation, is Reweighted Range Voting, see
> http://www.rangevoting.org/RRV.html

I'm strongly opposed to range voting. Range voting means you need to
know where the likely controversies are to effectively cast your vote.
This is because you need to know how other people are likely to vote
to know where to "spend" your influence.

So the extra expressiveness (being able to weight some preferences as
more important than others) is not a benefit in this case; it is a
hindrance because the appropriate way to vote so as to maximise the
desired outcome becomes hard to discover and compute.

Or to put it another way: range voting inherently implies making
tactical voting important. Eliminating the need for voters to vote
tactically rather than honestly should be high up on our list of
desirables for a voting system.

Hence my suggestion that we should use STV. STV does have some edge
cases and problems but they're rare and largely theoretical. With STV
voters can just rank their candidates and can safely do so without
considering the behaviour of the other voters, and the results are
reasonably proportional and rarely anomalous.

Ian.