[EM] multiwinner election space plots

[Kristofer Munsterhjelm]

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.

Do you have the source for this program, as well?

> 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, see 
http://www.votingmatters.org.uk/ISSUE17/I17P1.PDF ), even if the latter 
is nonmonotonic (to my knowledge).

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.