1 May 07:21 2006

### Looking for a little voting insight...

```I am putting together a web site which will, in addition to some other things,
illustrate different voting methods. I have approval and plurality voting
done and was starting to look at Condorcet voting and a couple of questions
came up. BTW I will probably use the rubyvote code as a starting point.

Questions:

1. Rubyvote has pure condorcet and cloneproof schwartz sequential available. I
want to keep things simple. Does it matter which method I choose? Is there a

2. Votes will be updated on the fly - does this distort or invalidate the
Condorcet method in any way? I.e. the voter can see the current results and
use that information in choosing their vote(s).

This is really only for fun but I am curious to hear whatever opinions people
have.

By the way it has been interesting to play with approval vs plurality voting
and to notice my own response.  Having both available now leaves me quite
annoyed when faced with a plurality only vote. However I'm noticing in some
approval voting scenarios I really wish I could articulate a hierarchy of
preference.

Matt
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1 May 21:29 2006

### Re: Proportional Condorcet Voting

```Antonio Oneala lamented that proportional Condorcet methods tend to be intractable.  This is because if
there are N candidates from which to choose K winners, there are  C(N,K)=N!/(K!*(N-K)!) subsets to be
compared pairwise, for a total of  C(C(N,K),2) pairwise comparisons of subsets.

However, suppose that instead of comparing all C(N,K) of the K candidate subsets, we just compare all
submitted proposals, including those sets that would be elected by STV under various rules (Droop Quota,
etc.).  There might be ten thousand such proposals. But that would only require  C(10000, 2) = 49995000
comparisons, a few seconds of CPU time on a second rate computer.

Forest
```
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```
1 May 21:51 2006

### Re: Proportional Condorcet Voting

```>From a theoretical standpoint, this may look intractactable, but for any
finite N,K the problem is solvable in polynomial time in a manner that
depends only upon N, K, and the number of voters. From a practical
standpoint, the calculation is not difficult for up to N,K=293 by
demonstation (I do that daily in my report of records vs common opponents
for division 1 american college baseball teams on a Dell laptop. It takes a
few minutes to run only because it is also producing 294 web pages, and all
that I/O slows it down).

_____

From: election-methods-bounces <at> electorama.com
[mailto:election-methods-bounces <at> electorama.com] On Behalf Of Simmons,
Forest
Sent: Monday, May 01, 2006 2:29 PM
To: election-methods <at> electorama.com
Subject: Re: [EM] Proportional Condorcet Voting

Antonio Oneala lamented that proportional Condorcet methods tend to be
intractable.  This is because if there are N candidates from which to choose
K winners, there are  C(N,K)=N!/(K!*(N-K)!) subsets to be compared pairwise,
for a total of  C(C(N,K),2) pairwise comparisons of subsets.

However, suppose that instead of comparing all C(N,K) of the K candidate
subsets, we just compare all submitted proposals, including those sets that
would be elected by STV under various rules (Droop Quota, etc.).  There
might be ten thousand such proposals. But that would only require  C(10000,
2) = 49995000 comparisons, a few seconds of CPU time on a second rate
computer.

```

1 May 21:56 2006

### Re: Proportional Condorcet Voting

```At 03:29 PM 5/1/2006, Simmons, Forest wrote:
>However, suppose that instead of comparing all C(N,K) of the K
>candidate subsets, we just compare all submitted proposals,
>including those sets that would be elected by STV under various
>rules (Droop Quota, etc.).  There might be ten thousand such
>proposals. But that would only require  C(10000, 2) = 49995000
>comparisons, a few seconds of CPU time on a second rate computer.

Yes, the objections to Condorcet proposals based on computational
intractability are pretty silly, based only on a theoretical idea
that all possible rankings will exist in the ballot population. But
the ballot population is a limited set, with almost certainly a high
degree of reduncancy. Systems that require all voters to rank all
candidates make it worse, to be sure, but even that will have a lot
of redundancy in it.

However, I'm not sure why one needs Condorcet Voting for PR.

Asset Voting should create a very accurate, non-party-list PR
assembly rather directly. Asset Voting, though, requires a
deliberative or bargaining step, which is a rather new idea, as the
election method itself does not suffice, without candidate action
after the election, to determine all the winners (it only determines
those who gain the quota in the initial balloting).

However, if Published Rankings are provided by candidates prior to
the poll and are used to automatically reassign votes, it might be
possible to have direct winner determination.

All excess or unused votes would be subject to reassignment. There
```

1 May 11:14 2006

### Re: Looking for a little voting insight...

```Dear Matthew Welland,

you wrote (30 April 2006):

> Rubyvote has pure condorcet and cloneproof schwartz
> sequential available.

At Wikipedia, "pure Condorcet" is called "Minimax
Condorcet":

http://en.wikipedia.org/wiki/Minimax_Condorcet

At Wikipedia, "cloneproof Schwartz sequential dropping"
is called "Schulze method":

http://en.wikipedia.org/wiki/Schulze_method

******************************************

You wrote (30 April 2006):

> I want to keep things simple.
> Does it matter which method I choose?

Yes, it does matter. Minimax and Schulze are different
methods.

Example:

3   A > B > D > C
```

1 May 23:52 2006

### Re: Proportional Condorcet Voting

"Simmons, Forest" <simmonfo <at> up.edu> wrote:
Antonio Oneala lamented that proportional Condorcet methods tend to be intractable. This is because if there are N candidates from which to choose K winners, there are C(N,K)=N!/(K!*(N-K)!) subsets to be compared pairwise, for a total of C(C(N,K),2) pairwise comparisons of subsets.

However, suppose that instead of comparing all C(N,K) of the K candidate subsets, we just compare all submitted proposals, including those sets that would be elected by STV under various rules (Droop Quota, etc.). There might be ten thousand such proposals. But that would only require C(10000, 2) = 49995000 comparisons, a few seconds of CPU time on a second rate computer.

Forest
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After reading up on the CPO-STV method, the mehtod I've just come up with actually seems to be simpler.  CPO-STV involves a complicated comparison of outcomes and the transferring of all votes to certain areas in each of these outcomes; mine only involves a complicated comparison of outcomes, giving a score to each outcome based on how many candidates are preferred more than the other outcome in the score according to the D'Hondt or Webster quotas, adding all of these up, declaring a pairwise winner, and then comparing all pairwise competitions to see which outcome won the most pairwise proportional competitions.  Wait.  That's more steps.  Oh well.  It is, at least, monotonic, and the direct application of the quota seems better than the use of the transferrable vote as a quota.

As for the other reply to my thread, I'm not a fan of asset either.  I have a feeling it will enforce party structures, as a candidate inside of a party is far more likely to give it to another candidate in the party than to and independent.  It also has the problem that a lot of systems do; it doesn't increase the amount of voting power per each voter to accomodate more candidates.  Therefore, it will lead probably lead to factionalization, or at least cannot handle more parties than there are seats.  I've come up with a formula, where V is the amount of voting power per a voter, and C is the amount of candidates.  The formula is, easily enough, C = V.  If the voting system keeps V stable as C increases, then vote-splitting will result.  If it adds more C then V as C increases, then teaming will result.  For instance, Plurality keeps V stable as C increases (as you always have only one vote), approval and Condercet increase V in proportion to C, and Borda increases V at a faster rate than C.  Asset seems to fall into the plurality situation, although it is a bit less vulnerable.  However, a moderate who has 20 votes as compared to the polar candidate thirty votes doesn't have much leeway to convince the other guys to send votes to him, his only choice would probably be to send his votes to the lesser of two evils.

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2 May 01:28 2006

### Re: Proportional Condorcet Voting

```At 05:52 PM 5/1/2006, Antonio Oneala wrote:

>As for the other reply to my thread, I'm not a fan of asset
>either.  I have a feeling it will enforce party structures, as a
>candidate inside of a party is far more likely to give it to another
>candidate in the party than to and independent.

Sure. And a voter is more likely to vote for candidates who belong to
the voter's favorite party. But the question is whether or not Asset
would "enforce" such structures and strictures, or would it make it
possible to move beyond them. Since Asset systems (Asset as
effectively free proxy voting or Published List) give the power
directly to the candidates, I strongly doubt that it will increase
party power and factionalism. Rather, when a candidate has excess
votes, that candidate will assign them where he or she sees will best
advance his or her interests, which are a proxy for the interests of
the voters who chose that candidate. If the candidate wants to
increase his or her party's power, that's what will be done, I'd presume.

But Asset makes it possible for candidates to run *without* party
affiliation. Normally, under every other voting system, if the
candidate can't make the quota, that's just plain suicide for the
voters and the candidate. Voting for the candidate effectively takes
the votes out of the system, making them irrelevant. But with Asset,
such votes aren't lost. They will normally be recast to create
winners at least friendly to the interests of the transferring candidates.

What I'd see Asset as likely doing is increasing the *personal* power
of candidates as distinct from parties. But at the same time, the
number of active and significant candidates would likely increase greatly.

>  It also has the problem that a lot of systems do; it doesn't
> increase the amount of voting power per each voter to accomodate
> more candidates.

I really don't understand this. Each voter has divisible voting power
in FAAV and in the original Asset. The number of candidates does not
really matter. The voter's vote is not wasted if it is cast for one
candidate, whether or not that candidate ultimately gains a seat. And
if the voter votes for ten, none of these fractions is lost unless
the voter votes for someone who fails to transfer them. And this
would be an action for which a candidate can and would be held
accountable. If I voted for Bozo, I'd really want to know why Bozo
let my votes die without reaching a winner!

Under Asset, votes would be traceable. If a candidate transferred all
of his or her votes to someone else, I'd have a very reasonable basis
for considering that person *my* representative, since my vote very
specifically brought that person toward the quota.

Ideally, under Asset, the quota can be very precisely V/N, and each
candidate ends up being elected by exactly the quota, excepting for
very minor roundoff error and the few votes lost. I've suggested that
seats remain vacant if no remaining candidate reaches the quota; if
it is allowed to be elected without the quota, if perhaps, say, the
last seat is won by the remaining candidate with a majority of the
vote, this would encourage intransigence by that candidate....

> least cannot handle more parties than there are seats.

Well, duh! Asset is *non-party* PR. Of course it can't handle more
parties than seats! It doesn't handle parties at all, not as part of
the system. If candidates choose to recast their votes within
parties, that's allowed. But it is not required. Party affliliation
is irrelevant to the method.

>   I've come up with a formula, where V is the amount of voting
> power per a voter, and C is the amount of candidates.  The formula
> is, easily enough, C = V.

If all voters have equal voting power, then it does not matter if
they have 1 or many votes.

>   If the voting system keeps V stable as C increases, then
> vote-splitting will result.

So? Under Asset, votes are kept whole or split. It does not matter if
one is splitting 10 votes or 1 vote; the only difference is that with
the former the total vote -- and the quota -- are multiplied by ten.

I'm not sure that the terminal simplicity of FAAV has been
understood. Every voter has 1 vote, and they may divide it among as
many candidates as they like. By voting for a candidate, they are
assigning a fraction of their vote to the candidate, the fraction is
of the form 1/N, where N is the number of votes they cast.

*They have exactly what was suggested: as many "votes" as
candidates.* But because all voters should be equal, no matter how
many votes they cast, the votes are normalized to a *total* of one
vote per voter.

(In standard Approval, the votes are not divided because standard
Approval is a single-winner system and the only votes that count in
the end are those cast for a winner. All other votes become moot.
the winner. They are moot; had they not been cast, the outcome would
not change. This is why standard Approval is, in fact, "one-person,
one-vote," in spite of charges made by some against it.)

>   If it adds more C then V as C increases, then teaming will result.

What will happen with Asset, certainly if it is free Asset, i.e., the
original proposal, not Published List, is that candidates who do not
reach the quota will negotiate with each other -- and with candidates
winners. So minor parties can still gain a seat by essentially
agreeing to share it, with a mutually acceptable winner. (I'd allow
candidates to recast their votes outside the original candidate list,
precisely to enable such compromises, seeking to find compromise
winners mutually acceptable to "losers," who, since they recast votes
to create a desired winner, are not quite losers in the same sense as today!

>   For instance, Plurality keeps V stable as C increases (as you
> always have only one vote), approval and Condercet increase V in
> proportion to C, and Borda increases V at a faster rate than
> C.  Asset seems to fall into the plurality situation, although it
> is a bit less vulnerable.

I really don't think Asset has been understood here.

>   However, a moderate who has 20 votes as compared to the polar
> candidate thirty votes doesn't have much leeway to convince the
> other guys to send votes to him, his only choice would probably be
> to send his votes to the lesser of two evils.

If you are running Asset for single winner, what would you expect?
However, even in that case you'd really need to look at the total
election results; what was stated here is not enough to even begin to
understand the situation. "The polar candidate"? There would
presumably be two polar candidates, in this single-winner situation.
And then the moderate would be able to choose, indeed, the lesser of
two evils. But what if the rules don't allow a winner without a

(I wonder why there is only one moderate.... Asset would make it
feasible to run for office without campaigning. Campaigns are
necessary because votes are totally wasted if they don't create a
winner. Once one has eliminated vote-wasting, people could simply
declare candidacies and allow those who trust them to vote for them.
Right now, that would be simply insanity.)

But we were talking about multiwinner PR, where "moderate" does not
carry the same meaning, and where the goal is to distribute
representation, not to have a winner and a bunch of losers. I have
yet to see any PR proposal that even approaches Asset in clear
democratic function....

This is the real beauty of Asset. The voters don't have to know all
the candidates; it is enough that they know and trust one. Presumably
a broadly-trusted candidate will know the other candidates reasonably well.

Some don't like this concentration of power, but the fact is that the
concentration takes place under other systems, but it is not by the
free and direct choice of the voters, it rather takes place in the
halls of the parties and those who fund elections.

What I'm trying to encourage, ultimately, is the concept that we can
*choose* our representatives, which is quite distinct from trying to
get them elected. Proxy representation is this, purely. And, beyond
that, I'm trying to encourage the choosing of proxies who are
personally known to the voters, who have direct communication with
the voters. Which requires, in a large jurisdiction, delegable proxy,
so that voters can communicate directly with their direct proxies,
and the direct proxies can communicate directly with *their* direct
proxies, etc.

It is a phone tree generalized into an organizational structure.
Fractal democracy.

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```
2 May 02:45 2006

### Re: Proportional Condorcet Voting

It's not a question of whether the method can be quickly worked out by a computer.  It's a question of whether the method is transparent enough for an average voter to look at a small set of data and quickly work out who the proper winner is.

Alex Small

Abd ul-Rahman Lomax wrote:
Date: Mon, 01 May 2006 15:56:10 -0400
From: Abd ul-Rahman Lomax
Subject: Re: [EM] Proportional Condorcet Voting
To: "Simmons, Forest" ,

Yes, the objections to Condorcet proposals based on computational
intractability are pretty silly, based only on a theoretical idea
that all possible rankings will exist in the ballot population. But
the ball ot population is a limited set, with almost certainly a high
degree of reduncancy. Systems that require all voters to rank all
candidates make it worse, to be sure, but even that will have a lot
of redundancy in it.

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2 May 03:13 2006

### Re: Proportional Condorcet Voting

```At 08:45 PM 5/1/2006, Alex Small wrote:
>It's not a question of whether the method can be quickly worked out
>by a computer.  It's a question of whether the method is transparent
>enough for an average voter to look at a small set of data and
>quickly work out who the proper winner is.

That would seem desirable. However, I'm not sure that it is more
valuable than the intuitive simplicity of choosing the Condorcet
winner. It might be quite adequate, for example, that the vote
results be available on-line, with a program that allows picking any
two candidates and which shows the pairwise contest results for them.

Plus, of course, that shows the overall pairwise winner, assuming
that there is one.

As long as the raw vote data is available -- quite practical --
anyone could write a program to analyze it, so it would be pretty
silly for the authorities to put up a program that generated
deceptive results. It would be caught and exposed immediately....

I've seen, among some election methods advocates, an assumption that
"the average voter" couldn't understand something like, for example,
a pairwise election matrix. Properly explained, I don't think the
average voter, and, indeed, some quite below average, would have any trouble.

However, as readers must know by now, I'm not in favor of elections
at all. I prefer that we choose representatives instead of electing
them. As to office holders, I prefer that we hire them rather than
electing them.... (that is, our chosen representatives -- or us
directly -- would make hiring decisions deliberatively, as is

http://metaparty.beyondpolitics.org

Hey! Don't just sit there staring at your computer! DO SOMETHING!

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```
3 May 07:31 2006

### Re: Looking for a little voting insight...

```Thanks Markus,

I don't follow the logic perfectly but looking at the example it seems that
intuitively "A" is the choice that would leave the least number of people
unhappy and since no-one has contradicted you I will go with that.

I think it would be interesting in a range of polls to have people rank the
comparative results of plurality vs approval vs condorcet etc.. Maybe it has
been done before. If anyone has pointers to such an experiment I'd be
interested. If it hasn't been done perhaps I can build it into my site. Of
course that begs the question - which voting system to use to measure the
quality of the voting system!

Matt
--

On Monday 01 May 2006 02:14, Markus Schulze wrote:
> Dear Matthew Welland,
>
> you wrote (30 April 2006):
> > Rubyvote has pure condorcet and cloneproof schwartz
> > sequential available.
>
> At Wikipedia, "pure Condorcet" is called "Minimax
> Condorcet":
>
> http://en.wikipedia.org/wiki/Minimax_Condorcet
>
> At Wikipedia, "cloneproof Schwartz sequential dropping"
> is called "Schulze method":
>
> http://en.wikipedia.org/wiki/Schulze_method
>
> ******************************************
>
> You wrote (30 April 2006):
> > I want to keep things simple.
> > Does it matter which method I choose?
>
> Yes, it does matter. Minimax and Schulze are different
> methods.
>
> Example:
>
>    3   A > B > D > C
>    5   A > D > B > C
>    1   A > D > C > B
>    2   B > A > D > C
>    2   B > D > C > A
>    4   C > A > B > D
>    6   C > B > A > D
>    2   D > B > C > A
>    5   D > C > A > B
>
>    Suppose d[X,Y] is the number of voters who strictly
>    prefer candidate X to candidate Y. Then we get:
>
>    d[A,B]=18
>    d[A,C]=11
>    d[A,D]=21
>
>    d[B,A]=12
>    d[B,C]=14
>    d[B,D]=17
>
>    d[C,A]=19
>    d[C,B]=16
>    d[C,D]=10
>
>    d[D,A]=9
>    d[D,B]=13
>    d[D,C]=20
>
>    Minimax chooses candidate B.
>
>    The strongest paths are:
>
>    A-18-B
>    A-21-D-20-C
>    A-21-D
>
>    B-17-D-20-C-19-A
>    B-17-D-20-C
>    B-17-D
>
>    C-19-A
>    C-19-A-18-B
>    C-19-A-21-D
>
>    D-20-C-19-A
>    D-20-C-19-A-18-B
>    D-20-C
>
>    Schulze chooses candidate A.
>
> Markus Schulze
> ----
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--

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```

Gmane