On Aug 13, 2009, at 9:18 AM, Kristofer Munsterhjelm wrote:
Brian Olson wrote:
http://bolson.org/voting/sim_one_seat/20090810/
I think a few of these plots show Single Transferrable Vote
behaving badly in the same ways IRV does, with discontinuities and
irregular solution spaces.
I also ran Condorcet and IRNR using combinatoric expansion.
Combinatoric variants of single winner election methods adapt to
multiwinner situations by enumerating all possible winning sets of
the available choices and using a simulated voter's preferences on
the choices in each set to determine a preference for each winner-
set. Voting on the n-choose-k preferences for winner-sets then
procedes as for a single-winner election.
How does the combinatorial expansion work? The way you describe it,
it seems like it's general purpose - that you could combine it with
any single-winner method.
It's pretty general purpose but works well when there are ratings
backing each voter. It's easy to derive a rating for a winner-set by
just adding up the individual ratings. There would be more ties if
there was an initial conversion from rankings to ratings, as 1st + 4th
would be equal to 2nd + 3rd.
Do you have the source for this program, as well?
There is a public read-only subversion repository, check it out with:
svn co http://voteutil.googlecode.com/svn/sim_one_seat
or browse at
http://code.google.com/p/voteutil/source/browse/sim_one_seat/
I think based on this I'm going to have to think more about making
native multiwinner methods. Combinatoric expansion gets pretty
expensive for large numbers of choices or seats to elect. I had
been kinda resigned to STV being the state of the art in
multiwinner methods, but we seriously ought to be able to do better.
You could try implementing my DAC/DSC-based method (see http://www.mail-archive.com/election-methods@lists.electorama.com/msg04001.html
) or Quota-Preferential by Quotient (QPQ, seehttp://www.votingmatters.org.uk/ISSUE17/I17P1.PDF
), even if the latter is nonmonotonic (to my knowledge).
Thanks for the links. Those both seem to be party-based proportional
systems and I have so far been going (for partly ideological and
partly technical reasons) for party-agnostic candidate-based systems.
But perhaps I have misunderstood 'setwise highest'. I must have missed
these the first times around and am now reading up and thinking about
them more.
It may also be that the construction of the voter preference
profiles (Gaussian centered on a particular point) means that the
ideal maps will look like Condorcet majoritarian elections. If so,
they won't help distinguish proportional methods from
disproportional ones, only show errors like clone problems.
Proportionality might show itself somewhat like the distortions Borda
counts show in single winner elections:
http://bolson.org/voting/sim_one_seat/zoomout/4a_Condorcet.png
http://bolson.org/voting/sim_one_seat/zoomout/4a_Borda.png
http://bolson.org/voting/sim_one_seat/zoomout/4c_Condorcet.png
http://bolson.org/voting/sim_one_seat/zoomout/4c_Borda.png
(above from this page http://bolson.org/voting/sim_one_seat/zoomout/ )
The lines shift a bit and twist in weird ways, but have basically the
same shape and none of the IRV discontinuities.
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