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.
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