Brian Olson | 13 Aug 12:46 2009

multiwinner election space plots

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.

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.
----
Election-Methods mailing list - see http://electorama.com/em for list info

Kristofer Munsterhjelm | 13 Aug 16:18 2009
Picon

Re: multiwinner election space plots

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 <at> lists.electorama.com/msg04001.html 
) or Quota-Preferential by Quotient (QPQ, see 
(Continue reading)

Abd ul-Rahman Lomax | 14 Aug 03:04 2009

Re: multiwinner election space plots

At 06:46 AM 8/13/2009, Brian Olson wrote:
>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.

Well, there is reweighted Range Voting, as to a theoretical system. 
As to one in actual practice, STV is pretty good. Those 
discontinuities are largely down in the noise, the more winners there 
are, the less important they are, they mostly affect the last 
determined winners.

But that assumes full ranking, and Lewis Carroll (Charles Dodgson), 
writing in 1884, realized that most common voters would really only 
know who their favorite was. So he hit upon what a number of writers 
on this list called Candidate Proxy and Warren Smith called Asset 
Voting. So Dodgson proposed that exhausted votes may be exercised by 
the favorite on the list. (I'm not sure of exact mechanism, I've 
never seen a copy of the original paper, only commentary on it.) It's 
actually better than a mere election method, because we can think of 
the secret ballot, if secret ballot is used, as creating a college of 
public electors, known individuals controlling blocks of votes, and 
that can be a standing college, used for many different purposes, 
including replacement of vacated seats midterm. The College either 
meets after the balloting, or electors may recast votes as needed by 
registering them. It can be used to create a floating-district but 
still geographically based Assembly, if electors choose to cast their 
votes in precinct blocks, while another seat may represent scattered 
votes over the whole jurisdiction.

It can also serve as a standing advisory network, where electors may 
(Continue reading)

Brian Olson | 14 Aug 04:55 2009

Re: multiwinner election space plots


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
(Continue reading)

Kristofer Munsterhjelm | 14 Aug 08:29 2009
Picon

Re: multiwinner election space plots

Brian Olson wrote:
> 
> 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.

So, basically, if you have a vote of the type A: 100, B: 50, C: 20, and 
there are two seats, you get:

(Continue reading)

Chris Benham | 14 Aug 06:15 2009
Picon

'Shulze (Votes For)' definition?

Marcus,
 
I have some questions about your draft (dated  23 June 2009)  Shulze method
paper, posted:
 
On page 13 you define some of the ways of measuring defeat strengths,
two of which are  "Votes For" and  "Votes Against":
 
<snip>
 

Example 5 (

votes for): When the strength of the pairwise defeat ef is measured by votes for,

then the strength is measured primarily by the absolute number N[e,f] of votes for candidate e.

(N[e,f],N[f,e]) for (N[g,h],N[h,g]) if and only if at least one of the following conditions is satisfied:

1. N[e,f] > N[g,h]. 2. N[e,f] = N[g,h] and N[f,e] < N[h,g].

 

Example 6 (votes against): When the strength of the pairwise defeat ef is measured by votes against,
then the strength is measured primarily by the absolute number N[f,e] of votes for candidate f.

(N[e,f],N[f,e]) against (N[g,h],N[h,g]) if and only if at least one of the following conditions is satisfied:
1. N[f,e] < N[h,g]. 2. N[f,e] = N[h,g] and N[e,f] > N[g,h].

 

<snip>

 

I am a little bit confused as to the exact meaning of the phrase "the absolute number ..of

votes for candidate E".

 

Does "the number of votes for E" mean 'the number of ballots on which E is ranked above
at least one other candidate'?

 

Or does it mean something that can be read purely from the pairwise matrix?

Does it mean 'the sum of all the entries in the pairwise matrix that represent pairwise votes for E'?

Do the two methods 'Schulze(Votes For)' and  'Shulze(Votes Against)'  meet  Independence

of  Clones?

I look forward to hearing your clarification.



Chris  Benham

 


Find local businesses and services in your area with Yahoo!7 Local. Get started.
----
Election-Methods mailing list - see http://electorama.com/em for list info
Kevin Venzke | 14 Aug 09:20 2009
Picon

Re: 'Shulze (Votes For)' definition?

Hi Chris,

--- En date de : Jeu 13.8.09, Chris Benham <cbenhamau <at> yahoo.com.au> a écrit :
> I am a little bit confused as to the
> exact meaning of the phrase "the absolute number ..of
> 
> votes for candidate E".
>  
> Does "the number of votes for
> E" mean 'the number of ballots on which E is ranked
> above
> at least one other candidate'?
>  
> Or does it mean something that can be
> read purely from the pairwise matrix?

It's the latter, read from the matrix. "Absolute number" is in contrast to
using margin or ratio.

Kevin Venzke

      
----
Election-Methods mailing list - see http://electorama.com/em for list info

Chris Benham | 14 Aug 15:42 2009
Picon

'Shulze (Votes For)' definition?

Kevin,
 
> Or does it mean something that can be
> read purely from the pairwise matrix?

"It's the latter, read from the matrix. "Absolute number" is in contrast to
using margin or ratio."
 
Thanks for that, but it isn't the concept of "absolute number" that I'm having
trouble with.
 
What I don't understand is the difference between "winning votes" (which I'm
familiar with) and "votes for",  as they are both defined on page 13 of Marcus
Shulze's paper, pasted below.


http://m-schulze.webhop.net/schulze1.pdf
 
<snip>
 

Example 3 (

winning votes): When the strength of the pairwise defeat ef is measured

by winning votes, then the strength is measured primarily by the absolute number

N[e,f] of votes for the winner of this pairwise defeat.


 

<snip>

 

Example 5 (

votes for): When the strength of the pairwise defeat ef is measured by
votes for, then the strength is measured primarily by the absolute number N[e,f] of

votes for candidate e.

 

<snip>


Chris Benham

Find local businesses and services in your area with Yahoo!7 Local. Get started.
----
Election-Methods mailing list - see http://electorama.com/em for list info
Kristofer Munsterhjelm | 14 Aug 15:45 2009
Picon

Re: 'Shulze (Votes For)' definition?

Chris Benham wrote:
> What I don't understand is the difference between "winning votes" (which I'm
> familiar with) and "votes for",  as they are both defined on page 13 of 
> Marcus
> Shulze's paper, pasted below.
> 
> 
> http://m-schulze.webhop.net/schulze1.pdf
>  
> <snip>
>  
> 
> Example 3 (/winning votes/): When the strength of the pairwise defeat 
> /ef /is measured
> 
> by /winning votes/, then the strength is measured primarily by the 
> absolute number
> 
> N[/e/,/f/] of votes for the winner of this pairwise defeat.
> 
> Example 5 (/votes for/): When the strength of the pairwise defeat /ef 
> /is measured by
> /votes for/, then the strength is measured primarily by the absolute 
> number N[/e/,/f/] of
> 
> votes for candidate /e/.

I'm not Markus (or Kevin), but "votes for" sounds like pairwise 
opposition. That is, the strength of "e beats f" is the number of voters 
who prefer e to f, whereas for wv, the strength of "e beats f" is the 
number of voters who prefer e to f if this is greater than the number of 
voters who prefer f to e, otherwise zero.
----
Election-Methods mailing list - see http://electorama.com/em for list info

Kevin Venzke | 14 Aug 16:01 2009
Picon

Fw: Re: "Votes For" versus "Winning Votes"

Hi,

I had written this privately.

Kevin

--- En date de : Ven 14.8.09, Kevin Venzke <stepjak <at> yahoo.fr> a écrit :
> De: Kevin Venzke <stepjak <at> yahoo.fr>
> Objet: Re: "Votes For" versus "Winning Votes"
> À: "Chris Benham" <cbenhamau <at> yahoo.com.au>
> Date: Vendredi 14 Août 2009, 8h26
> Hi Chris,
> 
> With WV you can't trace a beatpath through a pairwise loss.
> I believe that
> is the only difference.
> 
> Kevin

      
----
Election-Methods mailing list - see http://electorama.com/em for list info


Gmane