Multi-winner Condorcet, vs STV

From: Ian Jackson <ijackson(at)chiark(dot)greenend(dot)org(dot)uk>
To: spi-general(at)lists(dot)spi-inc(dot)org
Subject: Multi-winner Condorcet, vs STV
Date: 2009-12-08 16:59:16
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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.



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