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.
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```
13 Aug 16:18 2009

### 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
```

14 Aug 03:04 2009

### Re: multiwinner election space plots

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

It can also serve as a standing advisory network, where electors may
```

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:
```

14 Aug 08:29 2009

### 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:

```

14 Aug 06:15 2009

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,

<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

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'?

of  Clones?

I look forward to hearing your clarification.

Chris  Benham

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```
14 Aug 09:20 2009

### 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
>
>
> 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

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```
14 Aug 15:42 2009

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

<snip>

Chris Benham

Find local businesses and services in your area with Yahoo!7 Local. Get started.
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```
14 Aug 15:45 2009

### 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
>

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.
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```
14 Aug 16:01 2009

```Hi,

Kevin

--- En date de : Ven 14.8.09, Kevin Venzke <stepjak <at> yahoo.fr> a écrit :
> De: Kevin Venzke <stepjak <at> yahoo.fr>
> 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

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```

Gmane