[EM] multiwinner election space plots

[Brian Olson]

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.